We introduce a model that can accurately simulate radiation from undulator sources for ray tracing applications. It incorporates several key effects relevant to fourth-generation synchrotron sources, such as electron emittance, energy spread, and diffraction-limited beam size. This code has been developed as part of SHADOW4, the latest version of the widely used SHADOW X-ray optics ray tracing program. The approach relies on calculating the field distribution in the far field, which determines the ray divergences. The integration of existing models for electron energy spread is also addressed. Rays sampled at the source follow a size distribution derived by backpropagating the far-field radiation. These models are detailed, and several examples are provided.
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