Does hyperfocal distance apply in large format photography when using tilts or shifts?

Discussion in 'Large Format' started by alex_chen, Jul 3, 2002.

  1. I just started in large format photography, and I would like to know
    if I can apply hyperfocal distance focusing to maximize the depth of
    field. I understand that you can use tilts and/or swings to
    envision your focus plane in relation to the subject plane, because
    it's how you want to visualize the field of focus. Now my question
    is that can you use hyperfocal distance focusing after you make your
    tilts and/or swings to further increase the depth of field? Thanks
    for any response.
     
  2. Using a hyperfocal distance setting doesn't maximise depth-of-field. Only stopping your lens down all the way does that.<p>All that a hyperfocal setting does is to make sure that depth-of-field isn't wasted by extending it beyond infinity. It's a bit of a ridiculous concept anyway, for anything except a fixed-focus camera.<p>There is ONE point or plane of focus, and only ONE. Everything else will gradually get more and more blurred as you move away from that plane, until it becomes unacceptably blurred, and one person's idea of acceptable focus is anothers blurry mess.<p>Using a hyperfocal distance setting is a compromise between getting near and far parts of the subject in focus at the same time, and like most compromises, it usually fails badly, with nothing in particular being in really sharp focus. Whereas, the whole point of using swings and tilts is that you can make the plane of focus pass through the most important points or areas of the subject - you don't have to compromise.<p>Briefly: No, you can't use a hyperfocal setting with swings and tilts. The two concepts are mutually incompatible.
     
  3. While Pete is correct in his statement about there is only one plane of focus, I don't really agree to his thougths about "acceptable focus". A shot taken at e.g. f/16 and the film lens distance can look perfectly sharp in a 8X10 enlargement, while a blow-up to e.g. 16X20 viewed at a close distance really does become the "blurry mess" that Pete says. Please note that ALL DoF scales, no matter what camera or brand is calculated for an 8X10 print viewed at one foot distance. If you intend to print a 16X20 which you expect to be viewed at close distance, you of course have to compensate for that. But if someone says that my large prints are somewhat blurry and in the process of examining the print left nosegrease marks on the print, I'd simply ignore him. I hope you get my drift here.
    To the original question: The term "hyperfocal distance" is the distance setting for getting infinity into acceptable focus, while getting something closer to the camera into focus as well. (The subject says "shifts", and shifts doesn't change the hyperfocal distance at all. I assume Alex meant "swings".) Things do indeed get more complicated when you apply tilts/swings. As you tilt the focus plane, the DoF (which with straight camera settings can be imagined as a cube.) becomes triangular in shape. If you apply both tilt and swing, that shape is somewhat like a pyramid. A good book on View Camera technique will tell you all about it.
    If I read "between the lines" in the original question, I guess that Alex wants to know if he can find the "back" and "front" of that non-cube shape through some calculation or gadget. (With a lens forward tilt, the "back" and "front" really means "up" and "down".) There are DoF calculators that are really simple to use, and they do work with tilts and swings as well. (Including free ones.) All they really do is to measure the distance from the near to far and give you an f/setting. You should set the focus exactly in the middle of near and far focus settings. All Sinar cameras since early 70-ies (F../P..) does have this gadget.
    Robert Wheeler have done a tool for handhelds (e.g. Palm pilots) that calculate most (all?) the settings you'd ever want. Bob Wheelers photo site.
     
  4. Yes hyperfocal technique does have its application in view
    camera work. This is the heart of most depth of field calculators
    used for View camera work, whether built in (ala the Sinar
    cameras or the (now discontinued) Arca-Swiss Bra inbox) or the
    $35.00 Rodenstock depth of field/ tilt /swing angle calculator or
    the Palmpilot version mentioned above.<P>
    While is exactly right that in reality there only one absolute plane
    of focus projected by a lens, stopping a lens down creates zones
    of increasing distance from that one plane to achieve
    'acceptable" sharpness on either side of that plane. Of course
    one person’s criteria for what is sharp may differ from another’s
    criteria. The limitation is that beyond a certain f-stop (say f-32 for
    lenses shorter than 240mm that are used with the 4x5 format,
    and f/22 for the smaller 6x9 cm format) you start to lose
    resolution as light waves striking the edges of the aperture
    blades diffract and interfere with the light waves directly striking
    the film. (Because smaller formats need to be enlarged by a
    greater degree of magnification than larger formats for the same
    print size the practical limits for smaller formats are tighter. This
    is also what is meant by the differing sizes of "circles of
    confusion" for the various formats. But I think I have digressed for
    too long.) <P> but you can see that it is important that for the best
    technical quality that you don't stop down too far.<P> Here is
    where the tilts and swings come into play: with your camera
    zeroed (no tilts, no swings, no shifts, no rise and no fall) point
    your camera directly at your subject. Determine the one best
    plane to focus on usually this is near the base of the subject and
    near the top of the rear of the subject. If you have one of the
    calculators, determine how much tilt you need to make the plane
    that contains these two points your prime focus plane. Add that
    tilt to the front (lens) or rear (film) standard and refocus<P>(Yes I
    know, a plane is determined by three points but ignore that or the
    sake of my simplified explanation.)
    If you tilt the front (lens) standard all you do are doing is
    adjusting the plane of focus. If you tilt the rear standard you not
    only adjust the plane of focus but you also change the
    perspective rendering (the translation from 3 dimension reality to
    just 2D depiction) of the subject on the film.<P>
    Once this "best" plane is established you find the distance
    between the nearest point you want in focus to the farthest point
    you want in focus (by looking at the ground-glass) and use the
    calculator to determine the f-stop you need to make an
    acceptably sharp rendering -- of all of the space in between
    those two points and then basically you split the difference
    between how much you had to move the rear standard (I almost
    invariably focus using the rear standard and not the front
    standard but I use monorail cameras. For most (95%?) of the
    photography I do with large format cameras this will usually
    result in an f-stop in the f/22 to f/11 range. This is using
    hyperfocal technique in combination with using the Schiempflug
    principle (brief version of the S.P.: getting the plane of the
    subject, the plane of the lens and the plane of the film to
    intersect in a line.)
     
  5. Yes is the short answer but look at the archives under 'technique' (where your thread is currently top of the list) for more discussions of this subject.
     
  6. OK. You guys that think you can use a hyperfocal distance setting in conjunction with tilts and/or swings - How?<p>Setting the hyperfocal distance for any particular aperture means focusing at some middle-distant point determined from our chosen aperture, and whatever circle-of-confusion we decide is acceptable. Yes?<p>Now, swinging or tilting that pre-determined plane of focus through any one point of interest in our subject, may not get the focus anywhere near to where we want it to be at another point in the subject. If you follow.<br> In fact there's every chance that the swung or tilted plane will miss our chosen focus points by a mile, or at least by several metres.<br>This especially applies if our subject is close to the camera, and we're not really interested in having the horizon 'nearly' in focus.<p>So please explain to me how you can, on the one hand, focus on some arbitrary plane pre-determined by a hyperfocal distance calculation, and on the other hand, satisfy the criterion of having that focal plane pass through two or more points of interest in a subject that may not be anywhere near to that hyperfocal distance.<p>NOTE: We're not just talking about setting an adequate depth-of-field here, but about hyperfocal focussing. The two things are entirely different.
     
  7. Read Harold Merklinger's books, "The Ins & Outs of Focus" and "Focusing the View Camera". You will learn all you will ever need (or want) to know about this issue.
     
  8. There is a very interesting portion of Merklingers book, "Focussing the view camera", where he demonstrates with drawings how the hyperfocal distance does not change when using front tilt vs. a box camera!
     
  9. Schiempflug principle and hyperfocal distance are $1000 words for a two-bit concept. I agree with Pete. I work mostly at the opposite end of the spectrum with selective focusing. for me, it is much easier to simply visualize the focus plane, and then extend that idea to a focus frame or box with depth. the box contains a gradient surrounding the focus plane that changes with aperture. our view camera affords us the luxury of moving that box, tilting the box, swinging the box, around the subject, or positioning it to encompass several subject points far removed. the key is visualizing this moving frame, know that it has a graduated depth, and identify which controls on our camera affect its orientation.
     
  10. Let me add to the general confusion. Whatever the physics/optics of the situation might really be, I fail to understand how operationally hyperfocal distance can be combined with the admittedly very simple methods I use for using tilts and swings on landscape subjects when shooting typical near-far subjects. Usually the "far" part of the subject is distant enough (200 ft. or more) to count as infinity, and the "near" part is just in front of and below or to one side of the camera.

    First method: pick two points, one distant, one close in, and fiddle with movement until both are in focus. Second, preferred method: focus on horizon (i.e. bottom of GG), then tilt or swing until near part of subject snaps into focus; then correct horizon and near focus until acceptable trade-off is achieved.

    My question (with some of the previous posts): How is hyperfocal distance introduced into either of these procedures? Before adopting my two methods, I had previously *started* with the camera zeroed-out and focussed at the hyperfocal distance, but still ended up trying to find a compromise distance that would make both near and far acceptably sharp.

    Again, my question doesn't concern optics but procedure.
     
  11. I think the situation I had in mind for applying hyperfocal distance is where you want to get as close as possible to a foreground object that is at horizon level. If I know that the hyperfocal distance for a 150mm lens at f22 is say 40 feet (for the enlargement I have in mind) then I know that I cannot get closer than 20 feet to the subject and that the plane of focus at the horizon needs to be at 40 feet from the lens. The rest of the plane of focus can be to suit the rest of the shot.
     
  12. Please don't quote Merklinger at me. The guy doesn't even know how to calculate depth-of-field properly! (Spot the glaring mistake in his article "depth of field revisited", for example. Hint: DoF is not symmetrical about the point of focus.)
    OK. I've had time to think about this overnight, and the only conclusion I can reach is that hyperfocal focusing, and tilt/swing are totally incompatible.
    Let's just think about a tilted or swung lens. The plane of focus is always going to have a near and a far limit. At the nearest point of focus, the depth-of-field will be shallow, and more nearly symmetrical about the focal point (ie, the DoF in front of the point of focus will be similar to the DoF behind it). Now, at the furthest point of focus, the DoF will be much greater, and will also extend much further behind the focal point than in front of it. Agreed?
    So, what do we take as our focus point, or points, in order to use a hyperfocal ditance setting?
    Here's a worked example:
    Say we want to get two objects in focus; one at 3 metres from the camera, the other at 20 metres.
    [We'll asssume a 150mm lens on 5x4 and a generous CoC of 0.14mm]
    We could use a hyperfocal focus, but that would mean we'd have to stop down to f/22, and focus at around 5.3 metres, and it would also mean that our two objects are only just acceptably sharp.
    Now we swing the lens and refocus to get both object A, and object B, in the same plane. Both objects are pin sharp this time, but consider what's happened to the depth-of-field. The DoF at object A (3 metres), again with an aperture of f/22, extends from 2 metres to 5 metres, and at object B (20 metres) it extends from 5.5 metres to beyond infinity.
    Note: these distances will always be directly toward or away from the camera. Contrary to popular belief, the DoF isn't twisted by the tilt or shift. It merely varies continuously with the focal distance.
    So, I ask the simple question: Where, along that plane of focus from 3 metres to 20 metres, does one take the point of reference needed to calculate a hyperfocal setting? Since, at every slice along that plane, the focus and DoF are different.
    I suppose we could say that we don't want the DoF extending beyond infinity from our 20 metre object, and we could reduce the aperture to f/8 to rein it in, but this then means that we only have +/- half a metre of DoF at our near subject, and that almost certainly won't be enough for any practical 3 dimensional object. We end up throwing any hyperfocal calculation away, and just setting an aperture that gives us the depth-of-field needed by that particular scene.
    Sorry, but I can't see how hyperfocal calculations can possibly work practically, once swings or tilts are used. Especially since it's almost impossible to set an exact pre-calculated distance on most LF cameras anyway.
     
  13. WAn

    WAn

    The hyperfocal focusing technique (doesn't matter how good or bad is the very concept) tries to maximize focus from a certain distance till infinity. Please note: we speak about distance only: in fixed lens camera the direction is fixed (lens axis) and we may speak only in terms of distance.

    In view cameras we have to speak in terms of distance AND direction. If a tilt/swing has been applied, the DOF zone at certain direction does already touch the infinity (and the plane of focus does it also!). Therefore the term "h. distance" is strictly speaking just irrelevant in this case.

    What we probably can do is to recall what was the objective in that idea (maximization of sharpness zone) and to try to extend the definition of that term for the new situation. I think we inevitably have to consider the shape and orientation of the DOF zone and to decide whether a part of scene fits in this zone. It is simple and clear. I don't see how an extended concept of "hyperfocal distance-direction" is possible and how it can simplify something.
     
  14. 1.) Using a hyperfocus technique has NOTHING to do with focusing at "infinity". neither the camera or the geometries involved can know or hve a care about how distance theobject is from the camera. The problem you are having comes from the definition you are using.
    Pete Andrews writes: "So please explain to me how you can, on the one hand, focus on some arbitrary plane pre-determined by a hyperfocal distance calculation, and on the other hand, satisfy the criterion of having that focal plane pass through two or more points of interest in a subject that may not be anywhere near to that hyperfocal distance.
    Pete you are absolutely right: You can't set the camera to "focus on some arbitrary plane predetermined by ahyperfocal calculation." You have to focus on a plane chosen by direct observation ofthe subject as rendereded on the groundglass.
    the proof that you can use a hyper focusing technique with tilts and swings is built into the Sinar P camera
     
  15. Just to clear up some misconceptions that people might be having from believing Harold Merklinger's simplistic (and wrong) view of depth-of-field:
    Here's the correct shape of the DoF area with a tilted lens or film plane -
    [​IMG]
    And here's the way that Merklinger shows it.
    Where Merklinger's formula of "J = f/sin(a)" comes from, I just don't know. You can see that there's no way you can fit his mythical 'J' to the correct shape of a DoF plot.
     
  16. The way I like to personally look at it is that, when working with swings and/or tilts, instead of using a hyperfocal distance setting, we use a "HYPERFOCAL DISTANCE AND ANGLE SETTING." This approach is much more dynamic since (as has already been mentioned by others) we have a variable amount of DOF perpendicular to the plane of principle focus: very limited DOF in the foreground increasing to (theoretically) infinite DOF at true infinity.

    Based upon the actual definition of "hyperfocal distance", it is accurate to say that we do not use it when we are working with swings or tilts. However, we can work with something similar to insure adequate image sharpness on all planes. Let's start by taking a look at the basics.

    As we all know, when the film plane and lens plane are parallel, the plane of focus will also be parallel to them. If the lens plane is tilted in relationship to the film plane, the plane of focus will be tilted also. The film plane, lens plane, and plane of focus will all then intersect along a common line. These principle planes will then, in effect, radiate from this common line.

    Once the tilt angle has been set, we can then adjust our focus setting of the lens by adjusting the lens-to-film distance. This focus adjustment will alter the placement of the plane of focus, always maintaining the common line of intersection of the film, lens, and focus planes. As the focus setting is adjusted, the common line of intersection will be relocated along the film plane, resulting in movement of the plane of focus.

    Once we have set both the bellows extension for focus and the tilt angle, we can then stop the lens down to gain depth of field. The planes defining the near and far limits of acceptable sharpness will also radiate from the aforementioned common line of intersection, thereby giving us a wedge of DOF. As the lens is stopped down, the angles relative to the plane of focus of the planes defining the limits of sharpness will increase. According to generally accepted theory, 1/3 of the wedge of DOF will be on one side of the principle plane of focus and 2/3 will be on the other side. The planes defining the limits of acceptable sharpness will always maintain the common line of intersection.

    Now, an expample. Say we have a pool of water in the very near foreground and a tall waterfall in the background. The distance to the waterfall is much less than optical infinity for the focal length lens we are using. This situation would probably benefit from the use of a tilt. The appropriate placement of the plane of principle focus would be at an angle running from the nearest area in the pool to a point somewhere along the vertical plane of the waterfall. The optimum angle of placement for the plane of principle focus would be such that once we have stopped the lens down, the angular plane defining the far limit of acceptable sharpness would be along the surface of the water of the pool (assuming there are no areas in the scene lying below this plane) and the angular plane defining the near limit of acceptable sharpness would lie above the waterfall (assuming there are no areas in the scene lying above this plane.) By doing this we have set both a bellows extension distance and lens tilt angle, acheiving both a hyperfocal distance setting and hyperfocal angle setting.

    So, no, we don't work with a true hyperfocal distance setting. We work with something much more geometrically complex. At least, that's the way I like to look at it.
     
  17. "Please don't quote Merklinger at me. The guy doesn't even know how to calculate depth-of-field properly! (Spot the glaring mistake in his article "depth of field revisited", for example. Hint: DoF is not symmetrical about the point of focus.)"
    Pete, you have complete misunderstoond Dr. Merklinger's result.
    There are two approachs to DOF
    1. Traditional DOF: DOF is unsymmetrical vs point of sharp focus (page 15, The Ins and Outs of Focus )
    2. Object Plane DOF approach: the DOF IS symmetrical vs the point of sharp focus
    • You have mixed up the Merklinger's object field DOF theory with traditional IMAGE field DOF theory.
      Merklinger is correct.
     
  18. "Where Merklinger's formula of "J = f/sin(a)" comes from, I just don't know. "

    <p> That means you don't have a clue what Merkligner is talking about
    <p> Don't simply surf the net.
    <p> Get Merklinger's "Focusing the View Camera" read it throughly
    work it out, until you understand how J=F/sin(alpha), then
    talk about "the guy does'nt know how to calculate DOF"
    <P> Dr. Merklinger is a much better mathematician then you think
    <p> BTW J=F/sin(alpha) is a correct formula
     
  19. Ken, you raise some good points...and hyperfocal distance does not come into play when I use tilts. However, I would like to ask Pete Andrews something here. Pete you are one of the stronger mathematical minds on this list and I do respect your opinions, and most importantly your persistency in helping others, regardless of how bad you get attacked :) I don't want you to think I was quoting Merklinger at you - to aggrevate you, but rather to hear your opinion on the subject. As you know, I have laid low on these lists, but I am resurfacing since I am curious of peoples opinion on this subject. First I am curious - have you studied Merklingers two books? If so, can you point out where you feel he has been mistaken. This probably should be the start of a new thread.....If someone feels compelled, please start one. I would like to share my thoughts on both Merklinger books below, as I have studied them both very extensively, unfortunately a few years back.

    Focussing the view camera, is by far Merklingers better book. I give him this praise mainly for one reason, he wins by default. No one has tried to demonstrate mathematically the concept of tilts and swings like he has. Now, this does not mean I agree with every thing Merklinger has ever written! A fair warning to anyone who has never read his books....he is the worst writer I have experienced in my life. Although he is gifted at math, he has no technical writing skills whatsoever. You have to read his books a few times to grasp what he is trying to say...after awhile you start to understand him a bit better.

    Now, my first question Pete.... do you accept Merklingers "J" theory? I have to admit, I feel this is Merklingers biggest contribution to tilt math. He has developed a very simple way to determine where the plane of sharp focus will interesect under the lens. In situations where this is known, which is quite often, (or always if you are good at sketching geometry) this completly simplifies the tilt angle required. I have tested this for years - and all the frustrations I have faced with this books, well, this one concept makes it all worth while. Now, his other contributions towards view camera math are either less important or more complicated, at least in my opinion.

    When using front tilt, setting the tilt angle is by far the most important ingredient...get this wrong, and everything that follows will be wrong, it is clearly the starting point. Next is the focus distance, (which sets the angle of the plane of sharp focus) which Merklinger demonstrates mathematicaly...but considering how hard it is to focus the rear standard with mm numbers, it is very impractical in the field. You must know the lens nodal distance for each lens, film position, etc. So this is more easily accomplished via the gg and a few seconds of trial and error with the back focus. And if you set the tilt angle right, it works quite easy. The only other issue with tilt is making sure the DOF above and below the plane of sharp focus meets the needs of the scene.

    Merklinger demonstrates a way to determine the DOF above and below the plane of sharp focus at a specific distance, when using front tilt. He demonstrates DOF as being x number of J's above and below the plane of sharp focus, at a specific distance from the lens. This I have not seen demonstrated by others and can be quite useful. However, its not always a simple thing to determine, and more importantly, sometimes following his calculations, and bringing such to the field, my results do not always match perfectly....but, they are not off by much, which is somewhat comforting. (I would not doubt I have erroed at times also) So overall, I would offer Merklinger has defined mathematically the 3 most important aspects of tilt, angle, focus and DOF as well as anyone, although the most poorly written!.

    His contribution towards Hyperfocal distance and view camera, is very complex, and the example Pete showed us above is not the whole story. But by no means would I want to try to address this in a thread such as this. I personaly don't see why Merklinger attempted this, as there is little importance or significance between conventional Hyperfocal distance with non tilt cameras and vs. tilting applications.... But I will mention, all Merklingers J calcs and DOF calcs when using tilt, involve the use of the Hyperfocal distances of the lens for the completion of his formulas. I could go on about other topics for view cameras in his books, but I feel these are the key ones. I would love to hear from others on this.

    Now, here is the scary part. In Merklingers book, The Ins and outs of foucs, he discusses an entirely new concept of DOF which defies DOF calcs that has been around for hundreds of years. (this is for non view cameras only) He assumes the time tested DOF formulas are wrong today, as they were developed in times when there was very poor resolving lenses and films - 150+ years ago. He backs all of his tests / views up in his book with photos....He also disproves conventional DOF calcs with photos. Although his concept in some situations appeals to my common sense, overall, I feel his radical concept is totaly flawed. I think he may have been using a camera with a faulty alignment between film / lens / miror. He took all those pix with 35mm SLR. It's very possible, he may have tricked himself on this one. I have done several tests to be sure he is wrong.... and I am convinced his theory is flawed. Many others concur with me. But in a case like this, I doubt the author would ever come out and admit a book that is currently on sale at many retail outlets is flawed. This is unfortunate as there is not a lot of books written soley on DOF or focus.. so there is parade of newcomers who may be mislead by this book.

