Two-dimensional interferometric metrology of varied-line-spacing gratings with decoupled substrate and groove contributions.

Varied-line-spacing (VLS) gratings are pivotal optical components for achieving high energy resolution and focusing performance in synchrotron radiation monochromators and spectrometers. To optimize the operational performance and guide the high-precision manufacturing of these elements, comprehensive metrology of parameters such as groove density, groove bending, and substrate surface figure is essential. This work presents a high-precision, multi-parameter two-dimensional metrology system based on Fizeau interferometry. Specifically addressing the inherently curved diffraction wavefronts of VLS gratings, we implement a correction for retrace errors and investigate the measurement accuracy of VLS coefficients under a planar reference configuration. By analyzing the zero- and first-order diffraction wavefronts, the independent phase contributions of the grating grooves and the substrate figure are decoupled. Experimental validation on a 220 lines/mm grating (with a VLS coefficient a1 = 0.041 lines/mm2) demonstrates a groove density residual of only 0.0019 lines/mm and excellent agreement in groove bending compared with long trace profiler (LTP) results. This methodology provides a robust framework for the complete characterization of VLS gratings and offers an effective feedback mechanism for optimizing the fabrication of next-generation synchrotron optics.