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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.

We report on the design of an off-axis three-mirror freeform telescope with a large field of view (FOV) based on an integration mirror (IM). This design is the continuation of the authors' previous work. Based on aberration theory, we established a suitable nonrelayed three-mirror-anastigmat initial configuration for integration mirror design. For an optical freeform surface, we analyzed the qualitative aberration correction ability of a x-y polynomial surface that can provide a simple, convenient, and user-friendly relationship between freeform surface term coefficients and aberrations and then applied the x-y polynomial surface on the tertiary mirror to improve the system optimization degrees of freedom. In an example with a focal length of 1200 mm, an F-number of 12, and a FOV of 1°×30°, the tolerance performance was analyzed, and the system presented a good imaging performance. In addition, the IM structure and opto-mechanics support structure were designed and analyzed. The confirmatory design results showed that the integration of the primary mirror and tertiary mirror can improve opto-mechanical properties judged by multiple criteria. In conclusion, the integration of the primary mirror and tertiary mirror not only offers alignment convenience as described previously but also improves system opto-mechanical properties in multiple perspectives. We believe this large linear FOV system based on IM has broad future applications in the optical remote sensing field.