    I guess what I am getting at...and hopefully other Merklinger proponents or opponents will respond. If you read his flawed book first, and you discover these flaws yourself, you tend to be immediately anti Merklinger. The ol adage,, "throwing the baby out with the bath water" applies here.... but if you objectively make your way through his view camera book, I think you will find he does have some excellent concepts which have been explained like no one else up to this point in time. It's too bad the one book dedicated to the math and concepts behind veiw camera tilt, consist of near impossible technical reading, a flawed second book, and many opponents. But rarely do I see anyone attempt to technically disprove his fundamental concepts - i.e. the 3 ingredients of tilt that I mention above. Does this make sense? Pete, or anyone else that can provide such data should present it. This type of post shoud be archived on the home page as tilt is one of the most important aspects of using a view camera and Merklinger keeps getting new readers every year, and his proponets probably equal his opponents. But rarely is their positions clearly defined. There has been many threads on this in the past.....



     
  20. Bill
    <p> Your assesment of Merklinger's J theory is correct. It is his
    most important contribution to view camera photography
    <p> You still haven't got the essense of his Object Field DOF theory
    It is not flawed at all.
     
  21. There is a thread about Merklinger's Object field DOF theory in Leica Photography, where I provided a table, demonstrating why focusing at infinity instead of focusing at conventional hyperfocal distance yields sharper landscape pictures Focusing Leica: Merlinger Method
     
  22. Martin, I read the thread. I should have been more clear....it has been awhile since I read this book. Focussing at infinity vs. the hyperfocal distance.... that is one of the items I would not dispute. I was referring to his discussions on fouccussing on closer objects. The way he uses an inverted X to demonstrate focussing on closer subjects is where I found major flaws. My results did not concur with his. I have had several DOF gurus also concur with this. I wish I had more information, but it is all burried in a box right now. However, I apologize for lumping everything in the book together.when I made my comments.
     
  23. At least we now know why the good doctors' nickname is Murky
    Merklinger. <P>Anyone who makes something simple so
    complicated deserves to be ignored. I'm completely with Pete on
    this. merklinger is one of those people who make it impossible
    for people to concentrate on the important thing in photography:
    seeing. His jargon is so dense that even Sir Stephen Hawking
    and the late Richard Feynmann would be stunned into silence
    and Ansel Adams, John Sexton, Norman McGrath and Richard
    Avedon would have thrown away their cameras in djsgust.<P>No
    doubt his mathmatical explanation is correct, but learning to use
    a view camera his way is like having to do all of the engineering
    of tires, brakes, steeering, axles, transmission, motor, electrical
    systems, chassis construction and paint technology each time
    you wanted to go for a drive in your car.
     
  24. "Here's a worked example:
    Say we want to get two objects in focus; one at 3 metres from the camera, the other at 20 metres.
    [We'll asssume a 150mm lens on 5x4 and a generous CoC of 0.14mm]
    We could use a hyperfocal focus, but that would mean we'd have to stop down to f/22, and focus at around 5.3 metres, and it would also mean that our two objects are only just acceptably sharp.

    <p> Comment: You have transplated the DOF concept in tiltless camera
    to camera with lens tilt. <p>
    Now we swing the lens and refocus to get both object A, and object B, in the same plane. Both objects are pin sharp this time, but consider what's happened to the depth-of-field.

    <p>Comment yes, the first step is to use lens tilt to get object A and B on PLANE OF sharp focus. But that is not all. <p>


    The DoF at object A (3 metres), again with an aperture of f/22, extends from 2 metres to 5 metres, and at object B (20 metres) it extends from 5.5 metres to beyond infinity.

    <p> Comment :That is where you get it all wrong, you are using 35mm math here.

    <p> The near DOF limit and far DOF limit are not planes perpendicular
    to point A and point B. Rather the the DOF limit planes are like V shape, with the PLANE OF sharp focus still PASSING through A and B
    such that they are tack sharp. This plane of sharp focus is approximately dissecting the V shape. <p>
    <p> Take a simple case, if point A and point B lies in a flat field
    point A is a small flower, at point B is not a small flower, but a
    statue of certain height.
    <p> If you use lens tilt to bring the small flower at front and the
    FEET of statue into PLANE OF SHARP FOCUS, then the head of statue would
    not be sharp.
    <p> The right way to do is draw a slant line from the small flower (point A) to the MIDDLE of the statue, point C, select lens tilt to
    bring point A and point C into PLANE OF SHARP FOCUS.
    <P> Then select proper aperture, according the tables in Merlinger's book, such that near DOF limit plane passes the hinge point at one end and
    the HEAD of statue at the other; the far DOF plane passes the
    hinge point and the FEET of the statue. Now you get not only
    the front object: small flower sharp, you get the HANDS of statue
    tack sharp, but also the statue HEAD and statue FEET within DOF
    That is how dof comes into play when lens tilt is used
     
  25. "Where Merklinger's formula of "J = f/sin(a)" comes from, I just don't know"
    It is implicit in Fig 22 of "Focusing the View Camera"
    In that diagram, three lines intersect to form a right angle triangle:
    1. Optical axis passing through the center of lens
    2. Front focal plane
    3. Parallel to film plane, acronym PTF plane, ie a plane which is parallel to the film plane AND passing throught the center of lens
    • focal length f is the short side of right angle triangle
      J = lens to hinge distance is the hypothenus
      Front focal plane and PTF plane intesect at the Hinge line
      The angle between the front focal plane and PTF plane is alpha
      Therefore SIN (alpha ) = f/J
      and J = f/sin(alpha)
      This is quite elementary.
      The information on the Merklinger website is only a brief summary of what was discussed in depth in the books
     
  26. "Martin, I read the thread. I should have been more clear....it has been awhile since I read this book. Focussing at infinity vs. the hyperfocal distance.... that is one of the items I would not dispute."

    <p> Bill, this and your acceptance of 'J formula" means that you
    are 95% there :)

    <p> It is at once clear that you have a good understanding of
    Merklinger method.
    <p> When you have time, I like to know a bit more detail on your view
    on focusing closer object.

    <p> Imo, his view on focusing closer object is not flawed, just a different view point.
     
  27. Ellis wrote... No doubt his mathmatical explanation is correct, but learning to use a view camera his way is like having to
    do all of the engineering of tires, brakes, steeering, axles, transmission, motor, electrical systems, chassis
    construction and paint technology each time you wanted to go for a drive in your car.

    Ellis, I think this is a poor analogy. Sometimes the geometry of a view camera scene is complex and although Merklinger backs everything up with endless math, it is all reduced to simple tables and math you can perform in your head.

    You wrote...... Here is where the tilts and swings come into play: with your camera zeroed (no tilts, no swings, no shifts, no rise and no fall) point your camera directly at your subject. Determine the one best plane to focus on usually
    this is near the base of the subject and near the top of the rear of the subject.

    Ellis, what if there is several subjects and the best plane lies in un occupied space with no subjects so as to focus the subjects above and below the plane via the DOF of the Plane? This is not that uncommon?? Then how do you apply your method?

    You wrote..... If you have one of the calculators, determine how much tilt you need to make the plane that contains these two points your prime focus plane. Add that tilt to the front (lens) or rear (film) standard and refocus.

    Ellis, I do not have one of these calculators, can you describe what you plug into it? Without knowing the distance of the near and far subject, I am confused what gets entered? The distance and hieght of these two points will provide the proper plane of sharp focus, and the distance it would interesect under the lens, which then you can determine the tilt angle, but I am confused how any calculator can determine the tilt angle with out this information?.
    Can you please explain, hopefully without sarcasm?
    Thanks
     
  28. To the little hobit who lives the lens; his frame of reference is the lens axis only......All the cool world in the shire in front of him is to be photographed...The confused humans toil with where the film should be placed to get the shire in focus......Maybe thy should experiment with thy wax paper and a discover what the wizard knows; & get all the shire in focus..
     
  29. Martin: When you actually start using an LF camera instead of a Minox, then feel free to comment.<br>I see nothing in your posts but blind contradiction and attack, along with an unwillingness to properly read anything that anyone else has said.<br>If you wish to tell me I'm wrong, then please give your own working or mathematical model to prove the point.<p>To everyone else: Yes I, and I'm sure others, would gladly persue this Merklinger thing, but I think another thread is called for.<br>Incidentally, I do think that Merklinger has some good ideas and a novel take on a few things, but I just can't accept his rejection of conventional calculation when it comes to depth-of-field.<p>BTW. I've still seen nothing in this thread that actually relates a Hyperfocal distance setting to a tilted focal plane. All anyone has demostrated, is that it's desirable to have an adequate depth-of-field, and that's common ground. No-one is arguing that tilting the film plane completely does away with the need for DoF, or the need to do some calculation of it. But depth-of-field calculations STILL have very little to do with Hyperfocal focusing. The only aim of using a Hyperfocal setting, as far as I can see, is to get two separated objects both in barely acceptable focus.
     
  30. "Martin: When you actually start using an LF camera instead of a Minox, then feel free to comment."
    <p>
    Comment: I did use LF about twenty years ago, but got out of it, not completely, still has maintain some interest in this subject<p>

    I see nothing in your posts but blind contradiction and attack,
    along with an unwillingness to properly read anything that anyone else has said.<p>

    Comment: No so, it is your post that is full of blind contradition and attack on Dr. Merklinger, without understand what he is talking about<p>

    If you wish to tell me I'm wrong, then please give your own working or mathematical model to prove the point.

    <p>I doubt you understand simple math, from your comment on
    the J formular. In your own words: "Where Merklinger's formula of "J = f/sin(a)" comes from, I just don't know" <p>

    Did I just pointed out to you where the fomular comes from ?

    You probably still don't understand.<p>

    To everyone else: Yes I, and I'm sure others, would gladly persue this Merklinger thing, but I think another thread is called for.
    Incidentally, I do think that Merklinger has some good ideas and a novel take on a few things,

    <p> That is a step in the right direction.
    <p>

    but I just can't accept his rejection of conventional calculation when it comes to depth-of-field.
    <p> Comment : This is a gross misunderstanding. Dr. Merklinger DID NOT reject conventional calculation of DOF, he devoted a complete chapter 3 to discuss the conventional DOF theory in depth.
     
  31. WAn

    WAn

    Gentlemen, it is unnecessary to touch Merlinger books in this topic. The knowledge of Scheimpflug principle is enough. Or even better, the knowledge the Gaussian lens formula; the latter allows to deduce all the geometry of view camera. I'm sure it is better to discuss Merlinger's approach and his math in a separate tread (I'll be glad to contribute to the discussion).
    The asked question was relatively simple.

    I'm still convinced that the cause of the confusion is in using concepts suitable for box camera in the area where they aren't suitable anymore. Even the term "focusing distance" is ambiguous, to say the least. For example: I slightly tilt the front standard and superpose the plane of focus with earth surface; every tiny thing on the surface from my feet till horizon is absolutely sharp (is spite of DOF). – What is the focusing distance in this case? Should it be measured along the (tilted) lens axis or along other direction? – Several suggestions are possible but every choice will be more or less arbitrary. And if there is no focusing distance in this case then there is also no "hyperfocal distance". (Surely it is ok to speak in terms of distance when there is no tilt yet, bit once the tilt is applied there is no more such thing as focusing distance). It is better to think in terms of re-orientation the focus plane. Then even the very question about h.distance is impossible.
     
  32. The subject seems to be controversial, but it should not.

    First it depends whether you aim at distant objects, say more than 10
    times the focal length or in macro-photo.

    For distant objects, simplified formulae apply, and the hyperfocal
    distance is given by H=f*f/(N*c) with f=focal length, N f-number, and
    c circle of least confusion. Take this definition as a mathematical
    definition without physical meaning for the moment. As it is defined,
    H is a certain length. If you enter f in millimetres and c in microns
    in the formula, you get H in metres. For close-up you should use the
    more general formulae as presented on Nicholas V. Sushkin's web site

    http://www.dof.pcraft.com/dof.cgi

    Now used with a shifted or tilted view camera, the value of H has an
    interesting meaning.

    Assume that you focus on a slanted plane according to Scheimpflug's
    rule. Add a positive or negative suipplementary lens of focal length
    equal to plus or minus H to your view camera lens. Then through the
    supplementary lens you'll bring in focus the far and near slanted
    planes, limits of acceptable sharpness. OK this is just a theoretical
    approach since it is not convenient when H=5 metres to have a lens
    with a focal length of 5 metres (1/5 dioptre) however for a 35 mm
    tilt+shift lens, the hyperfocal for c=33 microns is something like 2
    metres @ f/18 (= f/16 - f/22) ; 1/2 dioptre lenses are readily
    available from your local opticist. So with a 1/2 dioptre, positive of
    negative lens you''ll be able to visualize DOF @ f/18 even with
    slanted or shifted planes for this f=35mm lens, with c=33 microns,
    without stopping down the lens to the actual f/18 value.

    For more details just refer to these documents in English on Tuan
    Luong's web site :

    http://192.147.236.3/~lfgroup/scheimpflug-bigler-english.pdf

    http://192.147.236.3/~lfgroup/scheimpflug-DOF-bigler-english.pdf

    Now for close-up including shift and tilt. Things become more complex
    although the formulae are no so complex ; Leslie Stroebel (Leslie D.
    Stroebel, ``View Camera Technique'', 7-th Ed., ISBN 0240803450, (Focal
    Press, 1999) page 156) shows an exact diagram for DOF lmits with
    slanted planes, and I have re-computed this here

    http://www.galerie-photo.com/hyperfocale_et_profondeur_de_champ.html

    This is an updated version in French of the previous document in
    English ; the English version will be posted to Tuan Luong's web site
    some day.


    I think there is nothing really mysterious. The approximate formulae
    yielding Merklinger's "sine" formulae are suprisingly good at
    distances likes 2f - 3f.

    For close up you should use the following formulae :


    H=f*f/(N*c) is the approximate hyperfocal distance

    H+f is in fact the true value for which the far-distant plane of sharpness goes to infinity, with exact formulae

    positions of far (p2) and near (p1) planes of acceptable sharpness for
    an object distance p:

    p1= (H.p) / (H+(p-f)) ; p2= (H.p) / (H-(p-f))

    OK for slanted planes no simple formulae exist since strictly speaking
    ar close distances those surfaces a re curved surfaces. But the
    computation can be derived from those formulae, assuming that you
    neglect the "ellipticity" of the out of focus spot in a slanted film
    plane. For a more detailed mathematical tretment see Bob Wheeler's paper

    http://www.bobwheeler.com/photo/ViewCam.pdf
     
  33. The correct pointer to a web document in French
    where I recompute Stroebel's DOF diagrams for slanted planes in macro-photo
    is :

    http://www.galerie-photo.com/profondeur-de-champ-et-scheimpflug.html

    Even if you do not read French, graphs are self-explanatory and perfectly match Merklingers approach as an approxiamtion of exact Stroebels curve in the close-up range.

    The English version is in preparation for Tuan Luong's web site.
     
  34. Pete wrote:
    "If you wish to tell me I'm wrong, then please give your own working or mathematical model to prove the point."<p>

    I do have a analytical mathematic model which I worked out a few years back; in the
    process I not only derived independently Merklinger's formular sin(alpha) =J/f, but also the formular for
    back tilt angle, which is not in his book " Focusing the View Camera" nor any other LF technique
    books I know of.

    <p>


    Back tilt angle = arctan( f/K ), where K is not equal to J in general, particularly
    in close up shots, to transfer back tilt to lens tilt, conversion from arctan to arcsin
    is necessary<p>

    See my comments in photo.net thread posted in 1998<p>

    http://www.photo.net/bboard/q-and-a-fetch-msg?msg_id=0005VJ

    <p>
     
  35. Martin. I think we agree at 100% that Merklinger's formulae are valid_
    but for large subject to camera distances only.

    If you revisit your 1998 computation, try to consider what happens
    when the viewcamera lens is fitted with a 'plus or minus H'
    supplementary lens and do a simple ray tracing. You'll find almost
    immediately the arc-sine and arc-tangent formulae. It's magic !
    ;-);-) but valid at large distances only, hence, IMHO, a
    part of the controversy.

    Now whether mathematical models are of any use in the field in another
    story ;-);-)
     
  36. If you use the two formulae:<br> Dn = fu(f + CN)/(f^2 + uCN) ; for the limit of near focus;<br> and Df = fu(f - CN)/(f^2 - uCN) ; for the limit of far focus;<br>then this covers every possible distance, from the nearest macro to infinty.<br>[f = focal length of lens; u = subject distance from forward node of lens; C = diameter of circle of confusion; and N = relative aperture number]<p>Those above formulae are THE recognised and accurate way to calculate depth-of-field. And if you apply them, you will readily see that the DoF surrounding an inclined focal plane is NOT a straight-edged wedge, but the DoF is bounded by two curved surfaces which bow away from the plane of focus with increasing distance from the camera.<br>This means that Merklinger's value of 'J' cannot be fitted at one single point on the plane of focus, to simultaneously touch both the near and far limits of DoF.<p>In fact, even the above given formulae aren't exactly correct. They are a very close first approximation. The ultimate in DoF calculation requires the solution of a quadratic equation - which isn't the sort of thing you can quickly pop out on a pocket calculator. However, for all practical purposes, the first approximation is more than close enough.<p>Martin: your bile runs off me like water off a duck's back. You don't do your cause any favours by simply insulting people.
     
  37. apologies to all that may be beginning their journey with Large Format, and about to put their camera up for sale on eBay after reading this thread. it is a great thread encompassing what is so wonderful about view-cameras ... user-controlled freedom.

    hyperfocal distance? from where to where? asking that question in concert with camera movements that create an oblique plane of focus makes little sense and certainly is not intuitive. does it exist, and could be we calculate it? of course, but it references a single distant point in front of our lens. the assumption is that this point is within the focus plane, but we now know that it may not be. we can arbitrarily move this plane independent of our lens. we have diverged from the rules of the road, and can no longer make the same assumptions nor follow the same guideposts. in fact, the distance markings on our lens become meaningless with simple movements, as do the principles that use it.

    simplify, visualize, 'open your eyes'
     
  38. Thank you Daniel, you make excellent points.
    Bill Glickman writes in italics:
    ... Sometimes the geometry of a view camera scene is complex and although Merklinger backs everything up with endless math, it is all reduced to simple tables and math you can perform in your head.
    Someone famous once opined that "writing about music is like dancing about architecture." Do all of the math you want to if you like, but all it is doing is describing what you can see directly on the groundglass. and taking you away from making the photograph
    Just think: if you could directly see what is on the groundglass and make your determinations from there only by using the camera or (if you use the little Rodenstock calculator , you wouldn't have to waste time or more importantly be distracted from the task at hand (making a photograph) by consulting tables and then worrying if you got the math wrong or if you were using the wrong formula.
    You wrote...... Here is where the tilts and swings come into play: with your camera zeroed (no tilts, no swings, no shifts, no rise and no fall) point your camera directly at your subject. Determine the one best plane to focus on usually this is near the base of the subject and near the top of the rear of the subject.
    Ellis, what if there is several subjects and the best plane lies in unoccupied space with no subjects so as to focus the subjects above and below the plane via the DOF of the Plane? This is not that uncommon?? Then how do you apply your method?

    Unless you are doing copy work or only photographing objects infinity there are always many potential subjects in the frame. You and you alone make the determination as to which are the important ones. Frankly I find it rather difficult to focus on things that aren't there so I use as near and far points the things that are there.
    You wrote..... If you have one of the calculators, determine how much tilt you need to make the plane that contains these two points your prime focus plane. Add that tilt to the front (lens) or rear (film) standard and refocus. Ellis, I do not have one of these calculators, can you describe what you plug into it?
    With the Sinar and the Arca-Swiss brainbox, I don't plug anything into it. I simply focus on those two points that I have chosen and with the Sinar, back up two stops (you have to see the depth of field calculator on the Sinar to understand this, try going to www.sinarbron.com for an illustration in their tutorial). with the Brainbox it is virtually the same. either way you are using the focusing drive on the camera to measure the difference between the two points and the camera or brainbox uses this information to tell both the tilt or swing angle necessary to place those two points on the same plane (with regard to the film and lens plane) or what f-stop you'll need to pull those two points into a hyperfocal relationship and where to refocus the camera to achieve that relationship. it takes less time to do this that it takes to read my description of how they work. With the Rodenstock calculator ($35) you again take the measure of how much the standard that you used to focus with moves between the two points and dial in a couple of other variables (format size, reproduction size) and use the f-stop suggested the refocus point. I haven't used the Rodenstock calculator to calculate Schiempflug tilt angles but it looks to be as direct as the Depth of Field calculator. The Rodenstock Calculator is essentially a circular slide rule dedicated to doing this work.
    Without knowing the distance of the near and far subject, I am confused what gets entered? The distance and height of these two points will provide the proper plane of sharp focus, and the distance it would intersect under the lens, which then you can determine the tilt angle, but I am confused how any calculator can determine the tilt angle with out this information?
    For the purpose of making photographs the distances between the camera and the subjects or the heights of the subject are completely irrelevant-- all you have to be concerned with is measuring the distance the standard you focus with has moved between those two points and finding a point in between those points and f/stop that will allow you to make a sharp (or sharp enough for the intended usage) image, if a well resolved image is a consideration for you . This is true whether you use no swings and tilts or use them extensively.
     
  39. At F1; who worries about depth of field!<BR><BR><BR><IMG SRC="http://www.ezshots.com/members/tripods/images/tripods-283.jpg">
    <IMG SRC="http://www.ezshots.com/members/tripods/images/tripods-284.jpg">
     
  40. Here the Industar -51 210mm F4.5 has a smaller aperture ( 46.7mm )than the 50mm F1.0 Noctilux..( 50mm ) <BR><BR>This is an interesting thread; I will study it some more...I'm not sure if everyone is using the same reference frame in this discussion...regards kelly <BR><BR> <IMG SRC="http://www.ezshots.com/members/tripods/images/tripods-285.jpg">
     
  41. Emanual, I went to your site, from the few words and names I recongnized, I know you have an interesting article, hope to read the English verion soon.

