Transport of intensity equation for beams in an arbitrary state of temporal and spatial coherence

Abstract

A general Transport of Intensity equation for paraxial optical wavefields in an arbitrary coherence state is derived. The equation provides an explicit relationship between the phase distribution in each monochromatic component of the beam and the propagation of its spectral density, and can be used as an efficient theoretical tool in phase imaging with extended and polychromatic sources. Our treatment of the problem suggests a new and simpler approach to the theoretical analysis of propagation of partially coherent beams than has hitherto been appreciated. Some applications to phase imaging with polychromatic radiation are described with particular emphasis on hard X-ray in-line imaging.