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Crop factor revisited - food for thought
A while ago, some people were discussing standard lense focal length and how it translates for digital cameras with less than full frame sensors in this forum.

Even though it was a GREAT thread with tons of information, I am still unsure about the conversions of focal lengths we commonly do, multiplying them by a crop factor.

I think, a lense with a specific focal length is characterised by a number of parameters:

1) its focal length
2) the angle of coverage
3) perspective
4) distortion
5) compression (=relation in size between objects close to the lense and objects further away)

(among others).

Possibly, compression is generally considered part of perspective, when we talk about these things.


Focal length determines the magnification of our subject on the picture.
Angle of coverage is a function of the focal lenght AND the size of the sensor

distortion and compression are functions of the ANGLE, and what I think this means, is, they are a function of the angle of coverage intrinsic to the lense.
when you use a smaller than 36mmx24mm sensor, the coverage of your LENSE does not change, only the coverage of your recorded IMAGE changes!! think about that. (this is why I kind of like using the term crop factor rather than anything else).

Contrary to what may be broadly assumed, the magnification a lense is capable of does NOT increase with decreasing sensor size.

To me this means two things:

1) If I think I can magnify a subject more than my full frame companion using the same lense, I am wrong!! all I do is to decrease the angle of coverage. compared to a picture taken with, say, a 300mm lense on a full frame camera, my picture taken with a 200mm (x1.6) lense will cover roughly the same area but will LACK DETAIL. (this is under the assumption that both sensors have the same resolution, only differ in actual size).

2) no less important, the compression and DOF of my picture taken with a 50mm lense are always going to be characteristic for a 50mm lense! there can be no conversion for these things.

Why is this important?
Well, why do we use 85mm lenses for portraits? Because we can't get close enough with a 50mm?!

No, it's because over a long long time, photographers have been finding, that a medium tele lense is optimally flattering for the subject. Think about the proportions in a wide angle picture, your subjects nose would inevitably be the most protuberant, dominant item in any frontal portrait.

I don't think a 50mm lense, although, by crop factor roughly equivalent to a 85mm lense, is the optimal portrait lense.
I would postulate, that the user of a digital camera with APS-C sensor should still use the 85mm lense because of its characterisics and will just have to move further away from his subject to cover the desired area.

Am I wrong? Do you think, the compression in a picture is a function of the actual covarage, determined by the sensor size, rather than by the lense-intrinsic possible coverage?

Or are you just as confused as me.....?

Perspective (and thus perspective distortion - which I take to mean either compression or extension) is entirely determined by distance to subject. I believe you are incorrect to say that "distortion and compression are functions of the angle." However, different angles or fields of view (from lenses with different focal lengths) can have an indirect effect on perspective because they necessitate a change in distance to subject if the photographer wants the same subject coverage within each shot, and that is when perpective changes (compresses or extends.)

Also, compression and extension are relative to something else, which in the context of 35mm cameras has traditionally been the "normal" 50mm lens. So a portrait taken with a 200mm lens will appear more compressed than one taken with a 50mm lens - when the camera with 50mm lens is moved closer to the subject so that it/he/she fills the frame the same as in the 200mm shot. Similarly, a portrait taken with an 18mm lens will appear extended (the big nose problem) relative to the other shots when the camera is again moved closer to the subject so that it/he/she fills the frame same as before.

Those examples hold the camera constant and change only the lens focal lengths. Now we can change the camera (well, the sensor size) and the perspective distortion effect changes too:

All else being equal, a camera with an APS-C sized sensor crops the field of view compared to a full-frame 35mm sensor. Given the same lens, the smaller sensored camera used only the center part of the lens, not the full optic. The 1.5x or 1.6x "magnfication factor" is misleading, but it's a useful reference. It simply means that the full-frame camera needs a lens with focal length 1.5x or 1.6x longer to achieve the same field of view as the one that is cropped when the camera is the same distance to subject. Because distance to subject is now unchanged, the perspective of an image taken with a 50mm lens on a "1.6x camera" is the same as one taken with an 80mm lens on a full-frame camera.

Bottom line is that changing focal lengths (and thereby changing angle of view) does not have a direct effect on perspective or perspective distortion. Similarly, cropping an image, either after the fact or "in camera" via a smaller sensor, has only an indirect effect.

I hope that is helpful.
Everybody got to elevate from the norm!
Well stated Slej Smile My understanding agrees exactly with what you say, and I couldn't have said it better.

I won't add anything because it can be a very confusing topic and I think he's managed to state it in simple terms (relative to the complex knots many threads on this topic end up tied in). Well done!
Adrian Broughton
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"Everything should be made as simple as possible, but no simpler." - Einstein.
Thanks Kombi. Cool

But notice I didn't touch the issue of DOF. Wink I've seen some very bizarre results when playing with an online DOF calculator, such that a camera with smaller circles of confusion (an APS-C DSLR, for example) actually generates less DOF than a camera with larger circles of confusion (a full-frame camera), using the same focal length lens at the same aperture and same distance to subject. Intuitively this makes no sense, as smaller circles of confusion (i.e., smaller sensors) should produce greater DOF when all else is held constant. I need to look further into that.
Everybody got to elevate from the norm!
thanks a lot!
great info, and I seem to have been misinformed about the effect of lenses.
What you say about changing the distance makes perfect sense.

slej, what was that calculator you used?

Hi Uli,

I used two actually; Dofmaster and Bob Atkin's.

Example: 50mm lens, f/2.8, 10 meters to subject. A camera with a 0.019mm circle of confusion (10D with 1.6x APS-C sensor) will show less DOF than one with a .03mm CoC (1DsMkII, full-frame 35mm sensor.) And, as I've since learned, this is 100% correct!