    <p> AS for mathematic is LF--- LF is the one photography format which
    has a lot of maths, and this adds to the fascination :)
     
  42. pete wrote:
    <p>
    "If you use the two formulae:
    Dn = fu(f + CN)/(f^2 + uCN) ; for the limit of near focus;
    and Df = fu(f - CN)/(f^2 - uCN) ; for the limit of far focus;
    then this covers every possible distance, from the nearest macro to infinty.
    [f = focal length of lens; u = subject distance from forward node of lens; C = diameter of circle of confusion; and N = relative aperture number]
    Those above formulae are THE recognised and accurate way to calculate depth-of-field.<p>

    My comment: the DOF formular are the recognized formula for box camera
    without lens movement. <p>



    And if you apply them, you will readily see that the DoF surrounding an inclined focal plane is NOT a straight-edged wedge, but the DoF is bounded by two curved surfaces which bow away from the plane of focus with increasing distance from the camera.

    <p> Comment: I question the validity of transplatation of box camera optics to LF. If
    you apply these formular to a BOX camera with no movement, you may
    get a curved near/far DOF planes. Because you can never get the whole inclined plane sharp from one end to the other in the first place with box camera.<p>
    <p> However, that does not apply to LF with TILTED LENS. With tilted lens under Scheimpflug principle, plane surface MUST transforms into planes, cannot be curved, otherwise there would be no Scheimpflug.
    <P> I believe planes transforms into planes is fundamental to Scheimpflug
    <p> Let me explain a bit more

    <p> Set up your LF, select proper lens tilt to get an incline plane
    sharply focused on the ground glass, we call this plane of sharp focus
    plane A, and called the position of film plane initial position
    <p> Now assume the film plane moved back in parallel manner a delta
    amount. According to Scheimpflug principles, there exist a plane which forms sharp image on this moved film plane. Call this plane B
    <p> Move the film plane from initial position parallelly in other direction, again a distance delta. According to Scheimflug, the
    conjugate plane must be again a plane, cannot be curved. Call this
    Plane C.
    <p> Plane A, B, C must all pass through same Hinge line. Therefore
    plane B, C is the boundary of DOF for plane A, exactly wedge shape
    boundaries.


    <p> In summary, in LF, you have to start with Scheimpflug principles
    and not trasnplating box camera optics
     
  43. Pete is clearly mistaken <p>
    <img src="http://www.photo.net/photodb/image-display?photo_id=857807&size=md"> is NOT the dof diagram of tilted lens with
    incline plane.
    <p> You tried, however you make the serious mistake of applying box camera DOF formular to LF, instead of applying Scheimpflug principles.
    <p> Merklinger's version is clearly the correct one, simply because
    it conforms to Scheimpflug principles: planes transform into planes
    <p> Your diagram shows only that with box camera, as distance increase
    the dof increase in non linear fashion.
    <p> The prerequisite condition for box camera
    DOF fomular: the camera lens has zero tilt angle.

    <p> Does the BOX CAMERA DOF formular tells you that you can get
    ALL the slanted line in focus all at the same times ? No, you plug in
    ONE point, the formular gives you two boundary points, you change to another point, the formular gives you another two points,
    While one point is in focus, the previous one
    will be out of focus already...
    <p> <p> Your diagram has nothing to do with LF dof
     
  44. Ellis, thank you for explaining. These things are sometimes difficult to discuss in a thread, vs. people in a room with a chalk board. So therefore, the easiest way I can explain my un ease with the systems you described is as follows. You may have a simple explanation as I may still be missing something here.

    YOu mention the distance of the 2 subjects in reference to the camera is not important. You also mention that the height or relative position in which the desired plane of sharp focus passes through each subject is not important for use with the devices you mention. If this is so, try this extreme example and explain how it would work.

    You have a high subject in the near, and a low subject in the far...you want to pass the plane of sharp focus through each. Now, without input knowing the hieght of the two points at each subject, the calc. or brainbox would have no way of knowing if the plane of sharp focus would intersect under the lens or above the lens. This is a a bit extreme example, but I think it hopefully it will deomonstrate my position more clearly.

    Of course in such case you would tilt the front lens board towards the film, vs. towards the subject. However, this example can be modified to demonstrate the differences between the plane of sharp focus that passes directly under the lens, say 1ft, vs. say 300 ft under the lens, my issue still being, without this critical subject information, I can't see how any device can assess the required tilt angle?

    As for your other point about seeing everything on the gg. If this was true, I would have never wasted all my time reading Merklingers books and studying tilts. Actually this issue is irregardless whether a view camera is used with or whitout movements. Just one qualifier first. If the goal is to make a contact print from the film, then yes I agree with you 100%. However, if you goal is to enlarge the entire film 10x for a print, now you are confronted with too many problems to see the real story on the gg. For starters, you would need to stop the lens down to the calculated f stop, say f32. In such case, there is insufficient light to even see the gg with such precision. Assuming you could see the gg well at f32, next, you would need to evaluate the gg at 10x magnification to inspect whether you are resolving the lpmm to film which you calculated for. Under no circumstances is a gg capable of resolving 10x magnification - i.e. for means of determing if something will yeild say 4 lpmm on print. A gg can normaly resolve a max of 2-3x magnification for such. It's simply the size of the grain the gg that determines this. This does not mean you can not use a 10x loupe on the gg, but the resolving capability is limited the gg grain, not the magnification of the loupe. Threrefore, even using box cameras, you can see the need for good DOf calcs that meet all your desired goals of the final product. I am interested in your comments.
     
  45. The following diagram from Merklinger is essential to understand LF dof<p>
    <img src="http://www.trenholm.org/hmmerk/MicroMov.gif"><p>

    The moving line in red represents the plane of sharp focus
    <p>As the film plane
    moves back and forth, this plane of sharp focus tilts up and down
    hinged on a line called the hinge line(yellow dot ), the blue dot
    represents the Scheimpflug line.

    <p> If the film plane moves back and forth only a small amount( depending on the size of circle of confusion ) the
    red line will move withing the limit bounded by two straight lines
    -- those are the near and far DOF of slanted object with a tilted lens.
    <p> Scheimpflug rules dictate that these boundaries must be straight
    lines.
     
  46. After watching Merklinger's movie diagram and goes back to
    <p><img src="http://www.photo.net/photodb/image-display?photo_id=857807&size=md"> where can one see that the plane of sharp
    focus swings between two curved boundaries ?
    <p> Further, Pete did not draw his diagram big enough, otherwise
    the purple line will goes to infinity, the blue line end up at
    hyperfocal distance H, and the yellow line end up at H/2
    <p> It is simply a diagram of box camera dof at various distances,
    nothing to do with LF, nothing to do with Scheimpflug.
     
  47. I am surprised the movie post worked, nice job! This is Merklingers second biggest contribution after "J". When using a camera with base tilts, the location of J is a bit different. But this is a minor point. I agree with your point here, as I too think some people have confused DOF of a box camera with DOF of lens tilt.

    Martin, you wrote.....If the film plane moves back and forth only a small amount( depending on the size of circle of confusion ) the red line will move withing the limit bounded by two straight lines -- those are the near and far DOF of slanted object with a tilted lens.

    I am not clear what you are suggesting here...... and it's possible I have overlooked a key Merklinger shortcut. Are you suggesting that by moving the back focus - up and back, you can center the psf where you desire between the two DOF near and far points? (which in this case is two points above and below the psf) To calc. the DOF, which is a cone starting at J, (the yellow dot), and extends outward equally above and below the psf..... I always used a formula, however, this trial and error would be much easier, assuming my assumption is correct here?
     
  48. when this thread runs its course, I can't wait to discuss the physics of pressing the shutter release.
     
  49. The 1946 Kodak Reference Handbook defines TWO different Dept of Field (DOF) methods....; plus several of my other Optical texts also<BR><BR>Method A , uses a fixed circle of confusion<BR>Method B uses a circle of confusion a fractional length of the lens<BR><BR>short fixed lenses on non view cameras use method A..the DOF tables for the Kodak Ektra and Bantam special they are for a COC of 1/500 inch...; for the Medalist the COC = 1/200 inch...<BR><BR>For the view camera Ektars and Anastigmats; (4" to 14" FL )the COC is 2 arc minutes....which is equal to focal length/1720...<BR><BR>Be carefull because different markers use different Circle of Confusions........
     
  50. Bill, for information on how the Sinar tilt/swing angle & depth of Field calculators work go to http://www.sinarbron.com/123.htm. Ifthat diirect link doesn't work go to sinarbron.com and then go to the Sinar P2 page and click on the link which takes you to the page I cited.
    Here is how the Rodenstock Depth of field calculator (system © Walter E. Sch on) works:
    1.) point the camera directly at the subject of your photograph and erect (make vertical the standards.
    2.) determine the angle of tilt (if any) between the base or monorail and the standards when the standards are vertical.
    3.) dial in the format you are working in (you are given choices from 6x4.5cm up to 8x10 inches).
    4.) determine and set the scale the subject will be recorded at on your film (from 1:1 to 1:?)
    5.) Focus first on the near point of your composition and then making note of that position refocus to your far point. measure the extention difference from the near point to the far point (in mm). 6.) Using this difference (on the scale), set the f-stop suggested for this difference and then refocus the camera half way between the two points.
    7.) look at another part of the calculator to see if any added exposure is necessary.
    8.) Close the lens,cock the shutter, load the film holder, pull the darkslide and make your exposure. You can first do a test on Polaroid Type 55 and examine the negative (assumes you know via testing that the film plane for the Polaroid holder and the film plane of the film are congruent.) I have been using this tool for not quite a year and it works for me. But then what do I know? After all I'm just a guy who makes his living making photographs and stakes his reputation on the quality of his images. If this system didn't work I'd rely on something else, even Merklinger. Some people like to make things very complicated: I don't unless I have too. I stand my position that the camera has all of the information you need to determine depth of field and any tilts or swings for any given photograph.
     
  51. In short :

    1)I do not know when Tuan Luong will update his web site, so
    people interested in the English version of my DOF + Scheimpflug paper can get it by mail

    send me a blank e-mail to bigler@ens2m.fr
    subject line should be

    send mime dof.pdf

    you'll receive a .pdf file as an attached file.

    2) about Sinar : Sinar has the Sinar E where all movements are
    motor-driven and computer-controlled to perfectly set for Scheimpflug and hopefully Scheimpflug + DOF ;-);-)

    3) the info about the Sinar E what pointed to me by a French professional photographer who makes a living by taking and selling top-quality pictures made will all kinds of cameras including view cameras. He never uses maths to compute depth of field ;-);-)

    4) the physics of the shutter release is something worth a long thread
    since it involves complex mechanical phenomena : friction, lubrication, elasticity, etc... not mentioning the fascinating world of mechanical shutters, just behind the release of a view camera lens ;-);-);-)
     
  52. Martin;

    Your Moving diagram is cool; this behavior applies for a single element box camera lens; two element achromat; 3 element cook triplet; 4 element Tessar; or 5 or 6 elemet Planar, ....etc etc...

    Lenses do not know whether they are in box cameras; 110 cameras, enlargers, Zorki's, check sorters, movie cameras, or view cameras....

    DOF rules apply to all optical devices; LF is no special case in optics

    High end Cinematographers have tilted fast lenses to get 2 parts of a candlelite scene for many decades...The American Cinematographer Magazine showed this about 3 decades ago; granded the most users of tilting are view camera guys; but their is no special warping of raw optical theory just because a view camera is used....

    I guess your continued reference to "box cameras" has me really wondering why ....Alot of better 1950 to 1960's box cameras have curved film planes; and most view cameras are stuck with flats sheet film holders......Most box cameras of that era have but one lens that is fixed focus meniscus design..The position of the stop is adjusted in the design phase to the best spot; ie minimum abberation....Many are F11 in F stop...

    This is a good thread:

    But I am puzzled as why the references to DOF in LF are different than any other optic device...Both the box camera and the LF cameras operate with the same optics laws....

    Dont take this as a rant; I am use to using optics from one field; and using them in a totall differnt matter..

    I am more puzzled than rant; about the box camera references...

    Regards to all Kelly
     
  53. Ellis....
    Bill, for information on how the Sinar tilt/swing angle & depth of Field calculators work go to
    http://www.sinarbron.com/123.htm.

    Ok, I have reviewed this page, and I hope someone else will support me here, but I beleive this method will work fine for close-up work. However, for landscapes,.... I just can't see this being as reliable as the less desired long hand method. But until I test it, I will stay a bit reserved.

    Here is how the Rodenstock Depth of field calculator (system © Walter E. Sch on) works:
    4.) determine and set the scale the subject will be recorded at on your film (from 1:1 to 1:?)

    Thanks for providing the input variables. Ellis, in landscape scenes, how does one determine the image size ratio? From reading this, it also seems mostly applicable to close up work vs. landscapes. As Mr. Bigler points out and his white paper demonstrates, there is BIG difference betweein focussing close with tilts vs. landscape scenes.

    you wrote..... If this system didn't work I'd rely on something
    else, even Merklinger. Some people like to make things very complicated: I don't unless I
    have too.

    I think its safe to say, we all prefer the easiest and fastest method that yields satisfying results.

    I stand my position that the camera has all of the information you need to
    determine depth of field and any tilts or swings for any given photograph.

    You never commented on the issue of gg magnification, I felt this was a key issue as to why your above statement is not true. Your comments? thanks
     
  54. Bill; several times in optical systems calculations I have found errors in were actually the lens was rotated..In 1979 I got the grand job of figuring out which optical program was correct...One physics guys progam was in basic on a commidore pet computer......My boss; the Phd in electical had his program on a HP basic program on cassette......<BR><BR>After getting lost in both guys undocumented software; I set out with my own check..<BR><BR>I did the ray tracing of the ray thru the tilted lens by rigorous geometry; defining each axis; where the lens was rotated about etc...I had the geometry of the 2 element lens; tilted with respect to the optical axis.. <BR><BR>I used snells law and applied the law at the 4 tilted lens/air interfaces..I used my HP-25; and filled about 13 pages of snells law and basic analylical geometry to 9 decimal places..<BR><BR>My totally independent check matched by bosses HP basic cassette model within 5 decimal places....<BR><BR>The physics guys answer was close; within 2 places at small angles; but enough off to be bothersome..His models results differed ALOT from the other guys model at large angles.. he had rotated the lens about a slightly different place in the lens..This write a optical program with no rigorous diagrams is dangerous..Sometimes two models will track well at small angles; and get horrid results at large angles....<BR><BR>
     
  55. Kelly wrote:

    Martin;

    Your Moving diagram is cool;
    <p> Not my diagram, it is Merklinger's diagram from his website

    <p>this behavior applies for a single element box camera lens; two element achromat; 3 element cook triplet; 4 element Tessar; or 5 or 6 elemet Planar, ....etc etc...<p>

    <p> That is correct<p>

    Lenses do not know whether they are in box cameras; 110 cameras, enlargers, Zorki's, check sorters, movie cameras, or view cameras....
    <p> But the law of optics knows


    <p> DOF rules apply to all optical devices; LF is no special case in optics<p>

    That is where you get it wrong.
    <p> The primary law of optics applies to all lenses, LF no special case<p>
    <p> DOF formula are not primary laws, they are deduced under the
    assumption that there is no lens tilt, hence not applicable to
    view camera.
    <p>Box camera ( means camera with no lens tilt ) and view camera
    has different DOF rules.
    <p>
    <p>
     
  56. Kelly wrote:

    "But I am puzzled as why the references to DOF in LF are different than any other optic device...Both the box camera and the LF cameras operate with the same optics laws...."

    <P>DOF formula is NOT primary optical laws--- it is a result.
     
  57. Bill wrote:


    "I am not clear what you are suggesting here...... and it's possible I have overlooked a key Merklinger shortcut. Are you suggesting that by moving the back focus - up and back, you can center the psf where you desire between the two DOF near and far points? (which in this case is two points above and below the psf) To calc. the DOF, which is a cone starting at J, (the yellow dot), and extends outward equally above and below the psf..... I always used a formula, however, this trial and error would be much easier, assuming my assumption is correct here?"

    Yes, but you have to get the psf first then moving the the film plane
    back and forth(such that the moved position is perfectly parallel to
    the initial position, with no additional back tilt being introduced ) you can swing the psf up and down and fine tune your psf
     
  58. Bill wrote:
    "I am surprised the movie post worked, nice job! This is Merklingers second biggest contribution after "J". "

    <p> Merklinger's biggest contribution to view camera photography
    is the rediscovery of Hinge line. At the time he published
    "Focusing the View Camera" he did not know whether there was any
    prior discusion of hinge line in literature.
    <p> Later he searched library archives and dug out Scheimpflug's original papers, and found that hinge line was already being
    discussed in the papers.
     
  59. I was reluctant to get involved in this discussion at first - partly because I've never read Merklinger, but mostly because these things are all so well worked out, and when you get right down to it are nothing more than a bit of elementary goemetry coupled to the thin lens equation, that I really couldn't be bothered to 'reinvent the wheel' by proving it all over again.

    However the fact that the argument seemed to rumble on and on made me begin to wonder, so eventually I put pencil to paper and started scribbling away. I'm happy to confirm again what I thought we all knew - that the planar DoF limits do indeed transform into tilted planes when the lens is tilted or swung.

    I can only think that Pete is forgetting that in the thin lens equation distances are measured perpendicularly to the lens plane so that when you swing the lens you change the distances involved. His worked example doesn't seem to take account of this. Apologies if this has already been pointed out - this is a long thread and I may have missed bits.

    To any who want to convince themselves again as I did, I suggest working through the goemetry with the lens fixed and tilting instead the film plane. It amounts to the same thing mathematically, but I think it is more straight forward notationally.

    Also I am going to slightly disagree with Martin here and say LF is not a special case - at least not in the usual mathematical sense of the term. It is rather the general case, and it is the application to rigid body cameras which is the special (i.e. restricted) case that most people are more familiar with.

    Finally, I am disappointed to hear again such villification of the whole principle of hyperfocal focussing. To me it is nothing more than an effort to make the best use of the DoF available. I've never yet used LF on a subject that was entirely two dimensional. We swing and tilt in order to improve things as much as we can, but there are still invariably objects in the frame that are sitting well off the plane of sharp focus. Somehow we have to deal with them. Hyperfocal focussing just gives us a way making optimal use of what is available by deciding where best to place the plane of sharp focus. I really don't see why some are so scathing about it. Relying on what you can see on the screen is fine, but personally I can't see an awful lot at f/64. I'm struggling at f/22, to be honest. I'll take any help from the mathematics that I can get.
     
  60. I don't know how I managed to spell geometry wrong twice in that answer. Apologies.
     
  61. Martin; Re " "In summary, in LF, you have to start with Scheimpflug principles and not trasnplating box camera optics" As a kid I cut out many a box camera and tilted the lens to learn how optics work ...; and the depth of field stuff shown above 40 years ago......

    All the optical stuff in this thread were known and documented decades before World War II..... My 1946 Kodak Handbook gives DOF calculations; and several of my prewar books due too..........For a tilted film plane each point along the film has a different focused point ; one can do this graphically also.....I know that the law of optics doesnt care about what box surrounds them; but my reading your comments; it sounded like you believed that LF lenses have special rules different than "box camera" lenses....It would be better to use proper terminology like cameras with fixed film positions perpendicular to the optical axis......... Your continued usage of the term "box camera optics" is bothersome to somebody who has worked with optics for 40 years..; and understands optics....
     
  62. Martin:

    RE:Merklinger's biggest contribution to view camera photography is the rediscovery of Hinge line. At the time he published "Focusing the View Camera" he did not know whether there was any prior discusion of hinge line in literature.

    The "hinge rule" is what I learned from an Old Speed Graflex guy; who also had a view camera...He had many Graflex lens guides and pre World War II Kodak guides....The intersection of the lens perpendicular, film plane, and subject planes in focus is documented in these pre World War II books the Graflex guy lent and Mentored me with....

    The loss and rediscovery of knowledge is an old problem....Most people shun old ways and the old books are chucked out....The focusing planes and hinge rule were probabaly well understood by Gauss; and maybe even Newton....

    Search the web for front load washing machines......

    Most all web sites state that they are more efficent; and shout out how the Neptune maytags are new to america; but have been used in Europe for decades.....

    "Appliance manufacturers have more recently developed new models of front-load washers which are smaller, more affordable and designed for domestic use."

    Westinghouse brought out front load washers in the mid 1940's; we got one in 1947......we used it until the mid 1970's and replaced with a brand new White-Westinghouse 1977 model; which we use still here every few days.............When the expert Maytag engineers Released the Newtune washer about 1997; they failed to understand the 1943 westinghouses subtle design features; and had stale stinky water collect in the rubber boot......After a year or two of problems in the field; they changed the design....which has no stink; like out 1947 westinghouse that lasted 30 years!

    [​IMG]
     
  63. <a href="http://www.arri.com/infodown/cam/manu/t_f_e.pdf">Here is a 256k PDF file on the three Tiltable ARRIFLEX a camera lenses the 24, 45 and 90mm lenses...several of the diagrams are interesting; showing the depth of focus in the subject area<a>
     
  64. Kelly, in your post where you discuss programming calculators for figuring lens geometry.... I am confused what your point was? Were you trying to support my post that some of the tilting methods above were applicable to close up photography, but not as accurate for landscapes? Also, the use of the term "box camera" is the simpliest way to designate a camera whereas nothing can move, film plane and lens planes are parallel.... we were not referring to box lenses. I assumed this was confusing you, and I apologize for not jumping in earlier.

    Martin, you seemed to agree with what I was suggesting, however, even if this trial and error method works for setting the position of the rear psf between the two points I want in focus.... I can see this being a simple way to place the psf accurately, but I don't understand how I would know what f stop to set to meet the DOF objective? Can you explain? I tried to be clear in my post, but possibly I confused you the first time around?

