Pupil magnification and depth of field

The following discussion about pupil magnification is a continuation of the discussion here:
https://www.cambridgeincolour.com/forums/thread3176.htm

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Originally Posted by McQ

The two* main factors controlling depth of field are aperture and subject magnification. Aperture is pretty straightforward: larger apertures (smaller f/number's) decrease depth of field. Magnification is where it gets more complicated, because it's actually comprised of two parameters at once: subject distance AND focal length. However, the net result is that higher magnification decreased depth of field for a given aperture.

Yes, focal length does not affect depth of field, but only if the magnification is kept constant. If you stay at the same distance from your subject, using a longer focal length will decrease the depth of field (because this increases subject magnification). This is where sensor size comes into play. At the same subject distance, a larger sensor necessitates that you use a longer focal length in order to produce the same composition. However, this causes the depth of field to decrease, so you also have to use a smaller aperture in order to produce a similar-looking image (both in terms of DoF and composition).

I think a big source of confusion is with the meaning of the word "magnification"; this isn't how big the subject appears in the image, but how much they have been enlarged in absolute terms (on your sensor itself). A larger sensor needs to magnify a subject more in order for the light from this subject to fill the sensor area.

*of course, one's definition of the circle of confusion also affects DoF, but for relative comparisons this value is fixed and standard, so it's irrelevant for the above discussion. Focal length also comes into play a little, but only for extremes of magnification.

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I get it, it has to do with pupil magnification. Of course, there's only one little tiny paragraph which starts with "For Macro Photography"at the end of the DOF article about this. How do you calculate it? How do you calculate its effect on DOF?

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Originally Posted by Flammel

I get it, it has to do with pupil magnification.

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Pupil magnification (P) is entirely different from subject magnification (M). Everything that was said before still holds true unless we're talking about extreme macro photos. Pupil magnification depends on the symmetry of your lens's internal elements. If your lens is highly symmetric, then P=1 and it doesn't affect depth of field. Highly asymmetric lenses will have a P which differs from 1.

The problem is that one 50 mm lens doesn't necessarily have the same pupil magnification as another 50 mm lens. P depends on the internal design of your lens. Very generally, telephoto lenses have a P<1, while wide angle lenses generally have a P>1. However, P isn't necessarily a strict function of focal length. P is really something that needs to just be looked up for your particular lens -- if it's even available. There are also ways of measuring P yourself, but that can be somewhat involved and largely irrelevant to taking good photos (you rarely need to know the exact DoF a priori; experimentation is definitely best).

However, if you want to get more technical, you can calculate the influence of P on depth of field using the following formula:

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Total DoF = 2NC(1 + M/P) / [ M^2 - (CN/f)^2 ]

where: N = aperture, C = circle of confusion diameter, M = subject magnification (discussed above), f = focal length

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For a symmetric lens, P=1 and therefore depth of field is equal to:

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Total DoF = 2NC(1 + M) / [ M^2 - (CN/f)^2 ]

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From these we see that when P>1 it acts to decrease DoF, whereas when P<1 it acts to increase DoF. Further, even when P differs from one, it only influences the [1 + M/P] term substantially when M is large. In other words: only for macro work.

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Originally Posted by Flammel

Of course, there's only one little tiny paragraph which starts with "For Macro Photography"at the end of the DOF article about this.

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Making pupil magnification and macro a more central part of the Depth of Field Tutorial would change its focus. It's intended to give a clear, concise intro to the main factors influencing DoF. Macro work is only a subset of most photography, and even then pupil magnification is often not as influential as aperture (N), the circle of confusion (C) and subject magnification (M).