For digital cameras, is circle of confusion based on one pixel, two pixels, or something else?
Asked 6/2/2013
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When calculating depth of field for a digital camera, should the minimum circle of confusion (CoC) be tied to pixel pitch, such as one pixel or two pixels, or is CoC defined differently? For example, on a full-frame sensor with roughly 0.0064 mm pixel pitch, should the CoC be about 0.007 mm, 0.014 mm, or neither? I'm trying to reconcile explanations that mention pixel size with traditional depth-of-field calculations.
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
13y ago
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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.
Originally by user15871. Source · Licensed CC BY-SA 4.0
user15871
13y ago
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For depth-of-field calculations, CoC is not fundamentally defined by 1 pixel or 2 pixels. It is a viewing criterion: how large a blur spot in the image can be enlarged to a final print/display and still look acceptably sharp at a normal viewing distance.
That’s why traditional CoC standards existed before digital sensors. Sensor size matters because it affects how much the image must be enlarged for the same final output. Pixel size mainly matters when you inspect at 100% or extreme magnification on screen.
At pixel level, a blur smaller than one pixel may be recorded mostly in one pixel; once it spreads larger, neighboring pixels are involved. But that does not make the DOF CoC equal to exactly 1 or 2 pixels in general use.
So the best answer is: neither. Use a CoC appropriate to the intended output and viewing conditions, not a universal pixel-count rule. If you are judging sharpness at 100% crops, then pixel pitch becomes relevant; if you are calculating conventional DOF for prints or normal viewing, CoC should be based on final image size, viewing distance, and sensor format rather than a fixed 1-pixel or 2-pixel minimum.
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