Design of a compact hyperspectral imaging spectrometer with a freeform surface based on anastigmatism.

Hyperspectral imaging spectrometers with a wide field of view (FoV) have significant application values. However, enhancing the FoV will increase the volume of the imaging spectrometer and reduce the imaging quality, so a wide-FoV spectrometer system is difficult to design. Based on the theory of off-axis astigmatism, we present a method that includes a "prism box," "partial anastigmatism," and a partial differential equation to solve the parameters of a freeform surface. In this method, a compact wide-FoV imaging spectrometer with a freeform surface is designed. The spectrometer is an Offner structure with two curved prisms as the dispersion elements. The primary mirror and tertiary mirror of the Offner spectrometer are an aspheric surface and a freeform surface, respectively, to correct the off-axis aberration of a wide FoV. The ratio of the slit length to the total length of the spectrometer is close to 0.4. In comparison to conventional spectrometers of the same specifications, the total length of the spectrometer is reduced by 40% and the volume by 70%. The compact imaging spectrometer has potential application in the field of space remote sensing. In addition, the design method of the spectrometer provides a reference for the design of other optical systems with freeform surfaces.