Comparative analysis of design algorithms for optical systems using composite holographic optical elements

Ахметов Д.М., Муслимов Э.Р., Харитонов Д.Ю., Павлычева Н.К., Гуськов И.А., Гильфанов А.Р., Терентьев А.И. Сравнительный анализ алгоритмов расчета оптических систем с использованием композитных голограммных оптических элементов // Оптический журнал. 2023. Т. 90. № 5. С. 63–75. http://doi.org/10.17586/1023­5086­2023­90­05­63­75

Akhmetov D.M., Muslimov E.R., Kharitonov D.Y., Pavlychevа N.K., Guskov I.A., Gilfanov A.R., Terentyev A.I. Comparative analysis of design algorithms for optical systems using composite holographic optical elements [in Russian] // Opticheskii Zhurnal. 2023. V. 90. № 5. P. 63–75. http://doi.org/10.17586/1023­5086­2023­90­05­63­75

Subject of study. Two algorithms for design of an optical scheme based on a composite hologram optical element aimed at optimizing the diffraction efficiency, the first of which is based on the successive partitioning of the hologram element, the second algorithm is based on averaging locally optimized hologram parameters. The aims of this work are to develop algorithms for determining the configuration of a composite hologram and its parameters in each of the subapertures, as well as their further use to achieve a high diffraction efficiency uniformly distributed over the working spectral range of the device Method. The algorithms are based on the application of the Welford equation for ray tracing through a hologram and the Kogelnik theory for simultaneous calculation of diffraction efficiency in several sub­apertures. Main results. As a demonstrative example, a design and analysis of a spectrograph optical scheme operating in the near infrared region with a high angular dispersion is given. 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 consists of a collimator, two volume­phase transmission holographic gratings, a camera lens, and a photodetector. It is shown that the greatest gain in diffraction efficiency for a composite hologram of three rectangular sub­apertures in comparison with a single hologram grating without parameters optimization reaches 5.1 times and is observed at the long­wavelength edge of the spectrum. Practical significance. The proposed algorithms will allow one to determine the optimal number, shape and location of the composite hologram sub­apertures. 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.