The second moment of the point spread function is related to the second derivative of the optical transfer function at the origin by the moment theorem. The second moment is the sum of a contribution of the aperture amplitude distribution, which yields a sometimes infinite term, and a term that is directly related to the wave front aberrations. In practical applications it is possible to redefine the second moment such that a quality parameter, identical to one successfully used in lens design, is obtained.
© 1979 Optical Society of America
Noah Bareket, "Second moment of the diffraction point spread function as an image quality criterion," J. Opt. Soc. Am. 69, 1311-1312 (1979)