A decomposition of the field at the aperture of an optical system in terms of the eigenfunctions of a certain integral equation is useful in analyzing the detectability of incoherent objects. The kernel of the integral equation is the mutual coherence function of the light from the object. The decomposition permits specification of the number of degrees of freedom in the aperture field contributing to detection of the object. Quantum mechanically the coefficients of the modal decomposition become operators similar to the usual creation and annihilation operators for field modes. The optimum detector of the object is derived in terms of these operators. Specific detection probabilities are calculated for a uniform circular object whose light is observed at a circular aperture. The modal decomposition is also applied to estimating the radiance distribution of the object plane.
CARL W. HELSTROM, "Modal Decomposition of Aperture Fields in Detection and Estimation of Incoherent Objects," J. Opt. Soc. Am. 60, 521-530 (1970)