Intuitively, I expected smaller CoC to equal more DOF. So a 10D should have more DOF than a 1DsMkII. And I'm correct - assuming the field of view is held constant. (Here we go again! :sigh: ) But of course, keeping the FOV constant means using two different lenses.

What I missed was the obvious: a 50mm lens on a 10D does not have the same FOV as the same lens on a 1DsMkII. I got trapped by "35mm equivalent" focal lengths, not actual physical focal lengths.

There's lots of math involved, and it's best to read about it here:

His summary follows:

Quote:1. For an equivalent field of view, the EOS 10D has at least 1.6x MORE depth of field that a 35mm film camera would have - when the focus distance is significantly less then the hyperfocal distance (but the 35mm format needs a lens with 1.6x the focal length to give the same view).

2. Using the same lens on a EOS 10D and a 35mm film body, the 10D image has 1.6x LESS depth of field than the 35mm image would have (but they would be different images of course since the field of view would be different)

3. If you use the same lens on a EOS 10D and a 35mm film body and crop the 35mm image to give the same view as the digital image, the depth of field is IDENTICAL

4. If you use the same lens on an EOS 10D and a 35mm film body, then shoot from different distances so that the view is the same, the 10D image will have 1.6x MORE DOF then the film image.

5. Close to the hyperfocal distance, the EOS 10D has a much more than 1.6x the DOF of a 35mm film camera. The hyperfocal distance of the EOS 10D is 1.6x less than that of a 35mm film camera when used with a lens giving the same field of view.
Everybody got to elevate from the norm!
Arrgh confusing indeed. As they say, ignorance is bliss! Big Grin

Nice explanations slej... now compare a focal length with film vs an equivalent focal length with digital... :o

I am coming back to this after years,
wondering if anybody knows WHY tele lenses have shallower DOF than wide angles?
Or is this a twist again and the apparent shallower DOF is really a compressed DOF?

I vaguely remember reading something along those lines, but am not sure, where it was.
Can't find it in any of the number of books by Andreas Feininger I have and usually consult for
matters of optics etc.

Excited to read your thoughts on this!

Cheers all,

I had to re-read my posts above to see if I still understand them. Fortunately the brain is still pretty sharp, even if the rest of the body is falling to pieces. :o


wulinka Wrote:wondering if anybody knows WHY tele lenses have shallower DOF than wide angles?
Or is this a twist again and the apparent shallower DOF is really a compressed DOF?
I've got a song in my head: "Let's twist again, like we did last summer! Let's twist again, like we did last year!" Cool

The perspective effects are tricking you. DOF is essentially the same when the lenses are stopped down to the same aperture setting and the subject fills the same amount of the frame.

Great examples here:

Most convincing is the enlargement of the 17mm shot at the bottom. Compare the tower in the background of that one to the tower in the 100mm shot. Looks pretty close to identical to me.

Big Grin
Everybody got to elevate from the norm!
Slej, that was the article I was going to look for, too.

The problem that I have with the L-L article is that it's really simplifying the question so that it gets the right answer. All it's demonstrating is that the DOF doesn't extend beyond the subject to infinity; at no point would I have expected it to. Even at the shorter focal lengths he's too close to the subject to reach the hyperfocal distance of the lens - if he shot the exact same test but with a beachball instead of a small toy as the subject, perhaps we'd see different results. Also if it was shot with the same rule about keeping the subject the same size, but was shot at an angle to a fence or some other object with fixed scale that recedes into the distance, we'd see the actual changes in the zone of acceptable sharpness.

Instead of looking at the CN Tower at infinity, look at the other details in the background, such as the trees and the cars parked in front of the building. There's clear differences in the amount of OOF blur, even between the 28mm and 17mm shots. While these still aren't sharp, the depth of field is changing, although with the reduced background at the longer telephoto length it's impossible to say just how much.

(Incidentally, I just went looking for information on one of my lenses with the google search 'dof 35-100', and my own website was in the first page of results. It shakes my faith in the whole Internet thing.)

And thanks for getting that song stuck in my head... Big Grin • @matthewpiers | | @thewsreviews •
I agree, Matthew, this should be tested in a more controlled setting. But, for many real-world situations, I think the examples hold up well.

Part of the optical confusion could be that total DOF (zone of acceptable sharpness) does stay pretty much constant, but the distribution of DOF in front of, and behind, the plane of focus changes rather dramatically at different focal lengths.

This page explains it pretty well, with a DOF calculator to play around with:

Another factor not mentioned there is the "quality" of the out of focus area (bokeh,) which can also vary dramatically from lens to lens, and could contribute to the apparent sharpness/softness.

Got another song in my head now, Rush's Camera Eye ... "the focus is sharp in the city!" Cool
Everybody got to elevate from the norm!
Thank you Mitch and Matthew!

the L.L. article supports my idea that DOF appears shallower when using longer lenses, due to the perspective "compression".
I am still ruminating about how it can be that if closer focussing distance should produce larger DOF, we
usally find that with wide angle lenses, which have to be used comparatively close to an object, we have the greatest difficulty blurring anything in the picture.
My explanation so far is that with a wide angle lense the field of view covers only a short distance, so that most if not all of the DOF lies within the FOV. Is that tentatively correct?

As for macro lenses and their specific peculiarities, I have to read more. I did not really understand the pupil magnification factor, and it is odd that with macro lenses, getting even closer DOF is reduced now.

Twisting my brain indeed! And having fun doing it too Smile


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