Transfer of radiance by twisted Gaussian Schell-model beams in paraxial systems

Abstract

The radiometric brightness theorem for a generalized radiance function is used to study the propagation of twisted Gaussian Schell-model beams in paraxial optical systems. First it is shown that a certain unique correspondence exists between the Gaussian radiance and cross-spectral density functions associated with these beams. The method is then applied to the passage of the twisted beam field through a thin lens, and the analysis yields algebraic expressions for the quantities characterizing the transmitted beam. The phenomenon of focal shift occurring in imaging by wavefields of this kind is examined, and the effects of partial spatial coherence and beam twist are elucidated.