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Numerically-Analytical Method of Optimization of Optical Systems with Concave Holographic Diffraction Gratings

Keywords:

J.V.Bazhanov, N.V.Zaharova


To compensate for aberrations, concave diffraction gratings used in a spectral device should have curved grooves and a variable spacing. Such gratings may be implemented by means of interference of two beams. In the present work, optimization of parameters is proposed to be obtained in two stages. At the first stage, optimization of parameters of an optical instrument is made, and at the second – calculation of a scheme of holographic grating recording providing compensation of aberrations of the spectral device. Aberrations of 1st – order, namely, defocusing and astigmatism have the maximum impact on total aberrations of system. For minimization of defocusing and astigmatism we use type (1) equations: (1) where are the expressions for corresponding aberrations, is the operating wavelength range, and is the parameter on which minimization is conducted. For an estimation of an optical system quality two criteria are used: the sum of squares of aberrations in the main cross-sections, averaged over the pupil of system, and the modulation transfer function. In the present work, minimization of cross-section aberrations of 2nd- and 3rd orders in a dispersion direction is conducted. We proposed a method of concave holographic diffraction grating recording with corrected aberrations of 1-3rd orders. In this me-thod, in one of the beams for recording an additional cylindrical mirror is used. Techniques for determination of optimum parameters of holographic grating recording are based on use of a “horizontal cylinder” (forming spherical surfaces lying in the meridianal planes) and a “vertical cylinder” (forming cylindrical surfaces lying in the sagittal planes). The described methods are implemented in the form of a complex of programs for a personal computer. Results of calculations of spread function half-width of a spectrograph for optimum schemes of recording with use of horizontal and vertical cylinders, and also without additional optical elements (recording by homocentric beams of rays) are given.
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