Propagation of partially coherent radiation using Wigner functions

TL;DR

This paper develops a phase space method using Wigner functions to model the propagation of partially coherent synchrotron radiation through beamlines with linear optics and apertures, validated by analytical and numerical benchmarks.

Contribution

It introduces a compact linear transformation and convolution framework for Wigner function propagation in beamlines, including an analytic solution for Gaussian beams with apertures.

Findings

Validated Wigner function propagation against analytical solutions.

Demonstrated application to Gaussian undulator radiation.

Provided a benchmark with SRW simulations.

Abstract

Undulator radiation from synchrotron light sources must be transported down a beamline 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 as is familiar in particle beam transport. We describe this process in the case that the beamline is composed of linear focusing and defocusing sections as well as apertures. We present a compact representation of the beamline map involving linear transformations and convolutions. We create a 1:1 imaging system (4f 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 beamline, 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.