Sorry David, I thought you were on to something that might have been correct in certain theoretical circumstances but unfortunately you are wrong in your use of the CoC term and everything follows from that.
Nick,
I think you almost got it, but somehow you managed not to trust your own intuition. I used the term "acceptable sharpness" above because historically that is how DOF was described for the optics of human vision before photography was even invented, and it is still used today in various fields (e.g., optometry). In these situations, CoC is indeed characterized by human visual characteristics involving "acceptable sharpness" such as acuity and the various viewing conditions as already pointed out. With the invention of photography, it became possible for film to quantify DOF into an objective value based on the resolution of its emulsion, rather than the subjective visual ability of any one person. To answer the other question posted here about variances in film, yes different film grain sizes mean different CoC values and likewise different DOF. It is no different for digital cameras. Digital cameras having different pixel sizes means having different CoC values for their rendering, which means having different values for the resulting DOF. Once again, I cite the spreadsheet by Alpa that explicitly shows how Alpa views objective CoC values that vary with pixel size and corresponding capture device.
Let me try one more time and hopefully my position will become more clear.
DOF is always and only defined in a three dimensional space and in relation to an optical axis. So, by viewing with your eyes a print, or a projected transparency on a screen, or a jpeg image on a monitor, etc., the DOF of all these objects as you look at them squarely must be essentially zero, since they are basically 2D planar objects along your axis of sight. For example, I can take a photograph of the Sydney Opera House and the Harbour Bridge together within the same DOF, which is something probably around 3 km (depending on the lens being used, my location and the CoC of the film). However, once this scene has been rendered into its 2D form, what is now the optical axis being used to view it as a print? The optical axis is now along your eyes looking at the print, and so the DOF in this situation can be nothing other than zero, since you are looking at a piece of paper and not the actual Sydney Opera House. Therefore, when you talk about "depth" in a photograph, as you correctly indicated in one of your previous responses, you are only talking about the
illusion of depth perception. This perception of "depth" cannot be said to be the DOF of the scene that was captured, since again DOF is a distance defined by the laws of optics in three dimensional space.
Yes, the perceived depth in a print can be related to the DOF of the underlying captured image, but the converse is not true and they are not the same thing. The perceived depth in the print may not only involve the subjective visual dependencies that have already been identified in this thread, but it can also depend on a wide variety of other things via software manipulation such as selective blurring or sharpening,
neither of which would change any CoC that may be associated with the print (or that of my eyes).
As an example, suppose I make a straight print of a digital image. Now suppose I slightly but noticeably blur only small selective parts of this same image using a Photoshop layer prior to creating a second print having the exact same size and under identical viewing conditions as the first print. All aspects of this second print are the same as the first print, except that it will have an illusion of slightly reduced depth due to my selective blur. None of the printing characteristics have changed, ink has not changed, paper has not changed, enlargement factor and print size have not changed, raw image file has not changed, viewing distance has not changed nor anything associated with the viewing conditions. Yet, I am able to produce for you a second print which is identical in every way to the un-blurred first print, except for its slightly reduced perceived depth. And, the blurring layer is carefully done using special brushes and cloning procedures to ensure that it cannot be claimed that I have changed the CoC of anything. You already agree that DOF must depend on a CoC. So, how do you now explain how these two prints can have different "DOFs" but without having different CoCs under otherwise identical conditions?
The answer is that you can't. Under otherwise identical conditions, only
perceived depth in the prints can be different without having a different CoC. This is because the digital printing process may include masks or filters that can change the perceived depth in the resulting print without changing any CoC. This cannot be true for DOF according to the physical laws of optics, and the DOF can only change if the CoC changes (all else being equal). Simply put, the printing process does not play any role whatsoever in the definition of DOF. Certainly, printing considerations are not needed when computing the DOF for lens systems such as eyeglasses.
Therefore, and my point in this entire thread, the
DOF associated with a captured image cannot depend on any particular print of it. The CoC used to define DOF must be that which is associated with the film or digital sensor used in the capture rendering process, and not the printing process.