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I read in this paper by Toshiba, which is in regards to optics in machine vision, that

In machine vision, which processes each pixel of an image sensor at high brightness levels, the permissible circle of confusion (δ) is calculated based on the pixel pitch (Ppix) or the diameter of the Airy disk (DAiry) that represents a limit to the optical resolution of an image created by a lens. In the case of monochrome cameras, the larger of these values is used as δ.

Nevertheless, I've also read many answers in regards to other questions on pixel size and Coc that pixel size tends to not be the limiting factor but rather other factors. Per the accepted answer to the question, Clarification for Effect of Pixel Size on Depth of Field:

Actually, this isn't right. The CoC criterion is the largest blur that will be perceived by the viewer as a point. At low resolutions, this may be limited by pixel size, but generally in real world use other factors are dominant ­— display size, distance of viewer, etc.

As well as the fact that circle of confusions tend to be much larger than even a grid of 2x2 cells on a sensor. (C.f.: the accepted answer to How do depth of field and the circle of confusion relate to pixel size on the sensor?)

I'm sure this might also relates to a demo I saw on Steve Yedlin's site, where he displayed that the difference between a 2k and 4k output is perceptually nothing, as the average viewer in average viewing conditions was not able to resolve the extra pixels.

To me it seems like that the first statement of circle of confusion criterion being equal to the size of either the airy disk /pixel pitch contradicts the other statement, where it pixel size doesn't determine the coc criterion.

What am I not seeing?

Side Note: I've already written quite a few questions and have gotten even more incredible answers, although I tend to take some time to truly grasp them. Nevertheless, if anyone knows any great reliable resources to learn a lot of these things, it would be much appreicated. I understand that searching on the internet may be the best tool, but obviously there is the dilemma of if the particular source is reliable resources.

scottbb
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vannira
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  • Where is the question? – Euri Pinhollow Oct 02 '23 at 09:57
  • Apologies I just edited the text. I hope my question or rather confusion is more clear now – vannira Oct 02 '23 at 10:16
  • As well as the fact that circle of confusions tend to be much larger than even a grid of 2x2 cells on a sensor. - is that a part of the quote? Please use quote formatting for quotes. – Euri Pinhollow Oct 02 '23 at 12:02
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    Please summarize your question into a single, complete sentence, that asks what you're trying to ask. As it stands, there are only 2 questions here: your title, which even though it ends in a question mark it isn't a question (it's just 2 related noun phrases); and "What am I not seeing?". The latter is very difficult to answer, because it asks us to assume about your assumptions. Thanks. =) – scottbb Oct 02 '23 at 17:20
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    Does this answer your question: For digital sensors and in terms of imaging medium, is the minimum CoC equal to the size of 1 sensor pixel or 2? And why? – scottbb Oct 02 '23 at 17:48
  • It is correct that the text of the “2x2 cell” is from the text I read, however it is not verbatim and rather just what I understood from it, hence why I didn’t feel comfortable quoting it, as it isn’t a quote. I do try my best to always correctly format the quotes with quote notions. – vannira Oct 02 '23 at 21:36
  • Thank you for the link scottbb, I will go check it out and hopefully it will help answer some of the confusions I have.

    Apologies for my question formatting or rather just the formatting of my whole text. I was aware that my question in the title wasn’t really a question. I suppose I was just trying to regurgitate a bunch of the things I have read about and was asking for help, in trying to fit the puzzle pieces together. Perhaps the question that could be derived from/within my long winded text could be “ I read these two things that seem juxtaposing to me. Are they ? If not why not ?”

     – vannira Oct 02 '23 at 21:38
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    @vannira You're doing really well here; thanks for accepting positive constructive feedback cheerfully. No need to apologize for formatting, etc. Some of us are happy to "spruce up" or polish questions for better readability; after all, people come across questions and answers here years after they were asked or answered. I think you're seeing first-hand how SE works best: straightforward & clear questions, followed by lots of answers that are happy to explain in varying detail. But if the answers have to first undo your assumptions, then clarify & answer, it gets wordy. =) – scottbb Oct 03 '23 at 17:21
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    @scottbb Thank you, I will try to improve the formatting of my questions. I think the issue is that sometimes, I don't even quite know myself what I don't understand. However, I do get that better formed questions, will make it easier for people to answer them. – vannira Oct 03 '23 at 18:29

4 Answers4

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Pixel pitch does not determine the standard CoC limit, and it is not a factor considered in the DoF calculations.

That's because the accepted CoC limit for normal viewing by an average individual is far less demanding. The CoC standard requires less than 2MP of image resolution for viewing any size displayed image... every camera far exceeds that requirement. I.e. the limit is human perception (~20/40 vision viewing an image from a distance equal to the image diagonal (~45˚ HFOV)). Note that most images viewed on your computer are at ≤2MP.