    Hugh, I just bought a brand new Neptune Maytag side load washer, and it still has water collection on the bottom of the door area... this proves my point....there quite often is tons of useful information floating around this world, but only rarely does it find its way into the hands of the people who need it the most. I find view camera geometry to be very similar...bits and pieces all over the place. Merklinger was one of the few who assembled it and presented it in what should be a useful book. I feel Merklinger fell a bit short due to his poor writing skills and he also fell short in his ability to make each step more field friendly. I personally feel the application of view camera geometry for landscapes has can be refined a bit more, just the application of it, not the justifications. After reading Mr. Biglers white paper, I feel he is our best hope, he truly has a grasp on this subject, IN DETAIL! I applaud his efforts.

    I am really curious if the Sinar method provided by Ellis's link above and the Rodenstock calculator are truly designed for close up work. The input data makes me confident this is the case. And just like macro photography, as Mr. Bigler points out, the DOF formulas do change based on how many fl's away the subject is from the lens. This is very clearly defined in DOF calcs for box camera macro work, but once again, I have never seen this clearly defined with tilting. It seems that all tilt math is "one shoe fits all" ...but Mr. Bigler did a great job dis prooving this.
     
  65. Martin; check out page 16 of the ARRI manual; which gives a very narrow focus on the object plane...This is a cool movie trick..; and not usually mentioned in LF books
     
  66. Bill; my point about the lens calculations,programming story was to mention that optical models do sometimes have "errors" built in because of subtle differences about how or where the lens is rotated about......<BR><BR>This geometry problem and sometimes small angle assumptions cause ones optical results to vary from one persons model to another.....<BR><BR>Thus model A and B might give almost exact results near a lens; and divert wildly as one approaches infinity ; or LARGE angle rotations..<BR><BR>Because I have toiled over this matter of different optical model/program's results; I wanted to share that it is GOOD to question EVERYONES models results ....<BR><BR>I was not confused about "box camera" lenses; but was wondering if Martins point was <BR>(1)the fixed film position of a box camera; OR (2)a simpler lens design may have alot more field curvature; and require alot more rigourous equations with their curved focusing properties at the film planes.....<BR><BR>Most cheap "box cameras" today are made out of plastic; their film rails are molded in a curved arc to get great focus..My 1950's/1960's Kodak Brownie Bullet and Holliday have molded bakelite rails in an arc.....<BR><BR>Because most LF uses flat sheet film holders; I wondered if the "box camera" comments was about the curved focus, fixed lens, etc<BR><BR>
     
  67. Bill;
    Re again "Were you trying to support my post that some of the tilting methods above were applicable to close up photography, but not as accurate for landscapes"

    I have seen optical models differ at extremes; and would not be surprised at all if some of the tilting models on the net and books do too..
     
  68. Sorry Bill - the washing machine post wasn't mine.
     
  69. WE all need Westinghouse Brand paper DOF slide rules!
     
  70. Thanks for providing the input variables. Ellis, in landscape scenes, how does one determine the image size ratio?
    Bill you have to use a variable: it is called common sense, to determine the reproduction ratio. If you are photographing a building that is 50, 100, 200 or 500 feet tall and the image of the building on film (or groundglass) is four inches tall, I think it is fair to say that the ratio is damn close to 1: infinity.
    As for the rest of your comments all I can say is: these tools and methodologies work for me. I'd rather make photgraphs than waste time doing unnecessary math. Sometimes in photography there is a very real need for some very intense calculations, but this is one area where that approach is just bunk and I think any one who actually practices making high quality photographs with a view camera on a regular basis knows this to be true. At some point you have to stop trying to make reality fit theorems and adjust your way of thinking to reflect realities. The deeper you lock yourself up in merklinger's geometries the more likely you are to make mistakes, and I remember well from many of your other posts that you have intractable problems getting sharp images.
     
  71. Ellis; good post!
     
  72. Ellis.... your wrote...Bill you have to use a variable: it is called common sense,

    I knew it wouldn't be too much longer till the Ellis sarcasm surfaced. Tough to keep it in, huh? Thanks Ellis...

    to determine the
    reproduction ratio. If you are photographing a building that is 50, 100, 200 or
    500 feet tall and the image of the building on film (or groundglass) is four
    inches tall, I think it is fair to say that the ratio is damn close to 1: infinity.

    How about a tall tree 100ft away? I know you can guess the real height of this, right Ellis? This is sloppy Ellis and not acceptable to me. I have always been excellent with judging distances and heights, I do it often in my engineering job. After buying a laser rangefinder and tesing myself in the landscape, I found it truly remarkable how far off humans are in estimating size and distances when there is no references such as windows of known hieght on a building. This has proven true with many other successful photographers and mathematical gurus who I travel with. So for starters, this variable can be way off without some cross checks.


    Ellis wrote..... As for the rest of your comments all I can say is: these tools and
    methodologies work for me. I'd rather make photgraphs than waste time doing
    unnecessary math. Sometimes in photography there is a very real need for
    some very intense calculations, but this is one area where that approach is
    just bunk and I think any one who actually practices making high quality
    photographs with a view camera on a regular basis knows this to be true.

    I have been practicing this for almost daily for the past 4 years, and would disagree with your "bunk" statement. Possibly my enlargement criteria is greater than yours, hence the reason I need to pursue such avenues. But I won't knock your style or technique if it works for you Ellis, I think you should offer the same respect to others.


    Ellis wrote.......At some point you have to stop trying to make reality fit theorems and adjust
    your way of thinking to reflect realities. The deeper you lock yourself up in
    merklinger's geometries the more likely you are to make mistakes, and I
    remember well from many of your other posts that you have intractable
    problems getting sharp images.

    For starters, my thinking does reflect reality, did you ever stop to think, I may be more thorough than you? Is that unacceptable to you? Merklinger has been a blessing to me.... his concepts made me highly accomplished using movements. Instead of making mistakes, I found his methods saved a lot of mistakes vsl associates who use other less honed methods. Just because I think a bit of refinement would be helpful, does not mean I disagree with Merklingers methodologies. If you read my posts, you can see I commended him many times, as well as some of the other math gurus on in this thread. As for my "intractable problems getting sharp images"....well Ellis, I think you better go re read some posts... after Merklinger, tilt has been a joy for me and I have taught countless others to adapt his methods. So instead of making false accusations to feed your superiority complex, why not just chill out and stop the personal attacks. You have a long history on this list..... once you get pressed with fair questions, you snap and turn things personal. A simple answer such as, I elect not to do Merklinger math or justify the ground glass magnification issue would suffice. I never know when you overlook a question I ask, or when you are just too defensive not to answer. It's tough to decipher Ellis...but I tried to be peaceful and respectful, but as usual, it serves no purpose. In the future, I will stay clear of your posts. I hope you do the same. End !
     
  73. "How about a tall tree 100 ft away? I know you can guess the real height of this, right Ellis? This is sloppy Ellis and not acceptable to me."
    Bill you miss the point entirely. How tall is the tree? Let's say that the tree is 80 feet tall. Let's say that 80-foot tree is recorded as 4 inches high on the film. That is a reproduction ratio of 1:240. This is what is meant by reproduction ratio: the size of the image of the object compared to the size of the object. What difference does it make how far the camera is from the tree as long as you have focused accurately so that the image of the tree is rendered at full resolution.
    ”I have been practicing this for almost daily for the past 4 years… Possibly my enlargement criteria is greater than yours.”
    Good for you. No doubt your “enlargement criteria" is "greater” than mine.
    But I still think your approach is “bunk” because it overly complicates something that doesn’t need to be. Using a view camera to make high resolution images while exercising great control over the distribution of focus and the control of perspective rendering is just nowhere near as complicated a proposition as the approach you apply makes it out to be.
     
  74. Bill wrote: "I can see this being a simple way to place the psf accurately, but I don't understand how I would know what f stop to set to meet the DOF objective? Can you explain? "
    • First of all, we need to estimate the J number
    • Then estimate the amount of DOF required
    • Calculate fstop required.
    • The concept of DOF in view camera is complex, but the formular is supprisingly simple, much simpler then in "Box camera"( ie, camera with no lens movment, this includes RF, SLR, etc, and Brownies..)
      The rule of thumb in LF dof IS
      At a point on psf, whose distance is one Hyperfocal distance, the DOF is approximately one J above and one J below. The near and far limits must be measured parallel to the film plane.
      The object of interest may not necessarily at Hyperfocal point and the near far limit may not be J, but not matter, as long as you get the proportion right.
      J/H determines the angle of one of the dof limit( two of them, one near limit, the other far limit)
      H =1500 * focal_length /Fstop
      Suppose the object of interest is at distance D, you want DOF to cover a height of h above and h below (measured in parallel to film direction)
      The require aperture can be calculated by
      Fstop = 1500 * Focal_length * h /(JD)
     
  75. Ellis, I certainly understand what the definition of reproduction ratio is. My last post explained where I saw the shortcoming of such. First, how do you know that tree is 240 ft high???? If you knew the distance the tree is from you, then you could check the angle from the base of the tree to the top of the tree and calc the height, however, you still need to know the distance for such. Get my drift here, in the landscape world, with no referenced subjects, I have never met anyone that can estimate heights and or distances as you describe. It's easy to be off 100%. I have been practicing this 20 years as I work with commercial buildings all the time, and I still am very inaccurate in the field with no references. And BTW, reproduction ratios are inputs to close up photography formulas, this further supports my position the Rodenstock calc. was designed for close up work.

    Ellis wrote...... No doubt your “enlargement criteria" is "greater” than mine. But I still think your approach is “bunk” because it overly complicates something that doesn’t need to be. Using a view camera to make high resolution
    images while exercising great control over the distribution of focus and the control of perspective rendering is just nowhere near as complicated a proposition as the approach you apply makes it out to be.

    We can just agree to disagree on this one. If I felt this is over complication, I would not be doing it. I have explained my reasons why I feel this is neccessary, and you have elected not to address them. So I will leave it at that...

    Martin, you wrote....At a point on psf, whose distance is one Hyperfocal distance, the DOF is approximately one J above and one J below. The near and far limits must be measured parallel to the film plane.

    Yes, I agree, this is what I have been using. And I also appreciate your formulas, but somehow everyone overlooks how one determines these distances....they are easy to plug in a formula, or a chart, once you have a way to figure them out! I find the DOF aspect a bit cumbersome in the field for two reasons. First, it's difficult to determine how far a subject is from you, i.e. x Hyperfocals, and it can also be hard to evaluate how far x J's extend upward or downard at a given distance. On a scaled drawing, this is very easy. I have worked this aspect the best I can in the field. I feel this is one of the most cumbersome aspects of applying Merklingers methods in the field. Quite often, I just make a quick scaled sketch, (takes less than 2- 3 minutes) it seems to solve the more complicated scenes. Even in Merklingers book, he does the same! :) The good news is, if the scene is totaly static, I can just stop down till the diffraction limit and be safe. however, when you are fighting for a few extra stops of shutter speed, this is when you want to use adequate f stop for desired DOF, vs. overkill DOF which can cost you a few stops of shutter speed.

    Even though I am a Merklinger fan, I will gladly disclose to those newcomers to tilt, sometimes his approach is a bit cumbersome in the field without additional tools, such as a laser rangefinder, angle finder and a sketch pad. It's imperative to get the tilt angle very close to perfect, and to do such, you need to have a method to calc. just how far under the lens the psf will intersect. In some cases, this is simple, such as a shooting in a lake with distant mountains, these are the times we love Merklinger. However, in more complicated scenes, it is near impossible to eye ball the scene and estimate J, without utilizing additional measuring tools. (assuming you want to be accurate) At least this has been my experience in the field. Under these circumstances, this is where people get frustrated with Merklinger methods and resort to, tilt for the near, focus for the far, types of methods. OK, I may go back to lurker mode for awhile, I'm burnt out!

     
  76. "Even though I am a Merklinger fan, I will gladly disclose to those newcomers to tilt, sometimes his approach is a bit cumbersome in the field without additional tools, such as a laser rangefinder, angle finder and a sketch pad.
    Exactly.Thank you for making my point Bill.
    Alex and other newcomers to large format work, please don't be scared off by their approach. Try it if you like but there are more much direct and just as precise ways to "skin the cats" of determining depth of field and using swings and tilts to make the shot and get the extremely high level of resolution your equipment is capable of.
    Happy Schiempflugging to all of us large format photography fans.
     
  77. Bill; do you own a SUUNTO Clinometer? They are great to measure the height of objects
     
  78. Kelly, yes I do, and I use it quite often and yes it does work very well! In conjunction with a cheat sheet and a laser rangefinder, I can tell the height of just about anything very fast.... I once saw a combination unit made, that included both into one. You pointed at the base, then the top and it gave you the height...it assumes a right angle at the base. Can't remember where i saw it.
     
  79. Out of curiosity, Bill how long does it take you to set up, do your
    measurements, draw your diagram (if necessary), make your
    calculations, double check all of the above apply them to the
    camera and make your image?
     
  80. Well Ellis, as you can tell from what I wrote above, this depends greatly on the scene. A best case / worst case scenario is like this.....

    Best Case....It's obvious where psf is intersecting below lens, do simple math in my head, fl/j*5 = tilt angle, set tilt, focus for the far, tighten controls and shoot.... very simple, - from the time camera and lens is on tripod, I can be tripping the shutter in less than 30 seconds, which includes light meter readings. I am very fast when things are simple....

    Worst case scenario, .... a complex tilt scene which involves, laser rangefinder, clinometer, scaled drawing, look up charts, etc.... well, this has taken me as long as 10 - 15 minutes at times. Considering you are tired, bugs bighting you, light changing, etc. it is not ideal conditions to be doing all this. But of course I apply some common sense.....If the light is changing fast, I won't even attempt all this - I just set up, make an educated guess, stop down to the max. and shoot.... sometimes I can squeeze a 3x enlargement out of rush shot, and sometimes I get lucky and get a full 10x. This is in essence what it all boils down to.... regardless of how I go about shooting the scene, the chrome always looks good on a light box, but my goal is to make big prints, so enlargement factor is a key...and when DOF values and the psf is not perfectly accurate, then enlargement potential is the penalty I must pay. This is why I stated early..... if my goals were making 8x10 prints from 4x5 chromes, I would never get bogged down with all this mess!

    Of course complex scenes that are worthy of all this time and effort, I may do the math one night, then when I re visit the scene the next day, of course I can set up in less than a minute.
     
  81. Bill; good story about the setup times..<BR><BR>Most of the SUUNTO Clinometers we sold were to cell phone tower survey guys..they want to quickly get a good height estimate ("survey of their competitions towers in the area")....at the standard 1 chain (66 ft) distance; the clinometer reads to 200ft height...Alot of tree guys use them also..<BR><BR>The Leica disto laser rangefinder is fantasticly accurate within 1/8 inch; the older models poop out a 300 feet.. The hunters and billboard guys go for the 300,400,500,600 yard laser rangefinders; their accuracy depends somewhat on subject shape; and usually is within a few yards..For signage studies I used a 30x40 foamcore white sheet as target; when going past the rangefinders specs! One old unit I used would roll over past 1000ft; and read 005 ; for 1005 feet....This was with the giant white target; and past the units 300 yard spec......<BR><BR>You are wise to use the clinometer and laser rangefinder.....Few people can estimate heights and distances consistantly well....Many Land Surveyors can
     
  82. Thank you Bill those times are both better and worse than what I
    expected. Most of my work gets used at everything from near
    contact print size,but quite often ends up being enlarged by a
    factor of 10 or 15X and occassionally larger (or a final print size
    of 40 x50 inches or even as large as 60 x 75 inches. <P>I think
    our misunderstanding seems to have been based on my use of
    the term reproduction ratio -- by which I meant to the size ofthe
    original object to it's reproduction on film, and your use of the
    same term which seems to me to refer to the enlargement of the
    negative or transparency to a print.<PP>Have you worked at all
    with the Durst Lambda process?
     
  83. Kelly, very few photographers seem to be familar with these tools. I find them mandatory, even for box camera DOF. With out tools, you are focussing in the dark. Most many rangefinders require an ojbect of known size to focus on, such as a golf flag, these can be purchased for $15. But they are useless in the middle of the a landscape scene where you have nothing to reference. Hence the reason I use the DMG rangefinder that is very accurate up to about 1200 ft. After 1200 ft, most of the time they are at infinity, or near infinity based on the fl lens used.

    Ellis wrote....I think our misunderstanding seems to have been based on my use of the term reproduction ratio -- by which I meant to the size ofthe original object to it's reproduction on film, and your use of the same term which seems to me to refer to the enlargement of the negative or transparency to a print.

    Not to beat a dead horse, but, I never confused the two issues. They are totally independent issues which both affect the final outcome on film. Your reproduction ratio input is required to set focus properly. If a tree is 200 inches high and it appears on the gg at 2 inches, that represents 100:1. With a known fl lens, you can reverse calculate the trees distance. That is why the calc. is asking for the reproduction ratio, it's ultimate objective is distance, but as you can see, its 6 of one, 1/2 dozen of the other. But it's my guess, the real reason it asks for reproduction ratio, is because in close up work, you can use a disc in the scene and re measure it on the gg which simplifies the entire process. That's why I feel so strong the Rodenstock calc. may be geared for close ups. Now, the coc we both used in our calc, which also changes focus position will dictate enlargement potential, HOWEVER, making an error with estimating height and / or distance / reproduction ratios, will create error in the focus position, which in turn will compromise the enlargement potential on film. Hence the reason I keep mentioning enlargement potential, it's the final result of all the input data, regardless whether its Merklinger, Rodenstock or Sinar. It's the ol weakest link in the chain principle.

    To make my point clear, if I could look at a tree and know the height, then measure it on the gg, I would not need all these other tools to accomplish what I am after. It does not matter if I am trying to estimate the height of the tree to enter a reproduction ratio in the Rodenstock calculator, or use it to determine where the psf will intersect under the lens for Merklinger, the bottom line is, I am still guessing the height of the tree. (Or more importanly for the psf, the distance of the tree, so as to determine the angle the psf will travel) So regardless of whether I wanted to use Rodenstock calc. or Merklingers, my point remains the same, in landscapes, it's nearly impossible to consistently guess these values. Land surveyors are good, but when you get in nature, there is so many false depth clues which throw you off, it's truly amazing. The only way someone will understand the difficulty of such, is go into the wilderness with a laser rangefinder, and possible a clinometer, and test yourself! Be sure to guess first, then use the tools! :)

    The real education I got in this area, was when I started shooting Medium Format Stereo with dual M7's. The film is used for the final product and seen in a stereo viewer with 4x magnification lenses. Our eyes can easily determine when something is not acceptably focussed. I had to perfect the exact lpmm on film, which turned out to be about 5 lpmm AFTER lens magnification, so it would appear sharp to our eyes! 2 lpmm after magnification appears fuzzy vs. 5 lpmm, however, 10 lpmm appears a tad sharper, but does not make the 5 lpmm look soft. So the film had to produce a minimum of 5 x 4 or 20 lpmm in every part of the scene, or the chromes were trashed. No Photoshop to save us here. (of course these lpmm get converted to coc in the DOF calcs) With such exacting requirments, this is when I finally discovered, without measurement tools, it was clearly a "hit or miss" proposition. After I perfected my DOF charts with the minimum coc my chromes can accept, I have had near 100% success rate getting each part of the scene to meet my min. sharpness objectives. As you can imagine, most scenes are pushing the envelope of DOF since there needs to be at least some near objects for the stereo effect. So quite often, I have to walk away from a good scene, as it's impossible to squeeze the DOF I want for asthetics with out compromising my minimum coc's. This is the utltimate lesson in coc's and accurately knowing distances in the field.

    Of course the M7's are box cameras, so therefore I only need to use the laser rangefinder for distances. Using the rangefinder, I determine the distance of the near object and far object, look them up on my DOF chart, it tells me what distance I must focus at to meet this criteria, I use the laser rangefinder to find something at that distance and focus on it. Quite often I have to take the camera off the tripod, look around, to find something at that distance when there is nothing in the scene at that distance, then just re compose. Shooting MF stereo with dual cameras makes Merklingers tilt math seem easy! The math / charts for interocular seperations can really get confusing!

    <PP>Have you worked at all with the Durst Lambda process?

    Yes, I have used Durst, Light Jet and Chromeria.....but I no longer use these wet processes. About 1.5 years ago I have fallen in love with ink jet prints on fine art paper - in my case, water color paper. Ink jets have come a long way, and gives the look of the print an "artsy" look vs. the ol standard glossy photo look. Not cheap though, the good papers and inks run about $4 sq ft + labor, waste, etc.

    Martin, I am still struggling with that final formula you wrote, did you get my spreadsheet I emailed directly to you?


     
  84. Hi all, after reading 82 responses I have a few questions...One, does hyperfocal distance apply to large format when using tilt? I would like to see a show of hands, I think this would be more useful to Alex than the discussion that has been done so far. Two, how come Adams, Weston, Caponigro, Sexton, manage to get such great images without all those gadgets like range finder, inclinometer, etc?
    BTW, my hat off of to those who understand and use Merkingler's method...I read the "in's and out of focusing" and frankly I could never figure out how to get that J distance...granted I am a chemist not a mathematician, but nevetheless I thought something this complicated would make photography stressfull, not fun.....
     
  85. Bill; Here the Billboard minimum spacing is 1500 feet; thus our local Billboard guy wants me to get him a laser rangerfinder that goes to 2000 feet; and reads in feet.....

    There are now several Laser rangefinders that go to 600 yards ++; but they only readout in yards......

    The divide by three "is too much trouble" !!!!! (his direct quote)

    I guess he probably wont be wandering into the DOF minefield here!
     
  86. Jorge.... One, does hyperfocal distance apply to large format when using tilt?

    My vote is for..... not in the conventional method we are used to using it. However, it is still neccessary at times for calculations involving tilt, such as Merklinger long version.

    > I would like to see a show of hands, I think this would be more useful to Alex than the discussion that has been done so far.

    I guess we should have started that new thread when we first suggested it, oh well, it ran its course, sorry Alex.

    > Two, how come Adams, Weston, Caponigro, Sexton, manage to get such great images without all those gadgets like range finder, inclinometer, etc?

