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.