Circle of Confusion

The Circle of Confusion is defined as is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source. The Circle of confusion is also effected by the magnification in size of the final print vs the original film( or digital scanner) size.

This is my theory on the Circle of Confusion, I have been unable to find a solid formula for the Circle of Confusion, and most information I have found states that the Circle of Confusion value is a set number with the assumption you are going to print an 8x10. Right there I say that's just crazy, Not all pictures I take end up as an 8x10, typically they end up as 4x5 proof prints for me, and they are also cropped in slightly which would increase the magnification of the film to print size. I'm going to keep it simple by not adding in the cropping assumptions, because not all pictures are cropped the same. Here is the follow formula I've come up with based that your enlargement be full frame.

1. calculate out the diagonal of the film format 35mm is 36mm X 24mm so the diagonal is is 43.26662mm.
2. calculate out the diagonal for an 8x10 print which is 12.8 inc or 325.2587mm.
3. Print diagonal divided by film diagonal divided by print resolution of 250 dots per mm, which comes to 0.03

Here is my magic formula for CoC:

C = (P / f) / 250

C = Circle of confusion
P = diagonal of print
f = diagonal of film focal plane

here is a table of some film sizes focal plane:

Format Size Diagonal
35mm 36x24 43.3
6x4.5 56x42 70
6x6 56x56 79.1
4x5 102x127 162.8
8x10 203x254 325.1

Here is a java applet to calculate out the different values.

Based on my experience, the larger the film size the smaller the depth of field, yet at the same time, the pictures seem sharper. We'll just keep with larger film size = smaller depth of field, with the depth of field formulas based off of Circle of Confusion it does make since. I'll next combine my theory on Circle of Confusion with Depth of field to see if my theory shows true.