“Formula” for ”minimum focuses distance” to prevent perspective distortion of wide angle lens or any lens.

yee_lee1 · May 6, 2009

Is there a "formula" to calculate the “minimum focus distance" between subject and camera with wide angle lens to prevent perspective distortion of wide angle lens by give lens in mm and film or sensor size?

I am not sure would different format of camera with different size of the film or sensor will make any more or less perspective distortion.

Thank you very much for the help.

Yee Lee

William Michael · May 6, 2009

My guess is when you write "Perspective Distortion" you are referring to "Foreshortening" and / or "Convergence".

If so, then my answer is: No.

The reason, because both these "distortions" are also factors of:

. Camera Elevation relative to the Subject, and

.Camera Viewpoint relative to the subject (especially - Perpendicularity).

WW

joe_c5 · May 6, 2009

Perspective distortion is caused only by distance, and has nothing to do with focal length or sensor size by itself. Viewing angle only seems to be related because people often fill the frame with the subject, which puts them much closer with a wide angle lens than a telephoto lens.

How much perspective distortion is too much is a matter of opinion that will vary from person to person, but a rough range would be from 2 to 4 meters. Too close tends to make noses look big, and too far tends to make ears look like they stick out. There is no formula for this, rather it has to do with how far away people are used to seeing other people.

Alan Marcus · May 7, 2009

Joe C is absolutely correct; Joe deserves a tip of the hat.

Now allow me to expand on his theme: It is widely acknowledged that we tend to view pictures from a distance approximately equal to their diagonal measure. That being true, an 8 x 12 inch print will likely be viewed from a distance of 14 inches (255mm). Now it’s also widely accepted that the “normal” lens, one that delivers a perspective about equal to the human experience, is one with a focal length about equal to the diagonal measure of the format. It’s no accident that these two facts are closely tied together. Take the full frame 35 mm format. It measures 24mm by 36mm and the diagonal is 43mm. However we generally round up to 50mm, a slight error. That’s OK these are not hard fast rules, just accepted norms. One more crucial fact: If a slide or negative or contact print is viewed from about the same distance as the taking lens focal length, their will be no perspective distortion. Now with modern miniature format it is likely impossible to view from such short distances. However it is quite likely that we will be viewing an enlargement, be it print or projected image or computer display. Thus we must add to the equation the degree of magnification utilized.

Back to the 8x12 print: To make we must enlarge the original camera produced image 8 ½ times. If the taking lens is about 43mm in focal length, the ideal viewing distance is 8.5 x 43 = 356mm or 14 inch.

Let’s try that again using a DSL size APS-C sensor 16mm by 24mm with a diagonal of 29mm. Thus the “normal” for this format is about 30mm. To make the 8x12 print we must enlarge using a magnification of 13x. Thus the viewing distance becomes 30 x 13 = 390mm or 15 inches.

If you follow the math you might understand why a “normal” lens, one not telephoto and not wide-angle is about equal to the diagonal measure of the format. This math tracks all format sizes from giant to miniature.

Now allow me address the actual question of wide-angle distortion. The answer is: If a print is made, regardless of focal length, and viewed from a distance equal to the focal length times the magnification required to make the print, there is no distortion.

Distortion sets in when these truisms are violated. If a 10mm lens is mounted on a full frame 35mm format, and an 8x12 print is made, the viewing distance should be 10 x 8.5 = 85mm or 3 1/3 inches. It’s not possible to view at that close distance unless you employ a strong magnifying glass. We will view this print from 14 inches and it will appear distorted.

Sorry if this seems like gobbledygook, nobody said this stuff is easy

William Michael · May 7, 2009

Yes:

1. Perspective is created by choosing the distance from the Focal Plane to the Subject.

2. Field of View is then created by choosing the Focal Length of the Lens.

Ask any Cinematographer or Director of Photography - those are the two prescriptive stages and the order of choice for them.

***

Perspective is not a distortion - it is just Perspective. IMO it was necessary to isolate what exactly we are talking about and to avoid it seeming like gobbledygook - it is not that difficult, actually.

If the question is about Convergence, or Foreshortening - then, as I wrote these are dependent upon Camera Elevation and Perpendicularity.

