Comprehensive performance domain tolerance analysis methodology for freeform imaging spectrometers

Abstract

In recent years, attention has been directed towards cost-effective and compact freeform Schwarzschild imaging spectrometers with plane gratings. The utilization of tolerance analysis serves as a potent approach to facilitate the development of prototypes. Conventional tolerance analysis methods often rely solely on the modulation transfer function (MTF) criterion. However, for a spectrometer system, factors such as the keystone/smile distortion and spectral resolution performance also require consideration. In this study, a tailored comprehensive performance domain tolerance analysis methodology for freeform imaging spectrometers was developed, considering vital aspects such as the MTF, keystone/smile distortion, and spectral resolution. Through this approach, meticulous tolerance analysis was conducted for a freeform Schwarzschild imaging spectrometer, providing valuable insights for the prototype machining and assembly processes. Emphasis was placed on the necessity of precise control over the tilt and decenter between the first and third mirrors, whereas the other fabrication and assembly tolerances adhered to the standard requirements. Finally, an alignment computer-generated hologram (CGH) was employed for the preassembly of the first and third mirrors, enabling successful prototype development. The congruence observed between the measured results and tolerance analysis outcomes demonstrates the effectiveness of the proposed method.