The main features of eigenfunctions and eigenvalues of integral equations connected with incoherent imaging through clear pupils are studied. As in the coherent imaging, both the object and the image can be expanded in eigenfunction series. On the contrary, the eigenvalue-step-function behavior typical of coherent imaging is not preserved when passing to the incoherent case. Upper and lower bounds for the eigenvalues are established in the one-dimensional case. They show that the eigenvalues, roughly speaking, decrease almost linearly with respect to the order index.
F. Gori, "Integral equations for incoherent imagery," J. Opt. Soc. Am. 64, 1237-1243 (1974)