    That's an easy one. For starters, most landscape shots are taken without movements. When movements are required, they often are quite simple as the example I stated above, no gadgets required, very simple math in your head, or quick trial and error on the gg, 30 seconds max. The complex tilt scenes (which pertains to all the above discussion) can be handled many ways.... they can be bracketed to increase liklihood of success. They can be worked on the gg for quite awhile until success is had. They can abandon tilt and squeeze all the DOF from conventional DOF tables. They can have a great image that has limited enlargement potential. etc. etc.... Making great images has virtualy nothing to do with tilt math. This is like asking how anyone traveled before automobiles were invented. People make the best of what is available to them. That does not mean more accurate or faster methods are not beneficial. Like everything else in the world, one generation grows off the next. Techniques, tools and methods become refined and improved through the years. Tilt math is one of the few areas that seem 150 years behind schedule! :)

    Kelly, DMG makes one that goes up to 2000 ft, and reads in feet. I know they did a few years ago. I also do not like the ones that read out in yards. They are quite often targeted to golfers and hunters. The only thing I do not like about my DMG is the read out is not visible through the rangefinder.
     
  87. Martin: The optical laws associated with a 'box camera', as you put it, are no different from those that control the DoF of an inclined focal plane. There is ONE SET of rules of physical optics which govern ALL focusing, whether the camera is a fixed lens box camera, or a 20x16 with all the movements.<p>My diagram is absolutely correct by all the recognised rules of optics. It's Merklinger's oversimplification which is wrong.<p>BTW. How do you suggest I show a linear graph which goes from 1 metre to infinity Martin? Do you have a computer monitor that's infinitely wide? Be sensible.<p>When you start to think for yourself, and are able to do more than just quote Mr Merklinger, then please come back with some real and intelligent thoughts on this subject.<p>Merklinger did NOT invent the concept of intercepting focal planes, and simply being able to show how a lever works is no proof of anything.<br>Even the formula given for the distance 'J' is incorrect - it should be f/Tan(a). This is a small but significant difference. Otherwise the focal plane doesn't lie exactly horizontal when the lens node is brought to 'f' from the centre of the film plane. f/Sin(a) gives the diagonal distance from the lens node to the Scheimpflug intersection line at infinity, whereas the value J is the vertical distance from the node to Merklinger's 'hinge point'. Therefore J must equal f/Tan(a), from simple trigonometry.<br>If you take the extreme case of a=90 degrees, then this still gives us a value of J = f, if we divide f by the sine of the angle, whereas the correct value is obviously 0 ( f/infinity ).<br>So much for Merklinger being a brilliant mathematician!<p>Something else to ponder: Can an inclined plane of focus be really flat?<br>Since the change of focus across the film plane is caused by a simple angular offset between the film plane and the lens's focal plane, then it follows that the change of effective lens extension varies linearly across the film. Now a given change of extension (delta u) has more effect on the focused subject distance (delta v), when the lens is close to infinity focus, than it does when the lens is focused close-up.<br>It follows, as night follows day, that the plane of sharp focus CANNOT be a linear slope, but MUST be curved. Think about it: A 1 mm shift in lens extension from infinty makes a huge change to the focused distance (from infinity to 22 metres with a 150 mm lens), but that same change, with the lens now focused at 22 metres only shifts the focus by another 11 metres.<br>Consider a lens focal plane, tilted such that there is a 2mm wedge between it and the film plane, across the film length (about 1 degree of tilt or swing). With the focus at infinty on one edge of the film, the centre of the film will focus at 22 metres, and the other edge of the film will focus at 11 metres. Now that doesn't really form a flat focal plane, now does it? And it becomes even more non-linear with increasing angle between the lens and the film, as we attempt to lower the angle of the plane of focus.<p>Come on!<br>Think guys, think!<br>Don't just take 'Murky's' word for everything.
     
  88. WAn

    WAn

    For sake of simplicity lets consider the vertical cross section of the whole picture (like in the demo picture above), so we have to speak about focus line instead of focus plane.
    Gaussian lens equation:
    1/v + 1/u = 1/f
    u – distance in space of objects (from lens to object)
    v – distance in space of images (from lens to film)
    f – focal length
    Lets consider a line in the space of objects. A line is fully determined by 2 points; say P1 with coordinates (X1, Y1) and P2 (X2, Y2). The equation of that straight line is
    A*x+B*y = C.
    (A, B, C can be found if X1, X2, Y1, Y2 are given)

    The equation maps P1(X1, Y1) and P2(X2, Y2) to G1(x1, y1) and G2(x2, y2): the x1, x2, y1, y2 can be found also. The straight line that contains G1 and G2 has the same form:
    K*x+M*y = N
    The coefficients K, M, N also can be found.

    Now lets consider a THIRD point P3 (X3, Y3) that is located anywhere in the first line, i.e. its coordinates satisfy the equation
    A*X3 + B*Y3 = C.
    We will prove the lens equation maps a line to a line if we show, that the image of P3, --- say G3 (x3, y3) --- does satisfy the second line equation:
    K*x3+M*y3 = N

    It is really boring to post all the algebra here.
    I hope everybody who is interested can do it.
     
  89. Pete, again I won't comment on the Merklinger stuff because I still haven't read it, but in your final paragraph you are now effectively claiming that the whole Scheimpflug thing has been wrong all along. Your argument for this is nothing more than arm waving, and I would have expected you to know better! You need to sit down with some paper, a pencil, and the thin lens equation and do some basic coordinate geometry. Planes do transform to planes.

    We are not talking about some deep, arcane, and complex mathematics here - I had a question involving manipulation of that equation in my O-level mathematics paper when I was 15 years old! Scheimpflug is not in doubt.

    Of course, if you want to get into the realms of considering the differences between realistic thick lenses and the idealized notion we tend to rely on, then perhaps things are different, and I wish you the best of luck. I think the thin lens mathematics is close enough for all practical purposes.

    Bill, just one point - I think you are mistaken if you think that most LF landscape work is done without movements. Probably the single most common set-up in landscape involves front (or possibly rear) tilt just to get things sharp from the foreground out to the horizon. Not complex, maybe, but still movements.
     
  90. WAn

    WAn

    Forgot to mention:
    The lens equation maps only x-coordinates. The y-coordinates can be found from the condition, that the line "point---its image" crosses the lens center: i.e.

    y/Y = x/X, i=1,2,3.

    And a note about imaginary contradiction "theory vs. practice": nobody asks to perform a math in field; the simple results obtained from the math that have been done in advance can be applied in the field. And an overall understanding never hurts, even in the field. And nothing is better for practice than a good theory!
     
  91. Jorge, yes certainly hyperfocal focussing 'applies' when using tilt. no matter what you do with your lens, film, and focus planes there are always DoF limits (as determined by a given positive CoC), and there will always be an optimal placement for the PSF and appropriate choice of aperture to get those limit planes where you want them. The question is not so much whether it applies as how to figure it out.
     
  92. Pete wrote:
    "My diagram is absolutely correct by all the recognised rules of optics. It's Merklinger's oversimplification which is wrong"<p>


    Do youa agree that three parallel DOF planes when lens is not tilted
    become three intestecting planes, and not two curved planes + one
    plane ?
    <p>
    I think Huw probably pointed out the problem of your diagram: you did not use the correct object distance: which is NOT the length of the line connecting the center of lens to the object, it must mulitplied by the cosine of the angle between the said line and the optical axis. <p>
     
  93. Pete wrote:

    "It follows, as night follows day, that the plane of sharp focus CANNOT be a linear slope, but MUST be curved."

    This it Pete rule of LF replacing Scheimpflug.
     
  94. "No issue is so small that it can't be blown out of proportion."
    - Stuart Hughes
     
  95. as fascinating as this may be, an hour with a set of wooden blocks and camera, positioned strategically, will shine more illumination than this glowing thread.

    for sale:

    Linhof Technikardan TK45S, mint, never used.

    Rodenstock and HP21 calculators, serviceable but severely worn.
     
  96. "you did not use the correct object distance: which is NOT the length of the line connecting the center of lens to the object, it must mulitplied by the cosine of the angle between the said line and the optical axis." - Huh?
    Nonsense! That's only true if the lens doesn't have a flat field to start with.
    Consider: There is absolutely no difference between tilting the lens plane, and tilting the film plane; apart from a difference in the aim of the camera.
    If you consider the lens panel and the plane of focus to stay vertical, and the filmplane to be tilted, then you can more readily see that the conventional conjugate focii formula of 1/f = 1/v + 1/u holds true for every point on the film surface. If you compute many of those points (not just two, Andrey) you can see that a tilted plane of focus is not linear across the film, and nor is the DoF.
    Is anyone disputing that a tilt of 1 degree on a 5x4 camera focuses one long edge of the film at 11 metres, and the other edge at infinity with the centre focused at 22 metres, (or at 3 metres and 4 metres, respectively with a mid focus of 3.4 metres)? It's easy enough to check practically, as I spent (wasted) some of my weekend doing.
    Martin: Moving the plane of focus is NOT the same as defining the limits of DoF. This is the fallacy that Merklinger perpetuates with his peculiar and simplistic outlook on DoF. It is an approximation which only works over a very limited focusing range, but it is not an accurate mathematical model of optical behaviour.
    Huw: Arm waving?
    To whom?
    Most people seem so blinkered and hoodwinked by Merklinger that I'm surprised they notice anything moving at all, outside of a very narrow field of vision. ;^)
     
  97. pete wrote: ""you did not use the correct object distance: which is NOT the length of the line connecting the center of lens to the object, it must mulitplied by the cosine of the angle between the said line and the optical axis." - Huh? Nonsense! That's only true if the lens doesn't have a flat field to start with."
    Your are really confused.
    With your way of calculation , a flat field will form a curved image,, hmm, that is what you got so far
    For flat field lens, D must be multiplied by the cosine




    * P2
    *
    *
    I1 ***** * *()* * * * P1
    *
    *
    I2 *
    In this diagram, P1, P2 are in the same vertical plane
    For flat field lens, image of I1, I2 are on the same vertical plane
    The object distance of P1, is the same as P2
    Image distance is also the same (along optical axis)
    A very simple question for pete
    In 35mm camera, do you think the object distance at the edge of viewfinder is the same as that object in the center ? Or do you think the object at edge has greater object distance than the center object ?
     
  98. That's an easy one. For starters, most landscape shots are taken without movements. When movements are required, they often are quite simple as the example I stated above, no gadgets required, very simple math in your head, or quick trial and error on the gg, 30 seconds max. The complex tilt scenes (which pertains to all the above discussion) can be handled many ways.... they can be bracketed to increase liklihood of success. They can be worked on the gg for quite awhile until success is had. They can abandon tilt and squeeze all the DOF from conventional DOF tables. They can have a great image that has limited enlargement potential. etc. etc.... Making great images has virtualy nothing to do with tilt math. This is like asking how anyone traveled before automobiles were invented. People make the best of what is available to them. That does not mean more accurate or faster methods are not beneficial. Like everything else in the world, one generation grows off the next. Techniques, tools and methods become refined and improved through the years. Tilt math is one of the few areas that seem 150 years behind schedule! :)
    Bill Thank You!!!!!! This is what I was wondering. Most of the discussion here has been of 200 feet tall trees and billboards 2000 feet away etc, and I was thing well jeezz everytime I am on the field I only need a few degrees here and there for tilt, what is all the fuzz about? Granted as you mention more advanced techniques evolve from the past, but if you ask me forget Merklinger's and buy the little Rodenstock gizmo....and save yourself a big headache.
     
  99. I'm sorry Pete, but I can only echo what Martin has said - 'you are really confused'. The distances are measured perpendicularly to the lens plane, and hence the cosine factor.

    Your weekend example could be expressed a bit more clearly, but I can't see that there is necessarily anything wrong with your measurements - you just haven't demonstrated that the transformed plane of focus is anything other than a plane, which is what you now seem to be disputing. That it is a plane is a straightforward corollary of the thin lens equation, and for those who don't like doing the mathematics it is trivial to verify experimentally, and photographers have been doing just that for generations.
     
  100. Huw: Then the proof is easy. Drag out your camera like I did, fit a 150mm lens, and set a 1 degree tilt or swing on it. Then measure the focus at the extremes of field, along with the central focus.<p>Sorry Martin, but you won't be able to verify anything with a minox or 35mm camera.<p>The focusing distance to the edge of the field is a complete red-herring, and varies with the part of the lens field used. You'll throw anything into the mix to confuse the issue, won't you?<br>Anyway, I deliberately picked a small angle of tilt for my example, so that things like that became a non-issue. Do some of the calculation for yourself for a change. Throw in your cosine 'correction' - it'll make very little difference - the field and the DoF still comes out curved.
     
  101. Pete, what do you mean - 'Do some of the calculation for yourself for a change'? I did, before I even entered this discussion. Scheimpflug is a corollary of the thin lens equation. The plane of focus transforms into a tilted plane. DoF limit planes transform into tilted planes.

    Who mentioned the 'focussing distance to the edge of the field'? I am simply pointing out a massive apparent error in your understanding.

    With regard to your easy 'proof' - the DoF with a 150mm lens focussed at 22m, even assuming a maximum aperture of f/5.6, will be so great that I cannot see any possibility of verifying field curvature in the way you describe - perhaps with some sophisticated instrumentation, but with what I have - no way, not even if I focussed a lot closer, unless you are claiming an extreme level of curvature. In that case, I return to what I said before - generations of photographers have been getting flat planes of sharp focus and nothing has changed.

    Perhaps you could be more specific about the measurements you took which you think prove curvature.
     
  102. pete wrote:\
    "If you consider the lens panel and the plane of focus to stay vertical, and the filmplane to be tilted, then you can more readily see that the conventional conjugate focii formula of 1/f = 1/v + 1/u holds true for every point on the film surface. If you compute many of those points (not just two, Andrey) you can see that a tilted plane of focus is not linear across the film, and nor is the DoF"<p>

    Again, your calculation is wrong: if you do it right, a plane's image
    must be plane.
     
  103. Jorge.....but if you ask me forget Merklinger's and buy the little Rodenstock gizmo....and save yourself a big headache.

    My posts above explain why this would not simplify anything. In both methods, it's required you estimate the size, distance or reproduction ratio of the object (s) in the scene. Therefore the same guessing is required in both methods to acheive accurate tilt angle.. And as I mentioned, but have not tested, I am confident the Rodesntock calculator is geared for close up photography vs. Merklingers methodology. Mr. Bigler explains this well in the pdf file he has offered to send above.
     
  104. Bill, I don't know if you have used the Rodenstock calculator, but I beleive is a lot easier than Merklinger's method. With the calculator you measure distances on the ground glass. Granted you still have to guess angles, but with an inclinometer this is a simple task.
     
  105. Thanks all for pouring their intellect and experience in their responses to my question! I didn't know it would generate so much emotions as well. This thread will surely take me some time to digest and absorb--considering all the math I've to grind through. Thank you!
     
  106. Bill wrote:"I am confident the Rodesntock calculator is geared for close up photography vs. Merklingers methodology...."
    You are confident, but you haven't tried it .You said the same thing about the Sinar P as well. So you are confident, but really much trust can we place in your 'confidence since you aren't in full possesion of the facts?
     
  107. Ellis, I agree, hence my reservations about not knowing for sure. Someone would have to run an example through both the Rodenstock calc. and Merklinger, and see how the results compare. I am willing to try off list if you are...then we can report back. I am very curious myself how close these two would yield in both close up, and landscape scenes? Let me know.... if your interested, this is how we can know for sure! It sure would be very helpful information for the list.
     
  108. Bill, you are on, why dont you set the parameters and we will work them out and see how the results compare. Have wheel will travel :))
     
  109. Now boys, the only thing that counts will be actuall images on
    film scanned at extremely high resolution. Both Bill and Jorge
    will have to be observed in action by an independent judge. All
    the users ofthe non merklinger methods have to do is make
    images that aew as sharp as the Merklinger method produces.
     
  110. Pete is correct; the DOF are curves and not straight lines
     
  111. Opps! I got straight lines; but they diverge not from the hinge point!..They intersect one focal length away from the lens (towards the subject); and this point lies on the subject focus line;about 2/3 ways towards the focus point................I used the 1946 Kodak databooks DOF equations; might be approximations so must check further and get out my Optical engineering handbooks...........Maybe tommorrow or later I will post a graphical diagram
     
  112. OK. I think this photo of mine clears up my confusion over 'curved' inclined planes.
    [​IMG]
    I was thinking too much about the image space on film, and not about the real 3D object that gives rise to it on the other side of the lens.
    If we describe an inclined line by its distance from the lens, and its height in the real world, as opposed to its image height on film, then we need to multiply its image height at each 'image sample' (delta h) by the optical magnification at that point/distance, in order to arrive at its real height in the object plane. I THINK if I apply that correction to the computed image height on film, then all should come good, and we have a perspectively correct rendering of an inclined plane on film, together with a straight real plane in front of the camera.
    Back to the spreadsheet to plug some more formulae in!
    I'm still not entirely convinced, since the plane of best focus that I was seeing in the actual camera appeared not to quite pass through points that I could clearly see were in a direct line with each other. Hmmm.
    HOWEVER.... this still doesn't alter the curved depth-of-field limits, which were computed on the assumption of a straight and flat plane of best focus in the object field anyway.
    If we believe the curves given by the standard DoF formulae, and I think we should, since they're based on over 300 years worth of optical theory and investigation, then the departure from the simplistic view of a flat sided wedge can definitely be put to some practical use.
    Here are two graphs of the DoF with a 150mm lens at f/8:
    [​IMG][​IMG]
    You can see that they don't differ drastically from the simplified 'wedge' view of depth of field. The wide aperture of f/8 means that this is pretty much what we see on the GG when we set up the tilt.
    But now look what happens when the lens is closed down to f/22:
    [​IMG][​IMG]
    Surprisingly, the 'vertical' component of near DoF rears up in the air as the lens is stopped down, when the plane is steeply tilted. Now this could be a VERY useful thing to know. Also notice that the depth 'below' the plane is much shallower than the imagined symmetrical 'wedge' given by conventional rule-of-thumb methods of visualising DoF.
    Incidentally: For generating those graphs, I used a MUCH stricter circle of confusion (0.07 mm) than the normally accepted one for 5x4 film.
    There's one point I do agree with Merklinger on, and that's that most DoF tables and calculations are far too sloppy.
     
  113. Pete,

    Probably a daft question, but could you explain the difference between the graphs you have shown above? For example, in the first set, both are described the same (Depth of field with a tilted image plane, f=150mm, N=f/8), but show very different curves, and I just don't understand why.

    Thanks
     
  114. David: It's not a daft question. I should have taken the time to label the graphs differently.<br>The difference is that the tilt angle of the plane of focus is changed, along with the distance axis to accomodate the shallower angle.<br>In the second set of graphs, the aperture has been stopped down to f/22.<p>The formulae used to calculate DoF were the same in all cases, and if you notice the grey lines, they show the DoF about a point on the plane of focus 7.5 metres from the camera. The distances from this point to the nearest and furthest points of acceptable focus are also shown.<br>You can see that in both the f/8 graphs the near limit of DoF is 6.3 metres, and the far limit is 9.2 metres. This extends to 5 and 15 metres, respectively, when the lens is stopped down to f/22.<br>You can verify these figures against a straightforward DoF table, provided the CoC is set to 0.07 mm.
     
  115. Daniel, I'll take the "Linhof Technikardan TK45S, mint, never used" but you can keep the calculator. I would however be interested in the wooden blocks and would trade my copy of Merklinger for them.
     
  116. Is Merklinger's book available in braille?
     
  117. Look at the glass grasshopper. Look at the glass. It doesn't lie.
     
  118. I dont know if it is available in Braille, but I hear they are comming out with an audio version! :))
     
  119. The glass may not lie, but it certainly gets pretty dim when the lens is stopped down to a working aperture!
     
  120. A little thought exercise for you.

    Imagine if you will, a world of fixed geometry cameras, where the special case of perpendicular optical properties are the norm. Let’s call this place “The Land Of The Little Cameras”.

    In this land, we can focus on an object at f22 and measure the distance of the far limit of focus (measuring only this for the sake of simplicity). We would get the following table:

    Object Dist._____________Far Focus Limit

    (inches)________________(inches)

    24______________________24.7

    48______________________51.9

    96______________________115.2

    192_____________________295

    384_____________________1343.3

    768_____________________Inf.

    As you can see, doubling the object distance more than doubles the far focus limit - the relationship is non-linear. In other words, a graph with the vertical axis being the object distance and the horizontal axis being far focus limit distance will produce a curved line for the far focus limit.

    Now drag yourself kicking and screaming back into the “Land Of The Large Films” (ie reality) and picture a real image where you are able to have fine focus on objects at all of those distances in a single plane (“IMPOSSIBLE!” I hear the Lilliputians cry). At the top of the image on your ground glass (where the object is only 24” from the lens), the far focus limit is only 0.7” further away. Another part of the image two thirds of the way down your GG (which represents an object 192” away) has the far limit of focus 103” further away from the lens. This model holds for all of the object distances in your photo, and is just as non-linear as in the “Land Of The Little Cameras”. Now the vertical axis of the graph has been rotated clockwise, the curve representing far focus limit is also rotated, and it is now possible to have objects both near and far within the limit of far focus without including the middle ground. The same thought exercise can be carried out for the near focus limit.

    The graphs that Pete Andrews displayed are correct (linear PSF & curved DOF lines), and can be verified empirically by finding a very flat subject (eg. a long flat road), focusing on a close object at f22 and tilting the front forward until the distant parts of the scene are in fine focus also (but no further). The middle ground will be out of focus, proving Pete correct (don’t try this at home if you only have a Minox, are a Lilliputian, or both).

    Regards,

    Graeme
     
  121. "Is Merklinger's book available in braille?"

    By necesity, it was written in braille.
     
