In response to some e-mail comments about my anti aliasing posts, I’ve been thinking about diffraction, and how it affects format selection. In order to clarify my thinking, I prepared the following spreadsheet:
In the first column is the f/ stop. The second column is the horizontal or vertical pixel spacing in micrometers of a sensor capable of resolving a diffraction-limited image at that f/ stop in green (530 nm) light. The next five columns display how many (monochromatic — this won’t work for Bayer sensors) pixels diagonally across each format just resolves that diffraction-limited image. You can see that bigger sensors provide better resolution, even when you take into account the unavailability of fast lenses in the larger formats. When you consider the resolving power of real lenses, the scale tilts even more in favor of the larger formats: photographic f/1.0 lenses are not diffraction limited.
The spacing of the pixels, given a constant fill factor, is proportional to the signal to noise ratio (the signal to noise ratio is proportional to the square root of pixel area, and pixel area is proportional to the square of the spacing). This quantifies something that we all know qualitatively: bigger pixels are less noisy.
In the next table, I consider how depth of field varies with sensor size. The standard circle of confusion diameter for depth of field tables or lens markings is 0.01 inch on an 8×10 print. This is way too fuzzy for critical work. I may have gone too far in the opposite direction, but I picked a circle of confusion diameter of 0.005 inches (127 micrometers) on a 16×20 print. I picked a lens focal length equal to the diagonal of each format, calculated the magnification required to enlarge the format size up to 16×20, then calculated the equivalent circle of confusion on the sensor. With a constant f/4 aperture, and all lenses focused at three meters, I calculated the depth of field in millimeters; you can see that smaller formats have more depth of field, with about an order of magnitude variation over the range of sensor sizes considered. I also calculated the diameter in micrometers of the diffraction (Airy) disk and scaled it to the print size; you can see that, at f/4 it’s smaller than the circle of confusion, which means that the image sharpness away from the focal point will be depth of field limited.
Then it occurred to me to find the aperture that caused the circle of confusion and the diffraction disk diameters to be equal. I reasoned that this would give approximately the same sharpness throughout the “in-focus” zone, which should in one sense be optimal. What surprised me was that this aperture gave almost the same depth of field for each format. Have a look: