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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 \$\gg f\$)

$$ \text{DOF} = \frac{2Ncf^2s^2}{f^4-N^2c^2s^2} $$

from Wikipedia DOF

\$c \approx\$ 0.025 mm for FF 35mm.
\$c \approx\$ 0.018 mm typical crop APSC.

see Wikipedia COC

Some more DOF calculators

Many provide hyperfocal distance as well.

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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.

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  • \$\begingroup\$ 1730 divided into a full frame diagonal 43mm yields .025mm. But the same print size from a 26.8mm diagonal Canon APS-C sensor would need a CoC of .0155. At d/1500 instead of d/1730 the numbers are .029 & .018 respectively. Each variation of the Zeiss formula or d/1500 I have seen includes accounting for the magnification factor of the print from the original image (negative or sensor) size, which makes sensor size the critical factor. But that still assumes a "standard" eyesight and viewing distance a la "Kodak (1972)". \$\endgroup\$
    – Michael C
    Feb 5, 2013 at 17:05
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    \$\begingroup\$ Circle me confused. Is the Zeiss formula for print size or sensor size? What if you have a 100% crop of an image? What is the acceptable CoC for viewing on screen? \$\endgroup\$
    – Rado
    Jun 7, 2014 at 14:14
  • \$\begingroup\$ @Rado That totally depends on the amount of magnification created by the 100% crop. A 36MP FF sensor with twice the resolution (4x the pixels) will be magnified twice as much on the same sized screen as a FF sensor with 9MP. \$\endgroup\$
    – Michael C
    Oct 5, 2015 at 11:21
  • \$\begingroup\$ What is the acceptable CoC (chaotic circle) diameter of an object (such as a car on the street) directly observed with the eyes? \$\endgroup\$
    – enbin
    Apr 5, 2020 at 13:26
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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).

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  • \$\begingroup\$ There are actually many DoF calculators that allow input from the user regarding viewing distance, display size, and even the vision standard assumed for the viewer. Some of them stray well away from the 1730 1500 "standards" interpolated for those varying conditions. Here's one such calculator (click on the "show advanced" button): cambridgeincolour.com/tutorials/dof-calculator.htm \$\endgroup\$
    – Michael C
    Dec 24, 2016 at 16:20
  • \$\begingroup\$ And if interested in intentionally blurring the background (interested in the CoC at the background) see scantips.com/lights/dof.html#calc \$\endgroup\$
    – WayneF
    Dec 24, 2016 at 16:51
  • \$\begingroup\$ That's a nice tool at the link. It does stay tied to 1730 and 1500, though. Different manufacturers have historically used different numbers based on their varying expectation of the viewer's visual acuity. The Zeiss standard assumes 20/15 vision. 1500 assumes 20/20 vision. \$\endgroup\$
    – Michael C
    Dec 24, 2016 at 17:57
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    \$\begingroup\$ CoC is not really arbitrary in the sense that the concept is based on the maximum blur that will still be perceived as a point by a viewer viewing the prescribed enlargement at the prescribed distance with the prescribed visual acuity. In that sense, even though the sharpest thing in the image is at the exact focus distance, we can't tell that it is sharper that anywhere else in the DoF where the CoC is still perceived as a point when we are viewing it. \$\endgroup\$
    – Michael C
    Dec 24, 2016 at 18:07
  • \$\begingroup\$ The background DOF tool correctly defaults to 1500, but it offers any choice of CoC that you want to use. And perception of CoC seems quite arbitrary. That's why we have many numbers. :) \$\endgroup\$
    – WayneF
    Dec 24, 2016 at 18:18

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