Abstract
The article is devoted to the theory of calculating mirror systems with anastigmatic properties, namely, the area of research in terms of developing methods for parametric calculation of dimensions and aberration correction. The such systems can correct three third-order aberrations. Mirror anastigmats allow developing the angular field of view of devices while maintaining a high numerical aperture, which allows them to be used in optoelectronic equipment operating in a wide spectral range. Complete absence of chromatic aberrations, high resolution, permissible wave criteria for image quality provide excellent opportunities for using mirror anastigmatic systems. General methodological approaches have been developed that can be applied to the creation of detailed engineering and technical methods for calculating a group of mirror anastigmatic systems. A serious drawback of reflective optics is center without central screening, which degrades image quality. To eliminate it, rotations or displacements of the mirrors are intro-duced, but non-elementary aberrations of even orders appear, which must be corrected. The creation of compositions with decentered catoptric elements requires further development of the calculation and methodological base. Mathematical solutions to the problem of creating basic models of non-centered mirror systems are presented. Accurate formulas are obtained for the calculation of real rays from the conditions of astigmatism and coma correction for the given angles of incidence of the chief ray on the mirror surfaces and the «oblique» thickness , which determines their relative position. Based on the proposed formulas, a new method for parametric calculation of decentered mirror systems has been created, which allows one to compose algorithms and design both basic models and complex mirror systems from off-axis mirrors. The development of new algorithms for two- and three-mirror decenter lenses will increase the accumulated potential of computational optics. The scope of the proposed technique can be expanded in terms of the number of components.
Highlights
One of the important areas of modern optics and optical instrumentation is the creation of mirror systems with astigmatizm aberration correction, which make it possible to develop the angular field of view of devices while maintaining a high luminosity, for use in optoelectronic equipment operating in a wide spectral range
Modeling and development of new circuit solutions for mirror systems have been intensively carried out for several decades; this direction is receiving a new round of development in connection with new impulses of research and technologies of space technology and the expansion of the spectral range of wavelengths in scientific research; development of new-generation optoelectronic equipment receivers, which determines the development of a number of other applications of mirror optics: UV microscopy, medicine, photolithography, microelectronics, military equipment, telecommunication systems, information recording [1; 2]
Taking into account formula (2), we present the final form of the condition for correcting the coma of a two-mirror decenter system
Summary
One of the important areas of modern optics and optical instrumentation is the creation of mirror systems with astigmatizm aberration correction, which make it possible to develop the angular field of view of devices while maintaining a high luminosity, for use in optoelectronic equipment operating in a wide spectral range. Let us transform the expression for the invariant of the meridional coma and, accepting the condition for the second order coma eliminating R'2=0, we obtain the relation: r1 sin. To solve the problem of evaluating second-order astigmatism, which affects the image quality over the field, it is advisable to use expressions for the socalled tilt invariants, which describe the relationship between the surfaces rotations and the tilts of the meridional ψ't and sagittal ψ't images relative to the chief beam when the entrance pupil is aligned with the surface apex. To eliminate the second order astigmatism associated with image tilts, it is necessary to equate the angles ψ'S2=ψ't2 (10), i.e. combine the straight lines formed by the foci of the meridional and sagittal infinitely thin beams, and combine the focal plane with them.
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