Optimization of a multiblaze grating in reflection using a free-form profile

Diffraction gratings are very important in hyperspectral imaging. Their desired diffraction efficiency is dictated by the sensitivity of the detector in the spectral band of interest and the luminance of the scene to be observed. If the desired diffraction efficiency curve is established in this spectral band of interest, the remaining work is to design a diffraction grating that meets this demand. This paper is concerned with blazed gratings in reflection, and the geometry of the grating will therefore depend on this reference curve, the spectral band, and the optimization order. The simplest form is a grating with a uniform profile that is optimized at a single-blaze wavelength. It is a monoblaze grating. When such grating cannot meet the requirements in terms of diffraction efficiency, a multiblaze grating optimized at several blaze wavelengths is required. The objective of this paper is to propose a method of optimization of this multiblaze grating, i.e., how to find the number of blaze wavelengths necessary as well as their value to answer the requirements in term of diffraction efficiency.