Aberrations in shift-invariant linear optical imaging systems using   partially coherent fields
  Here the role and influence of aberrations in optical imaging systems employing partially coherent complex scalar fields is studied. Imaging systems require aberrations to yield contrast in the output image. For linear shift-invariant optical systems, we develop an expression for the output cross-spectral density under the space-frequency formulation of statistically stationary partially coherentfields. We also develop expressions for the output cross{spectral density and associated spectral density for weak-phase, weak-phase-amplitude, and single-material objects in one transverse spatial dimension. 
Mario A. Beltran, Marcus J. Kitchen, T. Petersen, David M. Paganin
physics.optics