Diffraction and Circle of Confusion

Because of the wave nature of light, the image of a distant point of light is not an infinitesimal point, but a finite disc surrounded by a series of concentric rings.  The Royal Astronomer Sir George Airy worked out the mathematics of the effect of diffraction on an image in 1835.  The size of the disc depends on the diameter of the lens and the wavelength of light and is given by the approximate formula 

r = 1.22 * l * f / d  

r is the radius of the disc

l is the wavelength of light

f is the focal length of the lens

d is the diameter of the lens.

f / d being the focal ratio of a lens, we can use the focal ratio, N, instead of f / d.

r = 1.22 * l * N

In photography the diameter of the circle of confusion is usually used, so the diameter of the circle of confusion produced by diffraction is twice the radius of the Airy disc.

c = 2.44 * I * N

The wavelength of visible light ranges from about 400nm to about 700nm.  Using the middle of the range, 550nm, we get

c = 0.0011342 * N (in millimeters)

or

N = 882 * c

For an image to be seen as sharp in the final print the largest circle of confusion should be no more than the resolving power of the human eye viewing the final print at a comfortable distance.  Diffraction producing that much blur begins to affect the image quality.

On a 36x24mm, full frame sensor, c is typically given as 0.03mm.

N = 882 * 0.03

N = 26

Most full frame lenses stop down only to f/16.  A few stop down to f/22 or even f/32 (to increase depth of field).    

On a 17.3x13mm, Micro 4/3rds sensor, c is typically given as 0.0.15mm.

N = 882 * 0.015

N = 13

Under ordinary circumstances you would not stop down the lens on a Micro 4/3rds camera to more than f/11.