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 $1:1$ 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.

中文翻译：

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使用维格纳函数传播部分相干辐射

来自同步加速器光源的波荡器辐射必须沿光束线从光源传输到样品。可以使用维格纳函数在相空间中表示部分相干光子束，并且其传输可以使用粒子束传输中熟悉的一些相似技术。我们在光束线由线性聚焦和散焦部分以及光圈组成的情况下描述此过程。我们提出了包含线性变换和卷积的束线图的紧凑表示。我们创建一个$\mathrm{1个}：\mathrm{1个}$成像系统，在像面上有一个狭缝，并观察其下游的辐射。我们沿着该样本光束线传播高斯光束和波状辐射，从当前和未来的超低发射光源中提取参数。我们推导了部分相干高斯情况的解析表达式，其中包括通过单个狭缝孔径。我们将Wigner函数计算与解析表达式进行比较，并在同步辐射车间（SRW）代码中对部分相干计算进行基准测试。