A Takagi–Taupin-Informed Simulation System and Multi-Parameter Optimization Method for Doubly Curved Crystal Monochromators in X-Ray Fluorescence Spectrometry

Doubly curved crystal (DCC) monochromators for X-ray fluorescence (XRF) couple crystal material, mosaicity, source/sample distances, crystal dimensions, and the meridional and sagittal bending radii, but are usually tuned empirically or one parameter at a time. A Takagi–Taupin-informed simulation system turns this coupled design problem into a common limit of detection (LOD) optimization by chaining tube spectrum modeling, an approximate diffraction module, two-dimensional DCC focusing geometry, and an XRF forward model from the source spectrum to the LOD. Calibrated using laboratory reference measurements and evaluated through a synthetic perturbation-based internal self-consistency test over 13 configurations, the system supports comparative screening within the explored design space; absolute LOD prediction still requires independent experimental validation. The engineering-recommended LiF(220) benchmark achieves an Fe Kα LOD of 1.253 ppm under shared geometry, while a separate Ge(111) curvature scan reaches a conditional sampled minimum of 1.094 ppm at (Rm,Rs)=(75,20) mm; the two values arise from different conditions and are not directly rankable. Curvature parameters dominate the LOD sensitivity, followed by the source distance, crystal dimensions, and anode selection. The framework is element-agnostic and transferable to other crystals and target elements.