Convergence and Foreshortening, if present, will be noticeable in any print viewed at any distance. Granted it is difficult for the eye to scan the whole 8x12 print at 3 inches, but converging parallel lines, will still appear converging.

WW

Alan Marcus · May 7, 2009

While a more detailed presentation on perspective is available “Photographic Lenses” by C.B. Neblette pages 9 and 10 a partial quote.

“Fortunately except for special technical applications, we are not usually concerned with geometrically correct perspective, but only with perspective which appears false. In this respect there is considerable latitude, although our ideas of proper perspective may be offended by both short and long-focus lenses if used without proper regard to viewing distance and subject”.

This subject is covered in his book Chapter 1: General Properties of Lenses. Allow me to add that this is not the only text on this subject matter. If pressed I think I can produce several authorities who express the same.

William Michael · May 7, 2009

I do not see I have made any argument with what is quoted above. Which is indeed an opinion of what might generally concern us.

My aim was merely to define exactly what we were concerned with, in this question i.e. exactly what Yee Lee was asking about.

And then from that point keep it as simple as possible.

As this is a Beginner's Forum, it seems best to address the question - or clarify it - and then address the question in simple terms and with positive words which will encourage the understanding of same.

WW

yee_lee1 · May 7, 2009

Thank you very much to give me very useful answers, only if I can understand them all, which I still don't. I am sorry as a beginner to photo world and do not understand most photography terminology. Most likely I ask the question wrongly or not and I am not for sure either.

My problem was using a 16mm to 35mm wide angle zoom lens. When I zoom in and set at 35mm and take a picture of the subject and than zoom out and set at 16mm and take a second picture. Without anything else change like distance between me and the subject. I notice that the second picture taken with lens set at 16mm all the horizontal and vertical lines of the wall are curve much more then the first picture which lens set at 35mm. Of course the first picture's both vertical and horizontal lines also cure a bit, but not as much.

My question was "How much more distance I need to move back away from the subject in this case which is a wall with horizontal and vertical line and the curve line will be much more straighter and less noticeable?” I hope I am more clearly this time.

My camera lens was pointing perpendicularity relative to the wall. I know if I backing up very far away from the subject the curvature will be still there but much more straight line for both horizontal and vertical. Of course I know my field of view will widen and I will need to crop in to the subject for the final print, but I want to get closest to the subject as much as possible because of light lost.

What I really want to found out was the closest distance between me and the subject without too much curve lines for both horizontal and vertical lines on the wall using wide angle lens. That is why I ask dumb question to hope if give lens mm and then to found the minimum distance without too much perspective distortion. I hope anyone of you can understand what I am asking.

Can someone tell more about Convergence or Foreshortening?

Thank you very much for all the help.

Yee Lee

peterblaise · May 7, 2009

.

Yee, back at ya, what "... perspective distortion of wide angle lens or any lens ... " are you seeing? Can you tell us more of what you are looking at and why you think subject distance is the determinant, and if trial and error has apparently not resolved the issue for you? Rather than speculate, I'll wait for your answer. Thanks.

(None of my wide angle lenses have any "distortion" due to their wide angleness, by the way. All my wide angle lenses present an image of the subject that is essentially as accurate as the image my normal and telephoto lenses present. And none of my lenses have "perspective" distortion ... if there was such a thing a lens could have.)

----------

I'm thrilled, by the way, that the speculative answers here so far are not assigning any distortion to the lens, especially so-called "perspective" distortion, but rather acknowledging that the observed phenomenon is a total system characteristic, the difference between

<ul>

<li> -- the original subject viewer's perspective and </li>

</ul>

<ul>

<li>-- the subsequent image viewer's perspective </li>

</ul>

... "perspective distortion" is a capture-to-print/presentation thing, not a lens thing.

Of course we all know subjects look "distorted" up close even without a camera in front of our faces. Such accurate "distortion" of appearances has nothing to do with cameras; it only has to do with us looking from an unfamiliar position.

Back to you, Yee -- tell us more of what's happening for you. Would DxO Optics help (software to "fix" bent images)?

