DOF Master Question

[delucr]

Newbie question: I was reading about DOF, COC, and Hyperfocal distance etc and discovered this DOF Calculator (http://www.dofmaster.com/dofjs.html)

One thing that does not make sense to me is that I expected the results for the Hyperfocal distance for 50D and 35mm film to be the equal for Focal lengths that are the crop factor apart. Meaning, if I use the same aperature (say f/4) and 50mm for the 5dII and 80mm for the 50D (assuming cf of 1.6 is correct) then the hyperfocal distance should be the same, right? Is this a bad assumption or am I missing something? It looks like the calculator is using a crop factor of 1.3 for the 50D.

Any insight on this would be appreciated.

-Rich

[rent]

the coc (http://www.dofmaster.com/digital_coc.html), which is a variable used for calculating hyperfocal distance, is different for 50D and 5D.

-alex

[tzalman]

Sharpness and thus DoF depend on print size, i.e. on enlargement. The standard is an 8x10 print. For full-frame this is an 8X enlargement but for a 1.6 cropper it needs a 13X. Therefore, the smaller image must be held to a more demanding standard, a smaller CoC.

[delucr]

Thank you for the responses.

Tzalman, your explaination makes sense but why wouldn't the CoC be the same if the output medium is the same? Wouldn't the crop factor acount for the enlargement differences between FF and the cropper?

[20droger]

This has to do with how the Circle of Confusion (CoC) diameter is defined. The "visual acuity" version of the definition goes as follows. There are other ways to define the CoC diameter.

We capture an image using a 50mm lens on a full-frame (36×24mm) 35mm-film camera. If we then print the image at 12×8 inches (a 10×8 print expanded to the camera's aspect ratio) and view it at 16.7" (an appropriate distance for a print that size), we have what we may call a "actual-size" print. That is, the angular separation of any two points on the print is the same as the angle of view of those same two points when viewed by the naked eye from the camera's position. The "actual-size" print thus described was arbitrarily decided upon as a standard for depth of field calculations decades ago (back when 35mm cameras were new).

Here is where the angular part comes in. It is known that the average human eye with 20/20 vision has a visual acuity of about 1/3000 radian, or, very roughly, 1 minute of arc (1/60 of a degree). This means that the eye can distinguish two dots that are separated by 1/3000 radian or more. Any less separation, and they become one dot.

On our "actual-size" print viewed at 16.7 inches, this would be a separation of about 0.0056 inch. Tracing this backwards, this would be a separation of about 0.017mm on the film.

0.017mm, therefore, is the "perfect" CoC diameter for a full-frame 35mm-film image, or its digital counterpart.

Camera manufacturers, and optical engineers, had a problem with this "perfect" CoC diameter. It was completely swamped by other factors, such as the resolving power of the lens and the granularity of the film. Therefore, they decided upon a somewhat looser standard of about twice the "perfect" CoC diameter, or about 0.034mm.

However, not everyone agreed with this. Canon, for example used (and still uses) 0.035mm as its CoC diameter. Leika prefers a much more stringent 0.024mm. A compromise was reached by most (but not all) manufacturers (most notably, our favorite "N" manufacturer) of 0.031mm. Virtually all DoF calculators presume 0.031mm as the full-frame 35mm-film CoC diameter.

This 0.031mm is about 1/1400 the diagonal of the full-frame 35mm-film image (the negative). Because the CoC diameter is an angular phenomenon, if we wish to use a camera with a different size film/sensor to produce our "actual-size" print, we must trace backward from our "actual-size" print to that camera's film/sensor.

We find that the CoC diameter for any camera remains about 1/1400 the actual film/sensor diagonal. The ratio of the film/sensor diagonal to the diagonal of our original full-frame 35mm-film image then becomes relevant.

Put another way, divide the 0.031mm full-frame 35mm-film CoC diameter by a camera's sensor factor to get the CoC diameter for that camera. For a Canon APS-C camera, such as any of the Rebels or the XXD cameras, 0.031mm ÷ 1.6 = 0.019mm. For a Nikon DX camera, 0.031mm ÷ 1.5 = 0.021mm. For a "four/thirds" camera, 0.031mm ÷ 2.0 = 0.016mm. And so forth.

It all goes back to the "actual-size" 12×8 inch image (viewed at 16.7 inches) used as a standard, and the somewhat-but-not-completely-agreed-upon softening of the "perfect" 0.017mm CoC diameter to 0.031mm.

This all further complicated by the fact that each of us has a slightly different visual acuity, and it is the visual acuity of the viewer, not the photographer, that matters.

This should help you understand why it's called the Circle of Confusion diameter.

[delucr]

Wow, Circle of Confusion indeed! Thank you for your detailed explanation. It makes more sense now.

-Rich

[Willie]

The main reason for the difference is the fact that you are using different focal length.

[Wilt]

Perfect explanation about CofC, 20droger, providing insight which I have always been too busy or lazy to write!!!