Abstract

Subject of study. Two algorithms for designing an optical scheme based on a composite hologram optical element aimed at optimizing the diffraction efficiency are presented. The first algorithm is based on the successive partitioning of the hologram element, and the second is based on averaging locally the optimized hologram parameters. Aim of study. The aim of this study is to achieve high and uniform diffraction efficiency in the working spectral range using design and modeling techniques to determine the parameters of a composite hologram. This is realized by selecting the optimal configuration of the composite hologram and its parameters in each sub-aperture. Methods. The algorithms are based on the application of the Welford equation for ray tracing through a hologram and Kogelnik theory for simultaneous calculation of diffraction efficiency in several sub-apertures. Main results. As a demonstrative example, the design and analysis of a spectrograph optical scheme operating in the near-infrared region with a high angular dispersion are presented. A diverging beam with a numerical aperture of 0.14 is fed to the input of the spectrograph. The spectrograph operates in the wavelength range from 830 to 870 nm, the center of which corresponds to the emission wavelength of a standard laser source. The optical system comprises a collimator, two volume-phase transmission holographic gratings, a camera lens, and a photodetector. It is shown that the highest gain in diffraction efficiency for a composite hologram comprising three rectangular sub-apertures reaches 5.1 times that of a single hologram grating without parameter optimization, observed at the long-wavelength edge of the spectrum. Practical significance. The proposed algorithms will allow one to determine the optimal number, shape, and location of composite hologram sub-apertures. The obtained results will make it possible to design a spectrograph characterized by an increased and more uniform image brightness over the entire working range.

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