Design and Modelization of a convex grating for the hyperspectral imager Chandrayaan 2: spectral optimization based on free form profile

For hyperspectral imaging, diffraction gratings based spectrometers exhibit high spectral resolution and optical performance. Among those spectrometers, the Offner type (which consists of an entrance slit, two concave mirrors and convex grating) offers a lot of
advantages. In this paper, we propose the design and modelization of a convex grating which covers a spectral band ranging from 0.7 μm to 5 μm with a minimum diffraction efficiency of 20% at 8 00 nm, 50% at 3000 nm and 25% at 5000 nm. For a so wide band, a grating with a
single blaze cannot satisfy these requirements. Wewill therefore propose an approach of multi-blaze grating which is subdivided intodifferent sections each with its own blaze angle. Meanwhile, we perform the diffraction efficiency prediction using the scalar and rigorous
theories to prove the compliance of this design with the technical specifications. The rigorous theory will also allow us to study the polarization sensitivity of this grating and the calculation of the diffraction efficiency of a grating with a profile degraded by manufacturing
errors to assess the impact on the diffraction efficiency and the sensitivity to polarization.