  122. No, Pete's graphs are not correct - the DoF calculations for rigid body cameras have no relevance to the situation we have when the film plane and the lens plane are not parallel. They would be correct for objects lying on the lens axis, but nowhere else.
    <br><br>
    The attached diagram shows why. I'm afraid it is a bit rough and ready, but it illustrates the point nevertheless. It is meant to show the change in the DoF situation for an off-axis point source when you apply a rear swing/tilt and refocus to keep that source in the psf.
    <br><br>
    The conventional formulae for DoF assume that the lens and film plane are parallel, and cannot be applied without extensive modification to the swing/tilt situation. If you move that point source out to the indicated DoF limit its CoC is very different, simply because the film plane is no longer where those formulae assume it to be.
    <br><br><br>
    <img src="http://www.huwevans.plus.com/CoCDiagram.gif">
     
  123. No Huw. You cannot look at two offset axes like that. The near and far limits of DoF must be in line with the point of principal focus and the lens node for any DoF calculation to be relevent.
    All your diagram shows is that there is a change of focus at different points on the film plane when the lens or film plane is tilted. This is no revelation at all! It's the very reason WHY we tilt the focal plane in the first place.
    Calculate what happens to the near and far limits of focus when they're on the same axis as the point of focus, and you'll see that they don't change in the slightest with a tilted plane, (apart, that is, from the CoC, and every other image point, becoming oblique, instead of absolutely circular)
    You HAVE to consider each and every point on the film plane as having its own individual conjugate focii, and corresponding depth-of-field.
     
  124. I'm with Pete. I.e. that the film plane in image space defines a plane of focus in object space, but the DOF limits are curved surfaces. The Gaussian lens equation maps a plane in image space to a plane in object space. This is why Schiempflug works at all, and is true even with 'thick' lenses if you measure from the nodal points. This debate therefore reduces to the question of whether the loci of the depth of field limits in image space forms a plane. If they do, there will be planar DOF surfaces in object space. If they don't, there won't. My mucking about with paper, pencil and geometrical formulea says the surfaces are planar only if the tilt angle is zero - i.e. if the lens plane and film plane are parallel. The diagram shows what I think is the only natural extension of the conventional DOF derivation. Object A is focussed to position a in image space, B to b, C to c. The DOF is determined by the cross section made by the film through the bundle of rays coming from the exit pupil and (ignoring aberrations) meeting at a point on the film. For a circular aperture this cross section is elliptical and is largest in the radial, or saggital, direction. It therefore makes sense to define the the major axis of this ellipse as the limit of 'acceptable' blurring. In line with the conventional derivation, the film is conceptually moved backwards, keeping it in the same orientation, until the major axis of the ellipse is equal to our acceptable blur. This new position defines the points a', b' and c' which are the near DOF limits in image space. The question then becomes whether they lie on a plane or not. They don't. They lie on a curved surface *unless* the tilt angle is zero. The same is true if you move the film forwards to find the far DOF limits. There is one little practical problem, which is defining the position of the ellipse. The natural point to pick would be where the ray coming from the centre of the lens (or, in thick lenses, the rear nodal point) passes through the ellipse. That is what I have done here. Other options would be the "centre of gravity" of the ray bundle, or geometric entities such as the true centre of the ellipse. Unfortunately, both of these move as you stop down, which is why the ray from the nodal point is preferred. In any case, they don't lie on a planar surface either. As always, I am happy to be proved wrong, and ready to eat humble pie. Personally, I think this whole debate rests on just how much curvature those surfaces have. Merklinger's method is a (relatively) simple one that constructs two planes which are reasonably good approximations to the curves. I think it's a useful aim, particularly if you want three objects to be in focus and have to find and use a focus plane that passes through none of them. However, just as linear time/temperature formulea for cooking turkeys only work over a limited range of turkey weights, Merklinger's formulea has hidden gotchas. The bending of the far DOF plane if you try to lay it along the ground is one, stopping down more than you need to get tall trees in the middle distance in focus is another. Worst of all, his method involves far more calculation than I would ever like to do in the field, and for me at least is simply impractical. That said, if it works for you, go for it. In my idle moments I dream of a motorised LF camera, based around an adjustable space frame like those used to support flight simulators. You point to the ground glass (or an image relayed to your Palm Pilot) and say "I want this, this, and this to be in focus" and a few whirrs and beeps later, Bob's your uncle.
    003TQq-8676684.jpg
     
  125. I think this will be of interest to all who use Merkingler and the Rodenstock calculator. Bill G and I did an experiment and came out with greatly different response, his response for tilt was 3.1 mine was 9.0 degrees. Bill made a very nice diagram and I hope he posts it here so more people can work on this. I would post it but I dont have his permission to do so!
     
  126. And what did the film look like? That proof is the only "proof" as to
    which proves anything.
     
  127. amen ellis,


    somebody give the nerds a dektol atom to split! quick! it'll keep 'em busy and me from having to read another thread like this'n.

    thanks in advance,

    3rd
     
  128. Somebody forced you to read it, Triblett?

    Anyway, a last word from me. I've finally had a good look at the Rodenstock DoF calculator, and I was interested to note that like Merklinger, Martin Tai, and me, Rodenstock also, it seems, cannot cope with basic optical theory and elementary mathematical manipulation. Makes you wonder how they ever managed to produce all those lovely Apo Sironars and Grandagons.

    There's a vague notion lurking in the back of my mind - something about morons standing on the shoulders of dwarves, but I can't quite get it into focus. If only I'd known that 'the 'vertical' component of near DoF rears up in the air as the lens is stopped down, when the plane is steeply tilted.'

    Anyway, that brings me to my final word on the subject, which is to suggest, Pete, that you go back to the word 'surprisingly' in your post of July 9th, 05:42am, and work from there. You seem not to have heard the cacophany of alarm bells that should have started ringing in your head at that point at least, if not long, long before.
     
  129. huwie,

    i went to yer webpage. too bad there's not a differential equation for good composition huh?

    love,

    tribby
     
  130. Just in case anyone with a serious interest in this is still reading,
    it's worth reiterating that the proper question isn't whether Pete is
    right, but whether he's relevant. I think he is, but others obviously
    feel differently.

    If you can follow math - and want to - Bob Wheeler's notes on
    view camera geometry are much, much clearer than
    Merklinger's. They also conform to accepted optical theory -
    Merklinger, remember, is the man who thinks it's 'useful' to think
    in terms of a lens' focal length changing when tilted. Wheeler
    also steers clear of neoligisms. Björn gave the link above, but
    for those of you reading this via email, here it is in longhand:

    http://www.bobwheeler.com/photo/ViewCam.pdf

    In these notes he explicitly considers the variation in the size of
    the ellipse of confusion across the image field (see p. 34 and
    thereafter). He is of the opinion that the variation is irrelevant, but
    at least he admits it happens.

    Huw, when you come down from your Newtonian Hauteur you
    will perhaps remember that science advances by argument, and
    not arrogance and insults. Newton himself had a knack of
    revealing the faults in his opponant's arguments with undeniable
    logic and elegant proof. Repeatedly re-quoting the authority
    being questioned comes a very poor second.

    And in any case, I prefer "person of restricted growth".

    Pete, a tidbit: the sine-not-tan thing goes back to Abbe himself. I
    have various pre-Scheimflug textbooks here, one of which (pub.
    1880s) refers to an extensive historical trawl done by some
    diligent german professor (or, more likely, his student) that
    showed Abbe to be implicitly using assumptions that are not
    strictly necessary. Most people blindly followed the master,
    when it was 'obvious' that a tan was needed if you just looked at
    the diagrams. In the paraxial limit, x = sin(x) = tan(x) and all is
    well. Until the next time I need a leg up......
     
  131. Simple Depth of Field formula for view camera



    The depth of field of view camera has a simple relationship with
    the hypofocal distance: the slope of far/near limiting plane are
    simple multiple of the slope of the incline plane:

    If PSF_slope is the slope of an incline plane vs optical axis of lens

    PSF near limit plane slope: PSFn_slope = psf_slope*(1+D/H)

    PSF far limit plane : PSFf_ slope = psf_slope*(1-D/H)
    where D = "object distance" for a point seen in the center of gg



    Example 1 : In the above diagram, psf_slope =0.2( 11.31 degree)
    object distance ~~ 5.1 meter.
    D=5100 is the 'object distance'
    Lens focal length = 100
    coc = f/1500 = 0.06667 mm
    fstop = f/22
    H = f*f/(fstop*coc) = f*1500/22= 6817 mm

    The near and far DOF limits for f/22 are:
    PSFnl_slope = psf_slope * (1+D/H) = 0.2 * (1 +5100/6817) = 0.3466 ( 19.1 degree vs optical axis )

    PSFfl_slope = psf_slope * (1-D/H) = 0.2 * (1 -5100/6817) = 0.0504 ( 2.9 degree vs optical axis )

    The near/ far DOF limit planes are about 8 degrees above/below the PSF


    Stop down the lens, increases the depth of field.
    The near and far DOF limits for f/322 are:
    PSFnl_slope = psf_slope * (1+D/H) = 0.2 * (1 +5100/6817) = 0.417 ( 22.6 degree vs optical axis )

    PSFfl_slope = psf_slope * (1-D/H) = 0.2 * (1 -5100/6817) = -.018 ( -1 degree vs optical axis )


    The near/ far DOF limit planes are about 11 degrees above/below the PSF


    (Note: slope = dy/dx = tangent ( gamma), where gamma is the
    angle bewteen len's optical axis and a line.)
     
  132. Martin,

    Thanks for posting the maths here: that is exactly what I needed to prove that the DoF limits are curved when the psf is inclined. Using your formula and changing nothing but the distance to the object, you will notice that the slopes change as the object distance changes.

    For instance, you wrote:

    The near and far DOF limits for f/22 are:

    PSFnl_slope = psf_slope * (1+D/H) = 0.2 * (1 +5100/6817) = 0.3466 ( 19.1 degree vs optical axis )


    PSFfl_slope = psf_slope * (1-D/H) = 0.2 * (1 -5100/6817) = 0.0504 ( 2.9 degree vs optical axis )


    Where 5100 is the distance to the object.


    Substituting 2550 (ie 2.55 metres to the object) gives:

    The near and far DOF limits for f/22 are:


    PSFnl_slope = psf_slope * (1+D/H) = 0.2 * (1 +2550/6817) = 0.2748 ( 15.95 degrees vs optical axis )


    PSFfl_slope = psf_slope * (1-D/H) = 0.2 * (1 -2550/6817) = 0.1252 ( 7.19 degrees vs optical axis )



    Substituting 10200 (ie 10.2 metres to the object) gives:

    The near and far DOF limits for f/22 are:

    PSFnl_slope = psf_slope * (1+D/H) = 0.2 * (1 +10200/6817) = 0.4993 (29.95 degrees vs optical axis )


    PSFfl_slope = psf_slope * (1-D/H) = 0.2 * (1 -10200/6817) = -0.0993 (-5.70 degrees vs optical axis )


    All factors except distance to the object are kept constant. Thus, the limits to depth of field for an inclined psf with a constant f stop have a variable slope (ie. they're curved)

    Thanks for clearing that up Martin.

    Regards,

    Graeme
     
  133. Struan wrote:
    "They don't. They lie on a curved surface *unless* the tilt angle is zero.The same is true if you move the film forwards to find the far DOF limits."

    <p> You forgot one main point: only when the film plane is move forward or backward parallel, regardless of whether the lens is tilted
    or not, the minor axis of all the ellipses are identical, and equal
    to diamter of circle of confusion.
    <P> Now you suggest curved up loci surface such that the major axis
    are of of ellipses are identical -- the end result: minor axis of the ellipse become no indentical
    <p> By curving up, nothing is gained, ellipse is still ellipse.

    <p> Further the difference in major axis of ellipses is not that much.
    <p> Of the two axis of ellipse, the natural choice is the minor axis
    not the major axis, as it it the only invariant quantity vs tilt and
    possition on FP.
    <p>
     
  134. Graeme,
    <p>
    D is not the distance to any point on PSF <p>
    D is the distance from lens center to the intersection of
    optical axis with PSF. (the distance of such object which
    is at the centre of gg ) There is only one D for a PSF
     
  135. Martin,

    How then do you measure the distance to another object and calculate the slope of the DoF limit at that point? What happens when I employ rear rise or fall? The centre of the gg is a movable point which has no bearing on the object distance. When I keep all other factors constant and raise the gg, the centre of the gg now shows a point closer to the camera, but the psf has not moved, and the scene is still just as focused as it was before the movement. The DoF for the point in the centre of the GG is now less than it was before, but can still be calculated by your formula and remains exactly as before. Of course, lowering the rear standard has the opposite effect, but the scene also remains focused.

    "D" is simply the distance to any object in the scene. The D you refer to (ie. the one at the centre of the optical axis of the lens) only holds true for one case: the case you refer to as a "box" camera. Whenever the front standard is shifted, raised, tilted or swung, the centre of the optical axis moves acordingly and can only be made the centre of the GG by employing shifts and raises of the standards to match (rarely done in my experience, since the shifts and raises are used to avoid converging lines).

    Please consider your response carefully, and think about what I have said in my previous post and this one.

    Regards,

    Graeme
     
  136. Martin,

    Here is your diagram again with some of the more important parts put on it.

    Remember, D is the only variable in your equations when considering the DoF for any point on the PSF. D is not a constant as you contend, because the optical axis of the lens is not neccessarily (and not usually) aligned with the centre of the GG on a view camera. We are free to move the GG in any direction on the plane.

    Regards,
    Graeme
     
  137. Graeme,

    You are right, the optical axis of a lens does not necessarily
    correspond to center of gg, particularly when there is parallel shift
    involve. (When the tilt angle is small, and with no shifts, rise, fall
    then it is about at the center )
    For definition of D, please go to my complete article, there are
    detail diagram explaining the conditions.
     
  138. Shape and orientation of ellipse of confusion

    • The ellipse of confusion is smaller in the vertical dimension, (like an egg lying on side)
    • The ellipse of confusion has identical horizontal dimension across FP, and = diameter of circle of confusion
    • The vertical dimension of ellipse of confusion changes along vertical direction on FP
    • When lens is forward tilted, the vertical dimension of ellispe of confusion on top edge of FP is slightly larger than that at bottom
    • No dimension of ellipse of confusion > diameter of circle of confusion
    • Using diameter of circle of confusion as reference for DOF, provides conservative results, guarantee the zone between the dof planar boundaries will be sharp, i.e, = or < coc
     
  139. Graeme wrote:"How then do you measure the distance to another object "

    <p> apparently the gg method does not work, because of free movements
    of the back.
    <p> I think the most accurate method in measuring D is using a rangefinder which is
    mounted rigidly on the lens board, when the lens tilted, that rangefinder also moves, and its sight is parallel to the optical axis,
    the reading from the RF provides the accurate reading of D, which is
    the intersection of optical axis with psf.
    <p> How to measure slope ?
    <p> Using an angle measure device, measure the angle between PSF vs
    optical axis, gives the angle, the tangent of that angle is the slope
    <p> Alternatively, measure the angle between lensboard vs pSF,
    calculae the cotangent of the angle yields same result
     
  140. Graeme,
    The 'D' in my formula is not the same D in your diagram.
    See attached WhatisD
     
  141. OK Martin,

    It appears that your detailed maths relies heavily on the condition attached to the thin lens equation that the object distance D is measured along the optical axis of the lens. To prove you wrong I must show that the slope of the limit of DoF varies when the object distance is any other distance: no mean feat given my lack of mathematical prowess. Gaussian lens equations are called for, so I'll have to work with them for a little while and get back to you.

    I believe that what I will find is that the equations you have used are a close approximation of the general equations, and that PSF(n/f)l_slope = psf_slope * (1±D/H) will still hold true (approximately) for all object distances, thereby producing curved DoF limits.

    Regards,

    Graeme
     
  142. The following information is found on the web site http://scienceworld.wolfram.com/physics/ThinLensFormula.html and is a direct copy of that site but without the pretty formula writing:

    The paraxial approximation is an approximation to the full equations of optics that is valid in the limit of small angles from the optical axis. In the attached figure (Schroeder 1999, p. 6, Fig. 2.1), primes represent image angles and distances, and unprimed represent the object, with n the index of refraction to the left of the y-axis and the index of refraction to the right of the y-axis. The paraxial approximation then assumes that

    Sin T ~= T (1)

    Cos T ~= 1 (2)

    Tan T ~= T (3)

    Where T is any of i, i’, u, u’ or theta. This regime is known as first-order, paraxial, or Gaussian Optics.

    If the paraxial approximation is valid, it follows from the diagram that

    theta ~= tan theta = y/(R-d) ~= y/R (4)

    For d << R and

    u ~=tanu = y/s (5)

    u’ ~= tanu’ = y/s’ (6)

    (end of information on the scienceworld web site)

    This means that the thin lens equation is a good approximation when the angle of deviation from the optical axis is small.

    In the example offered by Martin and interpolated by myself, where the object distances “D” are 2.55, 5.1 and 10.2 metres, the thin lens equation holds true for at least the 10.2 metre distance after the following calculation is carried out:

    alpha =atan (10) – atan (5)

    = 84.29’ – 78.69’

    = 5.60’

    Where alpha is the angle of deviation from the optical axis when the object distance is 10 metres and the lens is aimed at an object in the psf 5 metres from the camera.

    The same formula gives an angle of deviation of 16.1’ for an object distance of 2.55m (this deviation may be too much for the paraxial approximation to hold true, so I will not use the 2.55m distance to attempt my proof – I only need to prove the curves do vary with an object distance different to Martin’s “D”).

    In the same example, and given a distance to the object of 30m, the angle of deviation from the optical axis is only 9.4’, still within the limits of the thin lens equation’s validity

    Since the angle of deviation from the optic axis is small for normal distances in a typical scene, the thin lens equation is a good approximation and is valid in Martin’s work. Thus, we CAN substitute normal distances into the formulae for calculating limits to DoF, and my earlier post proving that the limits to DoF are curved is valid.

    The following table arises from the example being used.

    Object Distance___PSFnl_slope______PSFfl_slope

    5_____________19.1’________________2.9’

    10____________29.95’_______________-5.7’

    30____________47.67________________-34.9’

    It can be clearly seen that the limits to depth of field vary with object distance and are indeed curved.

    Graeme
     
  143. Graeme, From you version of dof limits, they are indeed curved. Calculate the image of those dof limits. you will see that the conjugate images of your dof limits are themselves curves to start with.
    Of course, curve begets curve. That is where your problem lies
    Fuzziness in image is caused by focusing error, i.e, the lens extension is either less or more than what it should be.
    DOF calculation must met two conditions
    • Condition 1 Error in lens extension must be constant along FP, in 35mm MF or LF. Because that is why focusing error begins with in the first place.
    • Condition 2: blur image
    • Fuzziness caused by focusing error can be physically remedied, by racking the fp parallelly
      DOF limits are only meaningful, when you can turn you lens helix or rack the film back slight to bring every points on the near limit or far limits sharply focused.
      Merkliger's and my derivation both met these two conditions
      Graeme, peter and others based their calculation only on condition 2, forgot completely condition 1
      Graeme, peter et all, there is no ways you guys can moved your film plane in any way or anything at all to bring the so call "curved dof limits" sharply focused on FP. These curved dof limits, does not corresponds to any practical operation.
      To make the "curved dof limits work" you guys need curved film
     
  144. Martin,
    You're starting to lose me here. Can you explain a couple things a little more clearly:

    "Calculate the image of those dof limits". The limits to depth of field are intellectual constructs which don't actually exist in the scene. How can one form an image of them, or "calculate" an image?

    "Fuzziness in image is caused by focusing error, i.e, the lens extension is either less or more than what it should be. " My understanding of the view camera is that changing the geometry of the film plane relative to the optical axis of the lens effectively allows "focusing error" to be removed, by giving more extension to lens/film distance in the parts of the scene closer to the camera, and less extension for the parts of the scene further from the camera. Your next statement ("Condition 1 Error in lens extension must be constant along FP, in 35mm MF or LF. Because that is why focusing error begins with in the first place") does not hold for a camera with movements, because lens extension is definitely NOT constant when tilts/swings are employed. "Graeme, peter and others based their calculation only on condition 2, forgot completely condition 1". Condition 1 does not hold for our cameras, and should be forgotten.

    "Condition 2: blur image <= circle of confusion
    Fuzziness caused by focusing error can be physically remedied, by racking the fp parallelly". I'm not sure what blur image is, so I'll leave that alone, but the second part of this statement is only partially correct. The fuzziness can also be remedied by tilting or swinging. Again, bringing part of the film closer to the lens will allow further parts of the scene to be focused, and moving part of film further from the lens will allow closer objects to be rendered in sharp focus.

    Racking the film/lens forward and back changes the distance and orientation of the plane of focus. It doesn't allow any more of the image to be focused, it just lets you see where the limit is at that point in the image. In effect, racking the lens/film while you watch focus change moves the psf into line with the part of the scene on which you are concentrating (and correspondingly alters where the dof limit is). It doesn't allow you to assess where the new dof limit is once you've adjusted the focus

    "Graeme, peter et all, there is no ways you guys can moved your film plane in any way or anything at all to bring the so call "curved dof limits" sharply focused on FP. These curved dof limits, does not corresponds to any practical operation." Why would we want to bring the dof limits into focus? The subject should be contained within those limits if we want it to be sharp focus. If the subject extends beyond those limits we get a fuzzy picture. The "practical operation" is that those limits are not linear, so we (and you can also if you want to...)take advantage of the curved nature of the limits by having very tall objects in the distance apparently sharp.

    Curved film would only be useful if the Plane of Sharp focus was in fact curved. I don't think it is, and have never said anything to that effect.

