Propagation of partially coherent radiation using Wigner functions

Undulator radiation from synchrotron light sources must be transported down a beam line from the source to the sample. A partially coherent photon beam may be represented in phase space using a Wigner function, and its transport may use some similar techniques that are familiar in particle beam transport. We describe this process in the case that the beam line is composed of linear focusing and defocusing sections as well as apertures. We present a compact representation of the beam line map involving linear transformations and convolutions. We create a $1\ensuremath{\mathbin:}1$ imaging system with a single slit on the image plane and observe the radiation downstream to it. We propagate a Gaussian beam and undulator radiation down this sample beam line, drawing parameters from current and future ultra low emittance light sources. We derive an analytic expression for the partially coherent Gaussian case including passage through a single slit aperture. We benchmark the Wigner function calculation against the analytical expression and a partially coherent calculation in the synchrotron radiation workshop (SRW) code.