Analysis method of the Offner hyperspectral imaging spectrometer based on vector aberration theory

Compact hyperspectral imaging spectrometers with a wide field of view (FoV) have significant application value. However, the aberration field of such imaging spectrometers is sensitive, and varies for different wavelengths when reducing the spectrometer volume. It is difficult to explain the variation in the aberration field using traditional aberration theory. In this study, we extend the vector aberration theory (VAT) to the Offner imaging spectrometer. We deduce the expression of the aberration field decenter vector of the Offner spectrometer based on the real ray-trace method. Furthermore, we derive the expression of the third-order vector aberration of the system. Subsequently, we explain some common phenomena in the Offner imaging spectrometer. This new analysis method can provide useful guidance for designing a compact wide FoV Offner imaging spectrometer. With this new insight, we designed a compact wide FoV Offner imaging spectrometer with a freeform tertiary mirror. Compared to conventional spectrometers with the same specifications, the total length of the spectrometer decreased by 37%, and the volume by 75%. After the tolerance analysis, the freeform optics satisfied the existing machining technology. The analysis method presented in this paper furthers the designer's understanding of the aberration field of the Offner imaging spectrometer. The method is significant in the design of a compact wide FoV Offner imaging spectrometer with freeform optics.