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

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

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.

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

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.

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

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

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

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.

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 :)

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

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<div></div>

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

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

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

Graeme here is my calcution for the dof of a slanted line

<pre>

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

�

</pre>

Three straight lines

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

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.

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

Graeme<p>

"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.<P>

In the attach diagram, the red light bulb P is flanked by other

blue, green, violet bulbs.<p>

Obviously the red bulb can only move along the its own red color

radial lines to its near and far limit positions.<p>

It cannot move side way or perpendicular, without encroaching on

the image radials of other points (color bulbs )<p>

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.<p>

It is a natural result of the straight line property of light.<div></div>

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" :)

Graeme<p>

Checkmate !

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