<ul>

<li><a href="http://www.dxo.com/us/photo/dxo_optics_pro">http://www.dxo.com/us/photo/dxo_optics_pro</a> </li>

</ul>

.

Alan Marcus · May 7, 2009

A tip of the hat to Mr. Peter Monahon from Alan Marcus -- You nailed it - I could not have done better and that coming from me is a big complement.

yee_lee1 · May 7, 2009

Thank you very much for the info and now I understand it is not distortion.

How many mm human eyes are? How much mm zoom human eye can zoom? What is size of human retina? How many mega pixels? Those are not what I really need to know for now, but it would help or not.

What I really do not understand is: Why my eye does not see the straight line “curve” as much as wide angle lens for same “field of view” and same distance from the subject? Was something wrong with my eye? What are the different between human eye and lens/camera?

Sorry for the dumb question. Thank you very much for the help.

Yee Lee

William Michael · May 7, 2009

“I zoom in and set at 35mm and take a picture of the subject and than zoom out and set at 16mm and take a second picture. Without anything else change the second picture taken with lens set at 16mm all the horizontal and vertical lines of the wall are curve much more then the first picture which lens set at 35mm. lens was pointing perpendicularity relative to the wall Of course the first picture's both vertical and horizontal lines also cure a bit, but not as much.”

This is Barrel Distortion. It is because of the lens, and is common in wide angle lenses, and more common in wide angle zoom lenses, because zoom lenses have compromises in design to allow them to cover various focal lengths.

***

"How much more distance I need to move back away from the subject in this case which is a wall with horizontal and vertical line and the curve line will be much more straighter and less noticeable?”

It will always be there. The further you move away (the closer to the centre of the frame the walls sides will become and thus less noticed on the edges of the wall), but it the edge of the frame of your image will always have this barrel distortion.

***

I know if I backing up very far away from the subject the curvature will be still there but much more straight line for both horizontal and vertical. Of course I know my field of view will widen and I will need to crop in to the subject for the final print, but I want to get closest to the subject as much as possible because of light lost.

Yes.

In the link provided by Peter, the next menu down (optics distortions) opens up here:

<a href="http://www.dxo.com/us/photo/dxo_optics_pro/optics_geometry_corrections">http://www.dxo.com/us/photo/dxo_optics_pro/optics_geometry_corrections</a>

This is one tool for correcting the Barrel Distortion for you.

***

Can someone tell more about Convergence

Go outside with the lens set at 35mm take a shot of a tall building with the camera perpendicular to the building – OK there sides of the building might show a little barrel distortion, but for the sake of the exercise let’s say they are parallel. Now go closer to the building and point the camera upward and take another photo – the building’s parallel side are converging at the top – this is (extreme) Convergence. Convergence is often more noticeable when using WA lenses.

***

Can someone tell more about Foreshortening?

Using a WA lens take an image of a young child standing – say about 5yrs old - but ensure you are kneeling so that the camera is about chest height to the child – stand about 4 ft away from the child to take the image.

Then stand up and take a second image – in the second image the Child will appear deformed, with a very large head and smaller chest and tiny little feet. This is Foreshortening.

***

In my first answer, I did not dismiss any lens distortions – (like barrel distortion for example) – I merely gave two common traits of WA lenses and explained how those were linked to the camera’s viewpoint and perpendicularity to the subject.

I expected Yee Lee would provide more information or a follow up question if that answer did not suffice. It appears to me that Peter posted specifically asking for more information at the same time as Yee Lee was giving it.

I expect that if further information is required Yee Lee will ask.

It was not a dumb question.

WW

yee_lee1 · May 7, 2009

William, Alan, Peter, Joe:

I am very appreciating for all the very helpful answer. Now I understand a bit more. I am guessing "Barrel Distortion" was my problem.

Will high price wide angle prime lens do not have "Barrel Distortion" problem or at least not as much as zoom lens?

If I get a very good wide angle "prime" lens and do just what I was did early but now I move close and far away from the subject. Will the straight line stay very "straight" between both photos and/or at least the "curvature" of the straight line stays the same? or Will the straight line still become more curve as I move close to the subject and become straighter line when I move far away? I do not have wide angle prime lens to play with.

