How do you determine the acceptable Circle of Confusion for a particular photo?

Question

I've noticed that several online and/or downloadable Depth of Field Calculators use different values for the acceptable CoC (Circle of Confusion) for some of the same camera models/sensor sizes. This, of course, leads to different DoF (Depth of Field) results when any particular lens and aperture are entered. Below the rest of this question is a quote from Russell McMahon's answer to this question: Analysis of a macro shot with very fast shutter speed

Since the acceptable CoC entered in the formulas affects the DoF calculated, what criteria is used to determine acceptable CoC? The two numbers (0.029mm for Full Frame and 0.018mm for APS-C) listed in the Wikipedia article for CoC seem to be based on a set viewing distance and print size. Several of the online DoF calculators use different CoC values for cameras with sensors the same size as the FF and APS-C used in the Wikipedia CoC article. Wouldn't the acceptable CoC change for prints of different sizes from the same size image or a web displayed image at varying screen sizes/resolutions? How would you calculate an acceptable CoC for a given veiwing size and distance?

DOF

f = focal length
N = Aperture f number
c = circle of confusion
s = subject distance (assumed >> f)

from Wikipedia DOF

c ~= 0.025mm for FF 35mm.
c ~= 0.018mm typical crop APSC.

see Wikipedia COC

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Some more DOF calculators

Many provide hyperfocal distance as well.

• Bob Atkins - useful discussion and a useful tabular output calculator.

• Cambridge

• Canon

• Outsight

• AppBrain

• Simple DoF Calculator (iOS app)

Answer 1

The acceptable CoC depends on the point at which increases in resolution yield only a marginal increase is perceived detail. This in turn depends on your eyesight, distance from the media and properties of the media in question.

You can either determine this value yourself, or accept a figure that Zeiss (supposedly) came up with decades ago and divide the diagonal of your print size by 1730. Most do the latter.

One final note, the acceptable CoC for web sized shots is huge, so much so it renders DoF calculations almost redundant.

Answer 2

How would you calculate an acceptable CoC for a given veiwing size and distance?

Depth of Field is based on the arbitrary Circle of Confusion, used to define the blur. Decades ago, Gauss thought it ought to be CoC of (diagonal divided by 1730), but today (color is a significant difference), CoC of diagonal divided by 1500 is nearly universal (but is still an arbitrary guess about blur, which cannot be precisely defined... kinda depends, and it is arbitrary).

Coc is computed on the film or sensor diagonal. It's just an arbitrary rough guess attempting to measure blur, which is a very vague thing. Gauss also assumed the standard of viewing an enlargement of an 8x10 inch print viewed at 10 inches. Viewing enlargement is an extremely important factor in Depth of Field.

The question is, if converting to other viewing situations:

If viewing a diagonal twice as large as 8x10, then acceptable CoC is reduced to half diameter, simply because we see the blur in the enlarged copy better, enlarged 2x.
If viewing from twice as far as 10 inches, then acceptable CoC diameter is doubled, because we see it less well, half size.
And the vice-versas of course.

Computing on the diagonal attempts to equalize for different sensor or print shapes, but is of course a different number than computing on width. That difference supposedly affects the 1730 or 1500 decisions. Many vague assumptions are included.

It is an angular size concept, but there are no hard answers about Depth of Field. And Depth of Field gradually changes with distance, there is of course no sharp line at the computed limit. There will be virtually no difference slightly either side of the computed limit. Numerical Depth of Field is at very best, an extremely rough guide.

Understanding and using Depth of Field is MUCH LESS ABOUT any computed numbers, and VERY MUCH MORE ABOUT understanding how to use the factors that increase or decrease it (f/stop, distance, focal length, and sensor size).