Automatic design varied-line-spacing grating using ray-tracing method: A proof-of-concept study

Varied-line-spacing gratings (VLS-Gs) serve as key optical elements in spectrometers and monochromators. An ongoing challenge for AI-based automatic VLS-Gs design is integrating groove parameter calculation, focal position determination, engineering tolerance analysis, and performance estimation in a self-contained coding environment. In this article, we report a proof-of-concept study on designing a VLS spherical grating using the ray-tracing method. This approach demonstrates several advantages over conventional optical designs. First, the use of the ray-tracing method paves a direct way to calculate the groove parameters without requiring mathematical deduction of the light path function under Fermat's principle. Second, coma-free focal positions can be efficiently determined for different photon energies using Powell's hybrid method. In addition, the ray-tracing method offers novel insights for determining the acceptance angle limit and optimal grating length. This ray-tracing based VLS-G calculation method may prove valuable for future AI-based automatic design of spectrometers and monochromators.