On the basis of Abbe's diffraction theory of optical imaging, the appearance of a concave mirror with arbitrarily shaped small deviations in Foucault's knife-edge test and the new phase-contrast test is evaluated. The orthogonal "circle polynomials" are found and applied to the diffraction phenomena of circular mirrors.
Frits Zernike, Frits Zernike,
"Diffraction theory of the knife-edge test and its improved form: the phase-contrast method," Journal of Micro/Nanolithography, MEMS, and MOEMS 1(2), (1 July 2002). https://doi.org/10.1117/1.1488608