What I really do not understand is: Why my eye does not see the straight line “curve” as much as wide angle lens for same “field of view” and same distance from the subject? Was something wrong with my eye? What are the different between human eye and lens/camera? I will really appreciate if someone like to help me on the.

I am assuming the perspective control lens will help Convergence problem by "shift". Will that be correct?

How to taking care of Foreshortening problem? The same way or need to use Large format camera and how? Tilts and Swing both front and rear standards and shift too? I do not have large format camera to play with, but I would like to know how.

Is possible to "optically" build a fisheye lens and without the fisheye effect? A very "flat" image fisheye lens?

Sorry for the dumb question. Thank you very much for all of your very knowledgeable answer.

Yee Lee

peterblaise · May 7, 2009

.

Thanks, Alan, I'm truly grateful you found my exploration accessible. As mentioned, I enjoyed insights and references everyone else shared, too.

I think all answers are great so far. I think Yee is looking for a "formula", and so it makes sense to explore the math of

<ul>

<li>(a) the original taking distance and capture image size and </li>

</ul>

<ul>

<li>(b) the subsequent viewing distance and print/presentation size, and </li>

</ul>

<ul>

<li>making them proportional </li>

</ul>

... is quite useful, and is "just" math. Also, the general expectation that wide angle shots tend to surprise subsequent viewers as "distorted" more so than telephoto shots is prescient, even if a telephoto presentation may actually be more "distorted", few complain that telephoto images look unreal. Background as shared here is very supportive of helping Yee and others find authoritative understanding on the way to mastering what's happening in our photography.

Yee, I think you probably were seeing barrel distortion in the image, which would not be visible using your eye to look at the scene directly.

----------

A fish eye lens has a circular horizon as a fish would see under water looking up, all straight subject lines not going through the center of the image will be represented curved.

A full frame fish eye is a misnomer and is generally a super wide angle lens that permits a full frame rectangular capture, and may or may not represent straight subject lines as straight. A rectilinear wide angle lens tries to straighten lines.

Yes, a prime lens is simpler and usually has less pincushion and barrel distortion than a zoom at the same focal length, all other things being equal (which they never are, so it doesn't really matter).

----------

Yee, share some pictures AND share some technical specifications of your gear

<ul>

<li>-- lens make and model and focal length and aperture range, </li>

</ul>

<ul>

<li>-- camera make and model.</li>

</ul>

We all can calculate from there and do some research.

Note that some lens aberrations can be reduced by selecting smaller apertures, and some lens aberrations cannot. (Look it up?)

Also, different manufacturer's have different expectations of their lenses, some knowing that curved lines in close focus shots are accurate (separate from pincushion and barrel distortion), and some manufacturers cater to the rectilinear crowd. Which lens do you have? DxO Optics or equivalent may be all you can do for your existing images until you acquire a different lens.

----------

Yee, no questions are dumb, but sometimes a bit of research helps smarten the questioner real fast. I leave it to you to look up the words first and then ask us about what you read as you are learning about them, rather than merely asking us to explain new words for you without reading any reference first.

The web is your encyclopedia, and Google is your research librarian:

<ul>

<li>Google [define:perspective distortion] (your original inquiry best addressed to Google first) <a href="http://www.google.com/search?q=define%3Aperspective+distortion"> http://www.google.com/search?q=define%3Aperspective+distortion</a> </li>

</ul>

<ul>

<li>Google [define:foreshortening] (the first response here) <a href="http://www.google.com/search?q=define%3Aforeshortening "> http://www.google.com/search?q=define%3Aforeshortening </a> </li>

</ul>

<ul>

<li>Google [define:convergence] (also in the first response here) <a href="http://www.google.com/search?q=define%3Aconvergence"> http://www.google.com/search?q=define%3Aconvergence</a> </li>

</ul>

<ul>

<li>Google [define:barrel distortion] <a href="http://www.google.com/search?q=define%3Abarrel+distortion"> http://www.google.com/search?q=define%3Abarrel+distortion</a> </li>

</ul>

<ul>

<li>Google [define:pincushion distortion] <a href="http://www.google.com/search?q=define%3Apincushion+distortion"> http://www.google.com/search?q=define%3Apincushion+distortion</a> </li>

</ul>

... and so on.

