depth of field - 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?

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? For example purposes using a 35mm Full Frame digital sensor where the pixel size is 0.00639mm (and rounding up), is the minimum CoC 0.007mm or 0.014mm?

In What exactly determines depth of field? jrista says

Digital sensors do have a fixed minimum size for CoC, as the size of a single sensel is as small as any single point of light can get (in a Bayer sensor, the size of a quartet of sensels is actually the smallest resolution.)

However, later on jrista says

In the average case, one can assume that CoC is always the minimum achievable with a digital sensor, which these days rolls in at an average of 0.021mm, although a realistic range covering APS-C, APS-H, and Full Frame sensors covers anywhere from 0.015mm - 0.029mm

Using the number 0.015mm for minimum CoC on digital full frame sensors is about 2 sensor pixels in size instead of 1, does this not match up to what was said originally? Or does it, by implying (but not explicitly stating) the use of a bayer sensor which is said above to have a minimum CoC equal to a quartet of pixels, and that would be 2 pixels wide and ~0.0015mm?

And in Why do some people say to use 0.007 mm (approximate pixel size) for the CoC on a Canon 5DM2? Michael Clark says

With digital sensors, the size of the pixel determines the size at which the circle of confusion (CoC) becomes significant when viewing at 100% crops. Any blur circle smaller than the pixel pitch will be recorded as a single pixel. Only when the blur circle becomes larger than an individual pixel will it be recorded by two adjacent pixels.

However, this webpage that is very interesting says

The smallest size of the image CoC may be limited by other factors. For digital sensors, the CoC cannot be smaller than the physical size of two pixels (image elements). Obviously nothing smaller can be resolved. Typical pixel sizes for high resolution digital cameras are in the range of .006 to .012mm. These sizes yield resolution numbers of 83 lp/mm and 43 lp/mm respectively. These equate to CoC values of .012 and .023mm. A similar effect is unavoidable with film emulsions since the grain size determines the size of an individual image element. The typical “graininess” of film varies from .004 to .018mm.

The idea of using the size of 1 sensor pixel as explained by Michael Clark makes good sense to me, so I'm confused by the other website's idea above that it's 2 pixels, it's seems like everything else in that article is accurate and well said, it's hard to believe he's incorrect about the minimum CoC size.

j-g-faustus said and seems to imply diffraction/airy disk size is related, is he correct in saying 'the point where you can no longer tell two airy disks apart doesn't happen until the airy disk diameter reaches 2 pixels" -- I thought the airy disk became a problem when it was larger than 1 pixel or larger than the image's CoC???

@DavyCrockett I think using two pixels makes sense, by analogy with the diffraction limit - the point where you can no longer tell two airy disks apart doesn't happen until the airy disk diameter reaches two pixels. Similarly, a CoC of more than 1 pixel will bleed over and reduce the contrast between a pixel and its neighbour, but actual Confusion, the point where you can't tell two pixels apart, doesn't happen until CoC reaches two pixels. That would be my best guess, anyway

Answer

Imagine if a blur circle (or airy disc) is striking a sensor with the middle of the circle centered on the middle of a pixel.

• If the circle is one pixel or less in width, all of it will only strike one pixel.



• If the circle is from two to three pixels in width it will strike all of one pixel and parts of the eight pixels that surround that one pixel for a total of 9 pixels in a 3X3 square.


• If the circle is five pixels wide it will strike all or part of 25 pixels (5X5 square).


• At seven pixels wide, the blur circle will cover parts of 45 pixels (a 7X7 square minus the four corner pixels because the circle will not quite reach the four corner pixels). 29 of the pixels will be completely covered and the other 16 will be partially covered.The luminance values (derived from this single blur circle, not taking into account all of the other point sources of light and their resulting blur circles falling on the sensor at the same time) of the 25 would be higher than the varying luminance values of the other 16. Among the 25 pixels fully covered by the blur circle, those nearer the center would have higher luminance values than those near the edge.

Now imagine a blur circle centered on the intersection of a 2X2 square of four pixels.

• If the circle is one pixel or less in width, it will strike parts of the four pixels that form the 2X2 square.


• Even if the circle is up to two pixels in width, it will only strike parts of the same four squares.


• If the circle is over two and up to four pixels wide, it will strike all or part of sixteen pixels (a 4X4 square). Four will be fully covered, eight will be mostly covered, and the other 4 will be less than one half covered.


• At five pixels wide, the blur circle is striking all or parts of 32 pixels (a 6X6 square minus the four corner pixels).

I think where a lot of the confusion comes in is a misunderstanding of how demosaicing algorithms do interpolation to produce an R, G, & B value for each pixel in a Bayer type sensor. If the incorrect assumption is made that the lowest unit of color resolution using a Bayer type sensor is a 2X2 pixel square, then the CoC works out to two pixels in width if you also make the incorrect assumption that all blur circles are ideally centered to cover the minimum number of pixels for their respective sizes. It also depends on if you define resolution as the smallest unit a point light source can be represented as (one pixel) or the smallest unit that can produce contrast (two pixels). When resolution is defined in terms of line pairs as in the webpage you cited, the second definition regarding contrast applies.