LINEAR MAPPINGS OF CROSS-SPECTRAL DENSITY ONTO GENERALIZED RADIANCE

A class of generalized radiances characterized by filter functions was recently introduced into the statistical wave theory via the phase-space representations of the cross-spectral density operator. It is shown that if the generalized radiances are represented as linear transformations of the cross-spectral density, there exists a unique correspondence between the filter functions and the transform kernels within certain galilean invariant transformations. Explicit expressions are derived for this correspondence, and the radiometric meanings of the constraints placed on the phase-space filter functions are elucidated.