Finding the Diffraction Limit - doesn't it depend on focal length and pixel size?

I have a question regarding this site's diffraction limit calculator:

1. It says it compares the Airy disk diameter with the circle of confusion (CoC). However, I don't see any settings that are pertinent to the CoC calculations - like the lens focal length and the focus distance.

2. It does not look like that the results depend on the pixel size (the number of Mp). I can change the Mp anywhere from 0 to 100 MP and the diffraction limit has not change. I would assume (maybe naively) that if the pixel size is sufficiently large it can become the limiting factor and not the DOF or diffraction.

To elaborate on your queries:

1. The f-number takes into account both the absolute aperture size and focal length. Listing focal length would either be redundant or require the user to know the absolute aperture size. As for focus distance, this is a much higher order factor not necessary for the precision needed in this calculator. Other factors, such as the prevalence of a given wavelength of light, are much more influential (ie, blue light will reach its defined diffraction limit at a slightly larger f-number than green, then red, etc).

2. The results default to depending only on f-number, print size and viewing distance-- not absolute pixel size. The reason for this is to demonstrate that even if megapixels are not considered, there are fundamental resolution limits dictated by the optics alone. There is the widely held misconception that megapixels are the end all be all of resolution in a camera. In reality, as you are aware, the limit can be either the optics or the pixels, but in today's high resolution sensors, resolution is more often than not limited by optics (hence defaulting to this).

However, for the other scenario, there is an option to define the circle of confusion as being twice the pixel size (if this indeed is the limiting factor). This is why the absolute pixel size is also listed in the out box (so it can be compared to the airy disk). For quite large viewing distances, at the industry standard level of sharpness, one would be surprised how much an image can be enlarged before it becomes diffraction limited. There is much more on the topic of pixel size, diffraction and sensor size-- with a corresponding calculator for estimating the diffraction limited aperture for a given number of megapixels on the page about digital camera sensor sizes.

Hope this clears things up some.

I'm still a bit confused. The calculator is supposed to compare the C_airy and the CoC,

The Airy disk diameter indeed depends only on the relative f_number as C_airy=2.44*N*lambda ,
where N=f/d = f_number

However the CoC diameter, as you know, can not be expressed as a simple ration f/d. For example a CoC of a point object at infinity can be written as CoC=f^2/(N*F) where f is the focal length and F is the distance the lens is focused at. One can define the total blur as these two added in quadratures. This yields in an "optimum" N_opt=27*f/sqrt(F) . Below this number the resolution is DOF limited. Above the N_opt the resolution is diffraction limited.

As far as the pixel size I totally agree with you. I would only thought that if the pixel size is large enough then it would be a determining factor. So I thought plugging a small number of Mp would illustrate it.

Here's some more to address your questions:

First, the calculator is intended to demonstrate the absolute limit of maximally attainable resolution-- regardless of technique, composition and pixel size. The calculator therefore only considers objects that are on the focal plane. I think the source of confusion is the context in which you are used to using CoC. The arbitrary manufacturer standard for choosing *maximum* CoC is that on an 8x10 inch print, when viewed from 10 inches, the smallest distinguishable feature is 0.01 in (~0.03 mm on 35 mm film). This max CoC can be used equally for defining the limits of a depth of field and for defining the maximum enlargement size of a print. The diffraction calculator is only used to inform, for a given print size and viewing distance, when diffraction becomes visible-- not where to focus for optimal sharpness throughout.

When considering DoF factors, as you point out, the circle of confusion *at infinity* is CoC = f^2/(N*(s-f)) ~ f^2/(N*(F - 2f)), where "s" is the lens to subject distance. Further, assuming s >> f and s >> d, we arrive at the equation you showed below of CoC = f^2/(N*F). The CoC used here is variable and for a very specific scenario; it does not represent max CoC used in the context of defining a diffraction limit. I am much more familiar with the CoC=f^2/(N*F) formula being used for finding the hyperfocal distance when the CoC is treated as a constant and F is variable.

One thing to address from before. You had said that:

Quote:

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2. It does not look like that the results depend on the pixel size (the number of Mp). I can change the Mp anywhere from 0 to 100 MP and the diffraction limit has not change. I would assume (maybe naively) that if the pixel size is sufficiently large it can become the limiting factor and not the DOF or diffraction.

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Changing the number of megapixels for a given sensor size has no impact on whether the print itself has become diffraction limited. Of course, if there are too few pixels, the print can be become pixelated by camera resolution. However, this is still not caused by diffraction, and listing some other limit could defocus the reader from the main point of the page. This calculator is only for the diffraction limit, not assessing all components of the overall system including ccd/optics/printsize/viewing distance. There is always a trade-off between the number of input parameters they require and the ease of use of the average internet user. There are at least three factors at play here: (1) the total number and absolute size of pixels, (2) the f-number and (3) the CoC defined by the print size and viewing distance.

The interplay between (1) and (2) is in the "Diffraction Limited Aperture Estimator" at https://www.cambridgeincolour.com/tu...ensor-size.htm
The interplay between (1) and (3) is in the "Photo Enlargement Calculator" at: https://www.cambridgeincolour.com/tu...nlargement.htm
The interplay between (2) and (3) is in the "Diffraction Limit Calculator" at: https://www.cambridgeincolour.com/tu...hotography.htm

Each represents a limiting case for when the subject is on the focal plane; for subjects outside the focal plane there are pages on depth of field and the hyperfocal distance. Could all (1)-(3) be incorporated into a single all-purpose calculator? Of course. The only concern here is making it too complicated to use/interpret, or having the calculator require knowledge of information not discussed in the given article. I really try to define breaking points to separate each of the concepts into digestible chunks. It's like first learning Newton's laws and then later finding out that they are only a limiting case. Diffraction, DoF and pixel size can all dominate the print's perceived sharpness in limiting cases. Of course, as a research scientist you might want to see more thrown into the mix...

If anyone else has feedback that would also be helpful. These pages can always be improved..

Now I got it.

I think the reason of my confusion is that I understood the phrase from the calculator chapter too literally - ".... has become diffraction limited when the diameter of the airy disk exceeds that of the CoC....." It is clear now from your explanation that the assumption is ".... when the diameter of the airy disk exceeds that of the maximum CoC....."

Also, a comment on the Technical Note on the diffraction photography page: "Therefore the size of the airy disk only depends on the f-stop, which describes both focal length and aperture size." You may wish to mention that that statement applies to the 35mm format under discussion, since an f/22 on larger cameras (such as 4x5 and 8x10 view cameras) will actually be a larger opening.

You are right that larger format cameras do have a larger aperture opening for a given f-stop and angle of view. However, this is because larger formats also require longer focal lengths to achieve the same angle of view. F-stop takes into account both effects. Longer focal lengths require larger physical aperture sizes for a given f-stop, whereas the opposite is true for shorter focal lengths. The two effects, focal length and aperture size, effectively cancel such that only f-stop matters. Consider two scenarios:

(a) a long focal length and large aperture size
(b) a short focal length and small aperture size

There exists a combination of focal length and aperture size above such that the airy disc for (a) equals that for (b). For such a scenario the f-stop would be the same for (a) and (b). A longer focal length gives the light more distance over which it can spread out or diffract after passing through the aperture. Hopefully this has not added to the confusion...