    Regards,
    Graeme
     
  145. graeme wrote:
    "Calculate the image of those dof limits". The limits to depth of field are intellectual constructs which don't actually exist in the scene. How can one form an image of them, or "calculate" an image? "
    <p>
    Why not ?<p> It is easy.
    Given a far limit or near limit, you can always calculate the
    corresponding image points by <p>

    image of far limit = 1/(1/focal length - 1/distance of far limit)<p>
    same with near limit.<p>

    <p>The biggest difference between curved dof limits and
    planar dof limits is
    <ul>
    <li>your curved dof is constructs which don't actually exist in the scene.
    <li> Planar dof limits are actual reality, not only can be calculated
    but also experimentall tested:
    <p> In my case, I can hang three slanted straight wires, with xmas light
    bulbs, such that the center wire represent the psf, the top xmas light wire represent the near limit, the other represent the far limit. (The three wires are tied together at the Hinge point ) After set up view camera to sharply focus on the psf xmas
    light wire; without changing lens lit, I can rack the film back back
    very slight and bring the whole "near limit" xmas light wire into
    sharp focus on gg, every bulbs of them--- ie. the planar dof
    limits are not just mathematical compution, they can physically
    be check out. It is the real thing.
    <p> Now hang three xmas bulb wires, one slanted straight xmas bulb wire that is your psf, and two cureved xmas bulb wires as your far
    limit and near limit. You can set up your view camera to focus sharply
    on the psf,, then what ? There is no way you can ever focus all light bulbs on the curved wires on the film.
    <\ul>
    <p>
    Or you have other method to experimentally test out your "curved dof theory" ? I want to know how
     
  146. Martin,

    The equation "Image of far limit = 1/(1/focal length - 1/distance of far limit)" is valid only for the plane of sharp focus. That equation is the thin lens equation describing an image in focus ("image of object= 1/(1/focal length - 1/distance of object) ). It does not take into account aperture size or elipses of confusion, and so does not describe an "image on the DoF limit", or even where it is.

    To form an image at the edge of the DoF, simply rack your lens/film to suit until a point on it becomes focused, and (hey presto!) you now find a plane in sharp focus which goes through that point (one of your lines of christmas lights, for instance). Now, where is the DoF limit for this new psf? After all, what you're doing here is re-aligning the PSF, not defining the DoF limit. Yes, what you see is planar, because all you are seeing is a new PSF.

    Your example of the christmas lights on three lines joined at the hinge point describes exactly my point here. By racking the film back, you are realigning the PSF so that it matches the plane of the nearer line of lights. Of course it is planar - that line of lights is NOW the Plane Of Sharp Focus. You are not examining the Depth of Field of the set up when it was focused on the middle wire. You've only proven that Scheimflung works. If that experiment really did test DoF, you could have an infinite DoF by simply continuing to rack the film back and forward until you saw any part in focus that you choose.

    Now for my experimental proof (I've performed this and it does work):

    Find a long planar subject (a road, edge of building, salt lake, field of grass - you get the picture) and set up your camera on a high view point (top of car, roof top etc) so that the psf enters the subject (eg, if using a horizontal subject, the psf must be falling away from you). The best way to do this is to focus finely on the planar feature at your largest aperture, use the tilt to align PSF with the feature, then tip the whole camera forward ~15'. The next step is to slowly reduce your aperture size until the distant objects come into acceptable focus. Stop there, and you will be able to see that the middle ground is less focused than either the fore or background. This demonstrates that the near DoF limit is curved, because the middle ground of the image is outside the DoF limit but the rest of the image is within the DoF limit.The diagram attached here shows what the experiment prooves. If the "curved DoF limits" theory is false, then the middle ground in the subject will come into acceptable focus at the same instant as the fore and background.

    This experiment is testing the actual DoF limits, not a re-aligned PSF with its associated re-alignment of DoF limits. There is no re-focusing of the image by altering the geometry of the camera, only changing the extents of DoF (PSF retains its position in space).

    Regarding the statement " Planar dof limits are actual reality, not only can be calculated but also experimentall tested" - We seem to have already established that limits to DoF are not planar, using the formula that you posted earlier, because D need not be a constant. The thin lens equation can't be substituted for the formula that calculates the limits to DoF.


    Regards,

    Graeme
     
  147. Another experiment, impractical though it is, would be to leave the camera focused on your middle xmas lights line and close the aperture gradually until the any of the lights on the other lines became focused, stopping there and checking the focus of all of the lights. I propose that the far lights on the near line will come into apparent focus first. It can't be done easily, because you would need two very long lines of lights. Don't change the focus of the camera by racking the lens or film plane, because that swings the PSF.

    Regards,

    Graeme
     
  148. Graeme wrote: "We seem to have already established that limits to DoF are not planar, using the formula that you posted earlier, because D need not be a constant. The thin lens equation can't be substituted for the formula that calculates the limits to DoF. "
    The formula that calculates the limits to DoF is only the son of thin lens equation under certain condition, it is not another independent law of physics.
    Indeed, when you rack the film back, it does extablish two new PSFs Don't forget, you must rack the film back only by small amount to simulate focusing error.
    These three positions of film back corresponding to the psfnear, psf and psffar are called
    depth of focus

    Depth of focus is inversely proportion to the fstop, larger depth of focus implies smaller fstop. It is not free
     
  149. Martin,

    You have not introduced anything new here or adequately rebutted my previous assertations.

    Why would one want to simulate focus error in an uncontrolled manner? How far is a small amount, and what would it prove anyway? If I went too far, what does it show? Racking the film back or forward does not aid in getting the SUBJECT in focus. It just moves the PSF from the subject.

    Yes, the formula for calculating the DoF limits is derived from the thin lens equation, but that does not mean that the thin lens equation is relavent for calculating the DoF - it ONLY tells you the position of the PSF, which is somewhere within the DoF. The thin lens equation is not dependant on f stop, whereas DoF is. The thin lens equation is a linear function (producing a linear solution), while the equation for DoF is a trigonometric equation, producing a non-linear solution. They are not interchangable.

    "Depth of focus is inversely proportion to the fstop, larger depth of focus implies smaller fstop. It is not free" - I assume there is more to come on this. I think that anybody who has read this far understands the basic concept of depth of field and its relationship to depth of focus.

    Would you like to comment on our proposed experiments? Have you worked out why your one only proves Scheimflung correct and has no bearing on DoF when you've focused on your middle line of lights?

    I am glad we are having discussion and examining the thought processes that it is bringing out.

    Regards,

    Graeme
     
  150. Depth of Focus

    Depth of focus is the conjugate counter part of depth of field.
    For a 100 mm lens at f/22, the depth of focus is 1.47mm.
    What depth of field truely means is that for such a lens at such fstop, the film back can tolerate a focusing error of +1.47mm to -1.47mm
    That is what depth of field is all about
    You cannot understand the meaning of depth of field without understand the concept of DEPTH OF FOCUS.
    They are twins.
     
  151. Yes Martin, you are 100% correct that depth of field and depth of focus are twins, and directly correlate. Therefore there is no reason to introduce depth of focus into this discussion, since all we have already discussed regarding DoF applies equally to depth of focus on a smaller (and inverted) scale.

    I am not going to be distracted by that response - it is just as obviously wrong as saying that depth of field of a 100mm lens @ f22 +/- 2 metres. Spot the difference.

    Any response yet to the questions previously posed regarding the experiments?

    Regards,

    Graeme
     
  152. <img src="http://www.photo.net/photodb/image-display?photo_id=897489&size=md"><p>
    Graeme<p>
    Depth of focus is the image of depth of field<p>
    Where is your depth of focus for your curved depth of field ?
     
  153. I am sorry Martin. Your previous post said that depth of field and depth of focus were conjugates, with which I fully agree. Would you like to re-draw your diagram to show that the depth of focus is wedge shaped just as you've drawn the depth of field? I'm sure you'll agree that the only case where depth of focus is parallel to film plane is for your "box" camera.

    I'll also draw my version (with the curved depth of field and focus lines), though it'll probably be hand drawn.

    Any thoughts yet on our experiments?

    Regards,

    Graeme
     
  154. Graeme,
    The depth of focus in LF is parallel to FP, not wedge shape.<p>
    Parallel depth of focus correlates exactly to wedge shape depth of field
    as a consequence of Scheimpflug 1st and 2nd rules<p>
    <img src="http://www.trenholm.org/hmmerk/MicroMov.gif">
    <p>
    The depth of focus range is not as dramatic as Merklinger's diagram<p>
    For 100mm lens and f22, the back movement is only allow to err from +1.47mm to -1.47mm, and you get a wedge shape dof <p>
    If instead, you use f64, then the fp can tolerate a error of 4.26mm
    to -4.26mm, and you get a much wider dof wedge.
    <p>
     
  155. Here's my version of the depth of focus diagram.

    Martin, I notice that you have again proven with your diagram that Scheimflug does indeed work. By moving your film plane backwards and forwards, you've again rotated your PSF. I can use your diagram to theoretically get much more depth of field, just by moving the film plane more. Just like before, you still have not shown the depth of field at any of those new planes of sharp focus.

    "The depth of focus in LF is parallel to FP, not wedge shape." I've yet to go back over all the previous posts, but wasn't it you who previously stated that LF optics are not a special case? I may be wrong by crediting that to you, but the fact remains that for a thin lens, the optics are symmetrical about the lens plane. After all, you did say that there is a conjugate relationship between the depth of focus and depth of field. If you think that the depth of field is wedge shaped (rightly or wrongly) then you MUST also believe that the depth of focus is wedge shaped. Remember? You said they are twins!

    Regards,

    Graeme
     
  156. Martin,

    To get anywhere in this discussion, you've got to stop fiddling with the film plane/lens distance (focus length). If you were trying to demonstrate the depth of field in a 35mm camera, you would not touch the focusing adjustment - you would adjust the aperture only until all of the subject was in (or out of) focus. Changing the focus does not show where the depth of field limits are in any format. Why then, do you persist in adjusting the focus when trying to prove your point in LF? In LF, adjusting focus serves to confuse the matter, because when the optical axis is not perpendicular to the FP, the PSF rotates, as you keep demonstrating.

    Please try to think of a proof for your theories which does not involve focus adjustment (by which I mean racking the FP forwards or backwards). I already know that Scheimflug works for the PSF.

    Regards,

    Graeme
     
  157. Repost of my Depth of Field/Depth of Focus diagram (forgot the inverted clause of the optics....)
     
  158. Graeme wrote:"By moving your film plane backwards and forwards, you've again rotated your PSF. I can use your diagram to theoretically get much more depth of field, just by moving the film plane more. Just like before, you still have not shown the depth of field at any of those new planes of sharp focus.
    "<p> You are misunderstood.
    You cannot move your FP backward and forward without limit without lossing the
    orginal PSF you want-- it become unsharp isn't it ?<p>
    However, if you BY ERROR, move the FP only very little, then the
    original PSF will still be acceptable. <p>
    The attach EOC diagram shows how focus error and depth of focus is directly tie
    in with the dimension of ellipse of confusion (or circle of confusion)
    <p>The size of the EOC put a limit on how much you can err <p>
    The largest dimension of 100mm lens at f22 is only 0.067mm, you are
    not allow to move the film back very much, that is 1.47mm to -1.47mm! ONLY when you move the film no more than +1.47mm to -1.47mm, the image
    will still be acceptable-- because the new PSF is not far from the
    ORIGINAL psf, ONLY then, the dimension of ellipse of confusion will be <=0.067

    <p>
     
  159. Graeme, both of your depth of field diagram doen's look right
    show it be this ?
     
  160. Graeme,
    now, how do you relate your curved depth of field with ERRONOUS
    placement of film back ?

    <p>Depth of focus means the set boundaries within which the placement
    of film back is ALLOW TO ERR.

    <p> Within the boundaries ONLY ONE film position gives you exact pin sharp focus, the others are ERRORS. However, when the error is small enough you get a RANGE of PSFs which will form ACCEPTABE image. Those acceptably unsharp PSFs surround the orginal PSF like a wedge.

    <.
     
  161. Martin,

    Thanks for posting that curved DoF/ depth of focus image. I believe that the depth of focus part of the picture should actually be inverted, with the "mouth" of the depth of focus wedge pointing down (it is an image of the subject and so must be upside down).

    Back to your question of erronious film back placement: moving the film back only slightly rotates the PSF only slightly so that the subject still remains within the new DoF. Since it is still within the DoF, the subject is acceptably sharp. That's what depth of focus is: a range of distances within which a subject is rendered acceptably sharp. Moving the PSF such a small amount that the original subject is still apparently sharp doesn't prove a straight limit to the DoF.

    I don't believe there is such a beast as an "acceptably unsharp PSF" - it is contradictory to have an unsharp plane of sharp focus. What should be said is that EACH PSF has a zone (for want of a better word, since you want a wedge with straight lines and I want one with curved sides)where the EoCs are acceptably small.

    Regards,

    Graeme
     
  162. Martin,

    You state "You are misunderstood. You cannot move your FP backward and forward without limit without lossing the orginal PSF you want-- it become unsharp isn't it ?"

    Actually you can't move the film plane ANY distance without losing the original PSF. Of course it becomes unsharp if you go too far - the original PSF no longer lies within the new DoF. ANY movement of the FP also moves the DoF, and if you go far enough, your original subject falls outside the new DoF and gets fuzzy.

    Regards,
    Graeme
     
  163. Martin, This diagram (attached) shows the approximation to DoF which I believe you are using as the ACTUAL DoF. It shows that when small FP shifts are employed (thereby rotating the PSF) they act to approximate DoF at one point in the image (A or B). Provided the rotation of the PSF doesn't drag its DoF past the original subject PSF (at a or b), you will maintain an acceptably sharp image of the subject at that point. As an aside, the model predicts that rotating the PSF further (ie, the rotation excedes a' or b') will still produce acceptably sharp images further from the camera, because they will still be within the curved DoF at greater distances. So in summary, yes there is a wedge of PSFs whose DoFs will capture the acceptably sharp image of the original PSF. That wedge approximates DoF at a certain distance from the camera, but it is not the actual DoF of the orginal PSF. The actual DoF is a curve described by the formula: PSF(n/f)l_slope = atan(psf_slope * (1±D/H)) Regards, Graeme
    003WV6-8816484.jpg
     
  164. Graeme, I think we are a bit closer<p>
    However, whether I use analytical or simply used the classical
    box camera dof, adjusted for Y axis, I still come up with two
    STRAIGHT DOF boundaries.
    <p> There IS never such a thing as curved DOF in LF, somebody
    make a mistake in calculation and PLOTING ( such as uneven X axis
    on plot
    <P>
     
  165. Where do you put the fuzzy points

    Graeme, I think there are some key mistake people can make in applying classical DOF formular



    D * H
    near limit = ----------------
    (D+H)

    far limit = DH/(H-D)
    If used CORRECTLY, these two formular WILL give TWO STRAIGHT DOF lines surrounding the original PSF. There never is such a thing as curved dof.
    In the attach WHERE diagram, point A is on a slanted line where do you think the two fuzzy points (ie near and far limit) are ? Can you add the two points on the diagram and repost it here ?
    That is one place where people can make mistakes.
     
  166. Classical DOF Formular Map straight line into straight line

    The classic dof formular
    1/D1 = 1/D + 1/H ..............(1)
    1/D2 = 1/D - 1/H ..............(2)
    HAS EXACTLY THE SAME FORMAT AS lens equation
    1/u = 1/f + 1/v ............ (3)
    Lens equation (3) MAP A STRAIGHT LINE INTO STRAIGHT LINE
    So does DOF equations (1) AND (2).
    Equation 1 maps psf into near limit line psf_near
    Equation 2 maps psf into far limit line psf-far
    Somebody made serious mistake in using classical DOF formular they map straight line into curved lines !!!
    DOF equations (1) and (2) act line a LENS WITH focal length = H and -H
     
  167. Martin,

    We seem to have taken a few steps back here.

    Lets go back to your detailed maths on your web site (which I might add, is much more comprehensive than anything on the web by Merklinger, and why I keep referring to it. Your maths is good and detailed, whereas Merklinger hides many of the important formulae, saying things like "the algebra itself is a bit tedious, but the result itself is quite easy to understand." ["Depth of Field For Field Cameras - Part 1" Shutterbug Nov 1993] No scientist worthy of the title would hide the formulae used in calculating his/her tables). On your web site, you give another set of formulae for calculating the slope of the depth of field. Those formulae are:

    tan(nl_beta) = tan(beta)/(1+D/H)

    tan(fl_beta) = tan(beta)/(1-D/H)

    Where beta is the angle between the lens plane and the PSF or DoF limit, D is the Distance to the object from the lens and H relates to the hyperfocal distance of the lens/fstop combination.

    As the PSF beta approaches zero (i.e. the PSF becomes parallel to the film plane, see attached figure), the limits to DoF becomes linear (i.e. the rate of change of the curvature of DoF decreases) and DoF limit becomes parallel to the PSF. All of this results from the fact that points on the PSF are approximately the same distance from the lens, or put another way, D becomes a constant once focus is set. All objects on the PSF have the same D. This is how a "box" camera sees the world, because PSF beta is zero and film plane is parallel PSF.

    With a view camera, we are not limited to a PSF beta of zero. When PSF beta is some angle other than zero, D is not constant when focus has been set. All objects on the PSF have different values for D. Since D varies, the solution to the formulae vary and the slopes vary. Therefore, the slopes of the DoF limit are different for all values of D. I'll make my own sweeping statement here:

    All DoF limits are curved with the exception being the special case of PSF parallel to Film plane, where the curvature is zero

    Pete Andrews posted:

    Dn = fu(f + CN)/(f^2 + uCN) ; for the limit of near focus;

    Df = fu(f - CN)/(f^2 - uCN) ; for the limit of far focus;

    [f = focal length of lens; u = subject distance from forward node of lens; C = diameter of circle of confusion; and N = relative aperture number]

    To which you replied "the DOF formular are the recognized formula for box camera without lens movement."

    You are now quoting:

    near limit = DH/(H+D)

    far limit = DH/(H-D)

    as being the "classic DoF" formula.

    My information (based on the web site http://tangentsoft.net/fcalc/help/DoF.htm ) suggests that the actual formulae for calculating the near and far limits to DoF are:

    DoF_nl = hD/(h+D-f)

    DoF_fl = hD/(h-D-f)

    Where h=f^2/(fstop*circle of confusion), f is focal length of lens and D is distance to object.

    Before you again object that this refers only to a box camera, I'll explain why the formulae are relavent to all cameras. The distances DoF_nl and DoF_fl are measured perpendicularly to the PSF (see attached diagram), and is very much simplified in the case of a box camera, because D is a constant when focus is set. In a view camera with an inclined PSF, D is not constant, so the distances from the PSF to the DoF_nl and DoF_fl vary. Further, the limits vary in a non-linear manner (due to the f^2 portion of the formulae).

    Please explain what you mean by "CORRECT" use of the DoF formulae. If you mean making D a constant, it only can be applied "CORRECTLY" to a "box" camera.

    You ask me to indicate approximately the DoF limits in your diagram. I can't do that without more information. I need to know if we are talking about a view camera with movements or a camera without movements. With a view camera it is possible that the DoF limits never cross the plane you have drawn.

    The thin lens equation maps an object point to an image point. A straight line is made up of points which lie on a plane and a curved line is made up of points which lie on a curved surface. The thin lens equation will map a curved line to a curved line, a straight line to a straight line and a complicated object to a complicated image. I'll once again state that the thin lens equation does not substitute for the equations which describe depth of field.

    1/D+1/u=1/f IS NOT EQUIVALENT TO

    DoF_nl = hD/(h+D-f), DoF_fl = hD/(h-D-f)

    Where h=f^2/(fstop*circle of confusion), f is focal length of lens and D is distance to object.

    One is a quadratic equation, the other is not.

    Regards,
    Graeme
     
  168. Repost of that Diagram (used too high a compression factor)
     
  169. Martin,

    You state "There IS never such a thing as curved DOF in LF, somebody make a mistake in calculation and PLOTING ( such as uneven X axis on plot ".

    Your calculations on your web site show the DoF limits are ALWAYS curved when PSF is not parallel to the film plane (beta > 0).

    tan(nl_beta) = tan(beta)/(1+D/H)

    tan(fl_beta) = tan(beta)/(1-D/H)

    Regards,

    Graeme
    Graeme
     
  170. Graeme,
    Thank you for your kind words about my article on Scheimpflug, Hinge and DOF . It is a draft, I am still in the process of revising it. One area which I intent to concentrate on is add a lot more detail verbal explaination.
    Apparently I failed to describe clearly the meaning of D in my formular
    Psfnl_slope=psf_slope *(1+D/H)
    and psffl_slope=psf_slope * (1-D/H)
    The D comes from the c in a line ( plane with z collapsed ) equation
    PSF: X+aY+c=0
    psf_slope = -1/a
    when y=0, X=-c =D = the distance of lens to psf ALONG AXIS
    In other word, point D is the INTERSECTION OF PSF with X axis that is the optical axis of lens
    For every one PSF, there is only ONE such D point, and it CANNOT be any points on the PSF
    Any point on the PSF is given by ( X, Y) under the contrain of PSF line equation. The intesection of PSF with x axis is (0, -c) = (0,D)
    In other words, when a point on PSF with Y coordinate =D, it X coordinate cannot be anything else but zero.
    In the pass,I tried classical DOF formular to solve the slanted line question, and got wrong answers, so I thought the they are no good for three LF.
    However in the last couple of days, I keep thinking why so many people applied the Classical DOF formula and got curved DOF limits and I want to get to the bottom of it. And I found out why people stumbled.
    My statement that classical DOF cannot be applied on LF is prematured. It can, but there are a few stumbling blocks on the way, after clearing these stumbling blocks, I got exactly the same result as I would if using the dof formular in my article.
    I am learning, the more I delve into it the more I learn. For example I noted the simlarity of classical dof equation with lens equation, hence it must transform straight line into straightline that is a new insight, and I never read it anywhere else before.
    Every one can calculate DOF in box camera. It is easy
    However when it comes to using it to calculate DOF for view camera, supprizing not a small number of people stumbed.
    The procedure of how to apply classical DOF formular correctly to LF is too long to described here in detail. I intend to write it up and post it as a separate thread :"Common mistakes in the calculation of slant line DOF "
    Again, I repeat, the D in my formular is not any point on PSF, it is the intersection of psf with optical lens, that point must have X =0.
    In your graph, you D is the distance from lens to any point on the psf. That is not what my formular means. In my formular D is a CONSTANCE, not a variable.
    You D is sqrt(xx+yy)
     
  171. Graeme wrote:
    "1/D+1/u=1/f IS NOT EQUIVALENT TO <p>


    DoF_nl = hD/(h+D-f), DoF_fl = hD/(h-D-f) <p>


    Where h=f^2/(fstop*circle of confusion), f is focal length of lens and D is distance to object. <p>


    Graeme, if you want to learn more about it, you should tried to derived
    the DOF equation from thin lens equation yourself, it is enlightening. <p> DOF equation
    is only a result of 1/v=1/f+1/u. Of course these two are not
    equivalent. The thin lens equation is far more general and powerful, the dof is
    only one of its results.
    <p> Dof formular, Scheimpflug, Hinge etc are all derived from
    thin lens equation, as I had demontratedly in part in my article
     
  172. Kelly wrote:
    "Opps! I got straight lines; but they diverge not from the hinge point!..They intersect one focal length away from the lens (towards the subject); <p>

    So you got straight lines DOF. They are straight lines <p>
    The hinge point IS one F away from the lens. <p> You got the hinge
    point right too. The Scheimpflug point is in line with the lens.
     
