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In this paper, the impact of introducing freeform surfaces into the recording and imaging paths of holographic gratings on system performance is quantitatively investigated, and the performance boundaries of various systems are demonstrated. These performance parameters encompass numerical aperture, spectral resolution, spectral band, and slit length, among others. The results indicate that introducing a freeform surface in the recording path can significantly improve performance, surpassing the introduction of a freeform surface in the imaging path. Besides, the performance improvement is several times that brought by an aspherical surface. Therefore, by incorporating a freeform surface in the recording path and using simple spherical elements in the imaging path, a series of high-performance and low-cost imaging spectrometers can be achieved. Additionally, a high-quality imaging spectrometer with holographic grating is introduced, where all surfaces are freeform.
Tan et al. (Tue,) studied this question.