----------

Earlier: "... I notice that the second picture taken with lens set at 16mm all the horizontal and vertical lines of the wall are curve much more then the first picture which lens set at 35mm ... "

</blockquote>

Easy -- look inside the picture to see where lines are straight, and that is your required crop. If the only straight line is in the central 1/4 of the picture, then crop to 1/4 capture. Ouch! DxO to the rescue instead!

Also, many zoom lenses are most accurate closer to normal focal lengths, and are least accurate in the opposite direction. I imagine your 16-35mm zoom is "sloppier" at 16mm than at 35mm. That's typical.

----------

Conversely, aside from barrel and pincushion distortion , I think many of us have wide angle lenses that generally accurately showing us what our subject looks like from a close up position, and we're surprised that curved lines are captured as curved lines, especially when we "know" the architectural items themselves are straight in real life as we walk around them. But get rid of the camera and put our head in the same position, and we'll see that the straight architectural items actually look curved from there. The lens is accurate , and we want a lens that lies -- and that's called a rectilinear wide angle lens , which will reverse-curve the image curved subject lines and make them straight in the image.

I also note that any lens with a focal length that is 1/2 or smaller than the diagonal of the capture device (21mm on 35mm full frame, 14mm on APS sensors, 10mm on four-thirds sensors), especially when the lens must hang outside a flipping mirror box, well, the lens design is arduous, complex, and expensive to make accurate and also "fast" (wide aperture). Add zooming capabilities, and such a design is either expensive or inaccurate, somewhat. For landscapes, who cares? For architecture, I think you are seeing why architectural photographers use a monorail camera (look it up).

Alternatively, you can use a "normal" focal length lens, preferably a prime single focal length, one with probably less pincushion and barrel distortion, and back waay up to capture the same subject field, or stay at the same distance and stitch together a series of patchwork images of the scene (speaking of arduous).

<ul>

<li><a href="http://en.wikipedia.org/wiki/Image_stitching">http://en.wikipedia.org/wiki/Image_stitching</a> </li>

</ul>

----------

Tell us more and maybe we can help you find a new lens for your camera. What you are looking for is:

<ul>

<li>-- rectilinear prime (single focal length) wide angle lens</li>

</ul>

<ul>

<li>-- well reviewed to have imperceptible pincushion and barrel distortion </li>

</ul>

Also, share some image examples! EXIF data is very useful, too. Let us look at what you are seeing.

.

yee_lee1 · May 14, 2009

Peter, William, Alan, Joe:

I find the answer in page of 81 of June, 2009 issue of Popular Photography magazine. Canon EF 16-35mm f/2.8 II USM AF...Visible barrel distortion (0.59%) at 16mm - a vast improvement over the "Very Visible 2.9%" of the earlier lens... The earlier lens Canon EF 16-35mm f/2.8 USM AF which is what I got.

The conclusion I got was there is no such formula exist. It was a very dumb question to ask begins with. The % of distortion of the lens will be there don’t matter how far back I move. It just appears to be less as I move back and then crop into the center on the final image. Would that to be correct? I hope I finally got it right, or not. Please let me know.

Now, Is the % of distortion calculated by height of the curve divide by width of the curve line?

Just FYI, I did do some search of my own before I ask question, but my English are not good and do not know much of photography terminology to found the right answer and too dumb to ask right question. I may misunderstand it even if the right answer was right in front of me. I am very sorry for the trouble may cause you all. I am really appreciating all the very knowledgeable and friendly help from you all. You all are the best. I hope is not too much to ask to for you all to input much of your knowledge into <a href="http://www.wikipedia.org/">http://www.wikipedia.org/</a> and in the “words for most of people can understand” and not for people who already know what is going on and also with very good examples. I really do not like to running around too much in the internet because of virus. Or can you recommend me web sites have most information about photography that I can safe to go to.

Thank you very much for all the detail info and help.

Yee Lee

lex_jenkins · May 14, 2009

It was a very good question, Yee Lee, and helped generate some informative answers that will assist others as reference material.

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“Formula” for ”minimum focuses distance” to prevent perspective distortion of wide angle lens or any lens.

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