  173. Graeme, I add some data in to the WHERE graph.
    the position of lens, the position of object point A(x,y) are given
    and H is given. With D1= DH/(D+H) AND D2= DH/(D-H) calculate the
    near limit (x1,y1) and far limite (x2,y2). Forget about the f. All
    DOF formulas are approximation.<p>
    It is a view camera lens.
     
  174. Martin,

    "forget about the f" ??????

    How can I calculate a meaningful DoF without the focal length of the lens?

    When you've given me a focal length, and I've used the real formula for calculating DoF limits and given you an answer, it will be time for YOU to answer the hard questions that you've been conveniently avoiding. I'm getting tired of chasing tails here. I've offered rebuttals to all of your arguments already - you've yet to do me the same courtesy.

    You've got good mathematical skills, but you've been blinded by the assumptions that Merklinger imposed on his work. It is time for you to go beyond his simplistic (though confusing) solutions - you've already gone beyond his mathematics. Think about the questions I've posed: you will be required to answer them soon.

    Regards,

    Graeme
     
  175. Graeme
    The data provided are all that is required to calculate the DOF
    H already contain focal length, fstop and coc.<p>
    As for your "rebuttal" you math is far from enough yet :)
    All you did was to grapped my equations misused them.
    You really need to read up on DOF math, instead of waisting your time trying to "proof" dof are curves
     
  176. Graeme, in my article I already proved that
    "The near and far DOF limits are planes intersecting PSF at hinge line. " Under Depth of field section. <p>Perhaps I need to used bold
    letters to emphasis that statement. <p> No further prove is necessary
    It is my strongest proof. Approximations are not proves, they are
    demostrations, examples. <p> If you understand analytical
    geometry (ie, geometry in Cartesian coodinates ) you should comprehend
    my proof. Looks like you did noticed the proof was already there.
     
  177. Martin,

    The apparent similarity between the DoF formula and the thin lens equation is just that - apparent:


    DoF_nl = hD/(h+D-f) = h/(h+D-f) * D/(h+D-F

    does indeed look something like:

    1/v=1/f+1/u

    BUT:

    DoF_nl = f^2/(fstop*circle of confusion)/((f^2/(fstop*circle of confusion)+D-f) * D/((f^2/(fstop*circle of confusion)+D-F)

    looks NOTHING like the thin lens equation, because it is quadratic equation and has no linear solution. f^2 is f squared.

    The formulae I posted were changed slightly to match with your terminology (D actually should be s, the object distance and is not restricted to Merklinger's artificial and wrong restriction of the object being on the optical axis of the lens or the bore sight (whichever; they're both wrong)). Try plotting DoF for different distances (not D) using the real (quadratic) equation and tell me what you get when the distance alters.

    Now you're forgetting basic photographic principles; are you REALLY saying that DoF is not dependant on focal length? Are you trying to say that the depth of field of a (35mm camera) 24mm lens is the same as the DoF for a 200mm lens when both are focused two metres away?

    Yes I grabbed your formulae: they ARE correct aren't they? I don't have to re-invent the internal combustion engine to drive my car. I can use your formulae without having to go back to first principles. Your use of them is too restrictive. If you think I have misused them, please prove that they don't hold true for distances other than your defined D.

    I'll be using film over the weekend to record the results of the experiment that I proposed earlier. I'll post it as soon as it is ready. I would suggest that you hold off on starting a new thread if I have raised any doubts for you. You are wrong here, and posting a new thread before you have fully cleared those doubts will make you look illogical when I post the arguments that I have already given again. If you have no doubts, post away - you'll face the same barrage from me. Answering your questions has given me a stronger understanding of the principles involved. The next time I have to answer the same questions in your own thread, I'll be even more persuasive.

    The questions you have not addressed (please do so now):

    - Does the paraxial approximation hold true for small angles of deviation from the optical axis (say, less than 10 deg)?

    - Do your formulae describe the slope of the DoF limits?

    - Do the following formulae describe the DoF limits (notice I've substituted s for D to avoid confusion with your D):

    DoF_nl = hs/(h+s-f)


    DoF_fl = hs/(h-s-f)


    Where h=f^2/(fstop*circle of confusion), f is focal length of lens and s is distance to object.

    - If the answer to the above question is yes, how can you get a plane from the quadratic equation when "s" is not constant?

    - Why is your version of the DoF calculation not a quadratic equation and why does it not depend on the focal length of the lens (contrary to all literature)?

    - Is the image of the DoF (ie the depth of Focus) the conjugate of the depth of field? If the thin line equation describes a line to a line, why is your depth of field line at an angle to the PSF while your depth of focus line lies parallel to the film plane?

    - Does your experiment test the depth of field or does it REALLY show that the PSF rotates when the film plane is racked forward or backwards?

    - Do you believe that my experiment will prove my point (given that it works, and you will soon be shown that proof)? You have yet to comment on the validity of my experiment. Does it scare you? If one of your friends with a view camera can repeat the experiment, will you believe it? If your friend shows you and you see it with your own eyes, will you consider changing your mind? If you won't change your views, will you come up with some other theory (not your current one) which will explain what you have seen? Or will you blindly stick to your guns and claim there is some mistake, perhaps his lens is no good, maybe he has a curved GG?

    - Why are you altering film/lens distance when trying to demonstrate depth of field, which is dependant on fstop?

    - The thin lens equation cannot be substituted for DoF approximations. Do you think your " new insight" which you had "never read anywhere else before" might, in fact, be wrong, and that it was not previously published for that reason?

    Regards,

    Graeme
     
  178. Martin,

    The reason you need to answer these questions before you post your own thread is that I WILL keep asking these questions. If you can't answer them now, in the apparent privacy of our own little battle here, you won't be able to answer them in the harsh light of public scrutiny.

    Regards,

    Graeme.
     
  179. Martin,

    I apologise for the tone of my two previous posts. I'm getting frustrated that I just can't express a simple proof that will show you that the DoF lines are curved. I really don't want anybody to be made a fool of - I want you to be absolutely sure of your beliefs, but I also want you to be correct before you put out a theory for the others to read. Please bear with me on this exercise that I am now proposing.

    Here's another attempt at a proof which goes back to first priciples to some extent.

    We both agree that by using movements in the camera, we can have objects at many distances from the camera on the PSF. The slope of the PSF does not matter - only the distance from the lens. Why don't we both calculate some depths of field (near limit only) using the widely accepted formula for DoF near limit:

    DoF_nl = hs/(h+s-f)

    Where h=f^2/(fstop*circle of confusion), f is focal length of lens and s is distance to object.

    Let the circle of confusion be 0.067, fstop be f22, focal length be 100mm, and the object distances be 5m, 10m, 15m, 20m, 25m, 30m, 35m, 40, and 45m.

    We can then post our answers and produce a graph manually or using a computer, where the x axis is the distance to the object from the lens and the y axis is the near limit to the depth of field. Do you agree that the plot of the points on such a graph represents the depth of field (near limit) for that range of distances? If so, the graph will display the answer one way or the other.

    Will you do this for me and yourself?

    Regards,

    Graeme
     
  180. Graeme wrote:
    "Is the image of the DoF (ie the depth of Focus) the conjugate of the depth of field? If the thin line equation describes a line to a line, why is your depth of field line at an angle to the PSF while your depth of focus line lies parallel to the film plane? "<p>

    Graeme: FP is a LINE <p>
    The parallel moved FP' IS ANOTHER LINE, with same slope.<p>
    The beauty of Newton equation is: It map TWO parallel lines from
    one space into INTERSECTING lines in another space (object space to
    image space or vice versa ).<p>
    That is the essense of planar DOF limit, it transcends all numberical
    verificaion, approximation. It is the ultimate proof from the highest
    principles---Newton equation
     
  181. Martin,

    Correct - FP is a line (actually a plane, but I won't split hairs on that one).

    Correct again - moved FP is another line.

    FP corresponds to PSF on the other side of the lens.

    Moved FP corresponds to a DIFFERENT PSF on the other side of the lens.

    Isn't Newtonian Physics just great? We can keep shifting the PSF to almost any orientation we want, just by moving the FP backwards and forwards. Funny though, every time we move that PSF, the DoF just keeps moving out of the way, and we can never quite get a focus on it. Come to think of it, that darned DoF limit is nearly as slippery as a person who sidesteps questions all the time! Maybe if we look the other way, the laws of physics might forget to work just once, and when you look again, you'll see an image of the PSF which is just out of focus.

    What's this about "essense of planar DOF limit, it transcends all numberical verificaion, approximation"? Are we going to now talk of essences and spiritual well being?

    Time to stop playing around Martin. Answer the questions posed above.

    Here are the answers to the scale of focused distances, using the accepted near DoF limit formula. There is also a graph, but I couldn't get the x axis to be distance from lens, so the graph is on its side.

    Regards,
    Graeme
     
  182. Graeme wrote:
    "The slope of the PSF does not matter - only the distance from the lens.....
    and the object distances be 5m, 10m, 15m, 20m, 25m, 30m, 35m, 40, and 45m. "

    Graeme, that IS exactly where all your problem lies<p>

    We are dealing with PLANE here, if you consider each point at 5m, 10m, 15m are points. Unless you are dealing with level ground
    other wise each point need a coordinate such as (5m, 1m) (10m 1.2m)
    (15m,1.4m ) etc etc. You must specify the position of the lens, ie
    how tall you tripod is.
     
  183. Graeme wrote:

    "Another experiment, impractical though it is, would be to leave the camera focused on your middle xmas lights line and close the aperture gradually until the any of the lights on the other lines became focused, stopping there and checking the focus of all of the lights. I propose that the far lights on the near line will come into apparent focus first. It can't be done easily, because you would need two very long lines of lights. Don't change the focus of the camera by racking the lens or film plane, because that swings the PSF. "

    <p> Can you do it ? It will be great
    <p> Also do a set for a straight PSF with two curved dof limits<p>

    <p> That would be mighty interesting. Better than math :)
     
  184. Martin,

    DoF is measured perpendicularly to the PSF. If you don't understand that much, then we are doomed to failure here. Do the calculations as if we are dealing with a box camera if you like - it makes no difference. The formula for DoF does not require a slope - there is not even provision for it in the formulae.

    Just do the calculations or agree that what I have calculated is correct (even if it is only for a box camera). I'm trying to walk you through this one step at a time. If you don't want to follow, fine - I'll leave you behind.

    My alternative experiment is impractical, but keep the analogy in your mind. My next post will use your xmas lights to prove that depth of focus is wedge shaped when PSF is inclined.

    Keep thinking about those questions - if you want your logic to stand, you'll have to answer them. Not doing too well on the yet....

    Regards,

    Graeme
     
  185. Martin, Your attempt to explain depth of focus by racking FP back and forward is fundimentally flawed. Focus follows the simple equation 1/v=1/f+1/u Given two known factors, the third can be calculated. By altering the distance between the lens and FP, you are making both f and v unknowns, so the equation can't be solved. Lets go back (again) to your xmas light analogy, since you seem to be able to picture this example. I've attached a diagram which represents the lines of lights on PSF and a line of lights on the approximation to the near limit of DoF. Using the thin lens equation and a ray diagram, and assuming that all lights are "focused", it can be seen that the lights on DoF form an image in space on a plane inside the FP which is at an angle to the FP. This image is the conjugate of the object, as required by Newtonian physics. If you think that Newtonian physics allows parallel planes on one side of the lens to be represented by radial planes on the other side, you must be flabbergasted by John Sexton's images of parallel poplar trunks ("How did he do that? Must have one of those new Linhof anti-newtonian curvature correction backs! Maybe the trees grow radially?"). Parallel lines on an object are depicted as parallel lines on an image. (Yes, you can distort the image by tilting and swinging the back so that they look radial vis a vi perspective control, but the planes are still parallel in 3D space within the camera). Stop trying to baffle me with bullshit. This is science, not some arts course discussion of ethereal phenomena. Ask the questions. Form a hypothesis. Do the maths in the real world. Devise an experiment to prove your theories. Conduct the experiment. Question your results. Seek verification of the results from an independant source. Publish your findings. Quoting a source blindly without questioning the assumptions and science that the source has used is not science - it is cult worship. Graeme
    003X5k-8842584.jpg
     
  186. Martin wrote "We are dealing with PLANE here, if you consider each point at 5m, 10m, 15m are points. Unless you are dealing with level ground other wise each point need a coordinate such as (5m, 1m) (10m 1.2m) (15m,1.4m ) etc etc. You must specify the position of the lens, ie how tall you tripod is."

    Choose any plane you like Martin. I don't care what it is, where you choose to orient it in space. Make it horizontal, inclined, vertical. It doesn't matter. You don't even have to tell me what you've chosen. Do it three times and average the results, do it seven times and take one value from each pass. Try calculating while you stand on your head and whistle the star spangled banner.

    As they say in the Nike ads of old: JUST DO IT! Make sure you post your results though: I'd hate to try to deceive you by using my obviously spurious results. See if you can come up with some different results using these criteria.

    Do it now Martin. No excuses - you're starting to look silly.

    Graeme
     
  187. Good bye Martin,

    This is where I leave you behind. I am going beyond your understanding here, but if you do the exercise, you might pick something up.

    For anybody else who is still interested, I’m going to run through a practical exercise using the graph of the depth of field’s near limit. I’ll also post this in a new thread so the wider community can critique it.

    With the data generated from the inputs I suggested before, plot the depths of field on graph paper using object distance as the x axis and depth of field as the y axis. Join the dots and cut the paper along the x axis and the curve you’ve made (make sure you keep the distance marks on the paper – you may need to mark them on again after cutting).

    You should now be looking at a cut-off curved wedge shape. As you’ve probably gathered by now, the curve represents the near limit to depth of field for the given focal length, f stop and ellipse of confusion. There are two important facts to remember at this point:

    1) The depth of field for an object on the plane of sharp focus is measured perpendicularly to the PSF.

    2) Additionally, that DoF is constant for that object/lens distance when focal length, fstop and ellipse of confusion remain constant.

    Those two statements are fundamental and underpin the concept of DoF. The fact that DoF remains constant and is measured perpendicularly to PSF means that the curved wedge of paper you now hold in your hand is a very powerful visualisation tool.

    On a second piece of graph paper, draw a lens at zero and mark the same series of distance values that you used before along a horizontal line near the middle of the paper. Use the same scale as your wedge thingy.

    Most people have no problems visualising DoF in the world of the fixed body camera (35mm, MF, etc), so we’ll start with an example that relates to those systems. At one of the horizontal distance marks, place the straight edge of the curvy wedge vertically (curve closer to the lens) and slide up or down until the corresponding mark is aligned with it. What you’ve now done manually is demonstrated the DoF near limit for the distance marked at the straight edge of the curvy wedge, because the curved edge of the paper represents that value. We know that for the geometry of these cameras, DoF limit is always parallel to the film plane, so that value must be extrapolated vertically, but there you have it. Experiment by matching up other distance marks and confirm that this works before moving on to the next step.

    The straight edge of the curvy wedge represents the plane of sharp focus (PSF). If that statement disturbs you, think about what you are looking at in front of you. That is why we placed it vertically in the above example. Fixed geometry cameras have the PSF parallel to the film plane. In LF photography, we often try to rotate the PSF to optimise our focus. An often sought after configuration is to have the PSF horizontal, so let’s demonstrate that.

    Rotate the curvy wedge so that the straight edge (PSF) is horizontal, the curve is up and the distance marks are aligned. You’re done! No hard visualisation required – it’s right there in front of you. Every object under the wedge of paper will be in apparent focus.

    Want your PSF inclined and aligned with some other point in space? Rotate the PSF to the desired slope, align the distance marks, and once again, your done. Everything under the paper is in apparent sharp focus.

    The horizontal reference axis on the sheet of graph paper does not need to be horizontal (and probably should not be): rotate that as well to simulate the real world even more. Those distances marked are only object / lens distances, not horizontal distances. Go Wild!!!


    The rules dictated by Scheimpflug still apply, so in real life you can’t actually move the wedge willy nilly in space, but where the PSF is allowed to traverse, this demonstration is valid for a perfect thin lens.

    The same exercise can be carried out for the far limit of DoF, but you can attempt that in your own time. I’m going to bed!

    Regards,

    Graeme Hird
     
  188. Hi Martin!

    Interesting thread.

    Graeme Hird seems to be as frustrated with you in this thread as I was at:

    http://www.photo.net/bboard/q-and-a-fetch-msg?msg_id=002jtA

    The root of the frustration appears to be that when people ask you a question that would nail you down, you spin off a tangent argument or don't reply at all.

    When someone asks you a question, please consider answering it. Providing the answer might be uncomfortable for you, but in the long run, you'll be much more comfortable than having to read the likes of this post.

    I'm still waiting for your answers on the other thread.

    Mike Davis
     
  189. Graeme here is my calcution for the dof of a slanted line

    F= 150
    FSTOP =16
    COC = 0.1 mm
    H = 14.063 METER
    SLOPE OF PSF 0.2

    Followed data point in mm

    PSF DOF NEAR DOF FAR
    X Y nx ny fx f y
    2000 0 1751 0 2332 0
    3000 200 2473 165 3814 254
    4000 400 3114 311 5590 559
    5000 600 3689 443 7759 931
    6000 800 4206 561 10465 1395
    7000 1000 4674 668 13938 1991
    8000 1200 5099 765 18557 2784
    9000 1400 5488 854 25000 3889
    10000 1600 5844 935 34615 5538
    11000 1800 6172 1010 50510 8265
    12000 2000 6475 1079 81818 13636
    13000 2200 6755 1143 172059 29118
    14000 2400 7016 1203 3150000 540000





    Three straight lines
     
  190. Now Graeme,

    Show your calcuation for the same set of X, and Y <p>

    Don't jump to conclusion that my calculation shows curved
    lines because of the large numbers 3150000 , 540000. <p>
    Just plot a few points, and you will see the near/ far limits
    are two wedge shape lines on either side of original PSF
     
  191. Martin,

    I'll trust your data is correct - no need to dispute it.

    You wrote "Don't jump to conclusion that my calculation shows curved lines because of the large numbers 3150000 , 540000"

    Why should I not jump to that conclusion - that's what your numbers show. Your data shows the lines are curved. If these lines were straight, the difference between any two consecutive nx, fx, ny or fy numbers would be constant, just as the numbers that you plugged into the PSF X and Y were. For example, the difference between consecutive PSF X is always 1000mm. The difference between the nx for 2000mm & 3000mm is 722mm, while the difference between the nx for 13000mm and 14000mm is 261mm - ie, clearly not linear. As you have correctly pointed out, the last few numbers of your DOF far really start to fly off the linear approximation. And all you can say is "Don't jump to conclusions"? Your own data is showing you that the relationship is not linear and you choose to ignore it. Who are you fooling Martin? It sure as hell is not me.

    You've given yourself the luxury of choosing small distances from the camera, where the linear approximation of DoF holds up best, and still your own data show that the lines are curved. How much more evidence do you need. For your own peace of mind, try putting numbers in of the order that I originally suggested (ie around 25 to 40m). See if you can fool yourself then into thinking that the numbers you get from your calculations approximate the linear relationship that you think you are seeing. (I'm sitting here smiling at the thought of you redoing your work over and over, thinking that your computer MUST be wrong, throwing things around the room in frustration and finally pouting miserably at your screen).

    If you think your data shows three straight lines, you've lost it. I'll post the graph of your data soon just to show you. Maybe you can also post the graph?

    Keep on trying.

    Graeme.
     
  192. My apologies Martin, the lines do indeed plot as a straight lines on a scatter plot. After I had seen your alterations to your web site, I see where you are coming from, but I do not agree (yet) that the DoF is measured along the ray. I'll come up with some proof for my version (ie that DoF is measured perpendicularly to PSF)

    You have yet to come up with a valid method of experimentally testing and varifying your theorum.

    Graeme
     
  193. Graeme
    "Axiom : Dof limits of point P must lie on the same radial as as P" is the key in applying classic DOF formular to LF.
    In the attach diagram, the red light bulb P is flanked by other blue, green, violet bulbs.
    Obviously the red bulb can only move along the its own red color radial lines to its near and far limit positions.
    It cannot move side way or perpendicular, without encroaching on the image radials of other points (color bulbs )
    Grameme, can you think of any other way the bulb can move such that the red circle of confusion of red bulb P does not overlap the image of other bulbs ? I don't think this axiom can be derived from another basic law of optics. That is why I called it an axiom.
    It is a natural result of the straight line property of light.
    003XqB-8886584.jpg
     
  194. Graeme<p>

    When you finally figure out that the DOF limit points have nowhere
    to go but along the radial, don't forget to recall your 'visual tool' based on 'perpendiculars" :)
     
  195. Graeme<p>

    Checkmate !
     
  196. Martin,

    For the time being, I'm willing to concede "Check". Your diagrams and calculations do provide compelling evidence for your case, and I wish I'd forced you to provide them earlier. It would have saved a lot of frustrating tail chasing.

    I'm working on something a little more practical at the moment, but when I've finished with that, I'll think some more on this problem. Expect some more answers later, and if it turns out that I eventually agree with you, an apology will be posted.

    If you're ever in Kalgoorlie, I'll buy you a Fosters.

    Regards,

    Graeme
     

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