Walter’s Generalized Radiometry and Image Formation under Partially Coherent Illumination

Using the mathematical properties of the Wigner distribution function and the initial provisions of the theory of partial coherence, the quasi-homogeneity of the illumination source has been noted as a necessary condition for the transition from complex amplitude convolution (Fourier optics) to intensity convolution (the theory of image formation). Formulas that describe the influence of the source indicatrix (the radiation pattern) on 1) the point spread function of the optical system with aberrations and 2) the shape of the optical transfer function of a diffraction-limited optical system under partially coherent illumination are obtained.