But the airy disk most certainly relates to pixel pitch in terms of recorded resolution. If the airy disk is much smaller than a pixel, it cannot be resolved. As the airy disk becomes larger than the pixel, contrast is reduced (which is a large portion of our perception of sharpness/resolution). When it becomes ~ 2x the size of the pixel, recorded resolution drops (depending on contrast requirement). And when it becomes larger than the CoC limit, visible resolution decreases in the output image (when viewed according to the standard).

The scenario where the airy disk exactly matches the pixel pitch is less than ideal as well; because it results in aliasing errors when the two do not line up (which is more probable than not).

And for viewing conditions other than standard the standard CoC is not applicable. I.e. for a large format print to be viewed at short distance in a gallery, you might want to use a much smaller CoC limit (or for machine vision).

You might like to read this paper: Do Sensors Outresolve Lenses' Capabilities?

Steven Kersting
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  • First and foremost thank you for including a paper for me to read. – vannira Oct 03 '23 at 07:07
  • Nevertheless, I have a couple of more questions that have arises from your answer.

    1. I’m not sure what is meant by the “coc standard requires less than 2MP resolution for viewing any sizes displayed image”. I’m assuming this means that at that certain resolution something isn’t the bottleneck anymore, but ya I just don’t quite understand sorry.

    2. You mention how airy disks, if they are smaller than a pixel they are not resolved? Is it not when it’s larger than the pixel as you mention after.

     – vannira Oct 03 '23 at 07:17
  • You mention all these ways in which airy disks limit the resolution , e.g. such as aliasing; however if I am understanding on a perceptual level these reductions in resolution are not visible to the average viewer, unless the airy disks exceeds the COC (which is unlikely?). Or are the effects of aliasing and resolution drops already visible
    • – vannira Oct 03 '23 at 07:21
  • Perhaps I should also mention that I am more interested in the aspect of the effects on cinema. However, I am aware that with movies being watched in various displays it can become very convoluted. – vannira Oct 03 '23 at 07:26
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    @vannira, If the airy disks are smaller than the photosite multiple disks will fall on a single pixel and cannot be resolved; they will be resolved as a single larger detail, and in this case the image resolution is limited by the sensor, and not the lens/diffraction. You can calculate the number of airy disks at the CoC limit size that will fit on the sensor. If you use the standard CoC limit (i.e. 30 micron for a 35mm sensor) it is less than 1MP. And even if you consider nyquist and use 2 pixels per it is less than 2 MP (but you don't need to). – Steven Kersting Oct 03 '23 at 12:10
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    And yes, these reductions are not visible to the average viewer under typical conditions... particularly in cinema where things like out of focus regions and motion (blur) will tend to be far more limiting on resolution. I.e. no one benefits from 4k video according to the CoC standard. But that standard is very lax, and quite arguably outdated. According to the limits of human vision, the CoC standard should require ~ 12-14MP for the most critical viewing of a still image (as a whole) in optimal conditions. – Steven Kersting Oct 03 '23 at 12:19
  • I am not sure I understand, so to calculate the n of airy disks I would need to first calculate its diameter using the formula D = 2.44 * (λ * f) / D_aperture and then I would do: Number of Airy Disks (N) = (Width of sensor / D) * (Height of sensor / D), but what are the values I would plug in for the aperture and the wavelength of light. Also would this mean that the number I achieve from this, tells me that a sensor with pixels above this value would be redundant, or irather 2 times (cause of nyquist)would be redundant because the bottleneck is the diameter of the airy disks? – vannira Oct 03 '23 at 15:53
  • however, then you mention that the coc should actually be 12mp - 14mp and and not the theoretical value you just previously calculated of 1 or 2 mp. Why is that? I also am very interested on how much resolution is "too much", i often hear and have seen demos that show that 4k and 2k have perceptually no difference to the average human in average conditions and is it true that due to the Nyquist sampling theory, 4k and 2k acquisition is displayed as 2k and 1 k. – vannira Oct 03 '23 at 15:57
  • I also just realised that i don't see how coc, factored into the calculation for the number of airy disks that fit into the sensor size and this again makes it seem like that airy disks are actually the bottleneck, but as we discussed before airy disks < coc. I apologize if all my questions seem silly and that despite your answers I still find it difficult to grasp. – vannira Oct 03 '23 at 16:05
  • The paper I linked provides the minimum airy disk sizes for various wavelengths (RGB) and various apertures (absent any optical aberrations). Let's move this to chat... – Steven Kersting Oct 03 '23 at 16:44
  • Let us continue this discussion in chat. – Steven Kersting Oct 03 '23 at 16:44