Y.V. Bazhanov1, A.P. Perikov2

1JSC "Precision Systems and Instruments" (Moscow, Russia)

2Moscow State University of Geodesy and Cartography (Moscow, Russia)

The design of a two-mirror off-axis optical system in which three reflections of a beam of rays occur is carried out. The optical system of the lens is a three-mirror, in which the primary mirror and the tertiary mirror are integrated on the same surface. We can call such a lens a two-mirror lens, since the surface of the integrated mirror is expressed by one analytical expression. The calculation of such a system turned out to be possible thanks to the use of mirrors with freeform surfaces, which are being put into practice abroad. The theory is based on Seidel's formulas for third-order aberrations, which have been presented by K. Schwarzschild so that they are expressed by mutually independent variables only. D. Korsh obtained a solution for such a construction with zero Petzval curvature. We also used this method because it simultaneously with the parameters of the system allows us to calculate the conical constants of the mirror surfaces included in it.

The Korsch method has obtained a number of centered three-mirror schemes with corrected image curvature for different values of the screening coefficient, while the radii of curvature and the conical constants of the first and third mirrors are equal. The field of view of the selected systems was decentered, and the minimum distances from the second mirror to the beam of rays before the first reflection and after the third reflection were calculated, as well as the distance between the light beams on the common mirror. These values, together with other restrictions on the circuit parameters, were used to optimize the off-axis lens. Optimization was carried out using the ZEMAX program using a free-form surface in the form of a power polynomial.

Based on the calculation method of two-mirror off-axis schemes with three reflections, various variants of lenses are calculated, the image quality of which is limited by diffraction at the aperture. The characteristics of lenses with a focal length of 50 mm, a field of view of 6°×6°, a relative aperture of 1:3.5, as well as a focal length of 100 mm, a field of view of 0.5°×13°, a relative aperture of 1:6 are presented. Since the integrated mirror is described by one expression, it can be manufactured from a single installation on a multi-axis diamond turning machine. Another advantage of this type of lens is that the mounting of mirrors of two-mirror lenses with three beam reflections is an axisymmetric design. The alignment of such schemes is much easier compared to two-mirror lenses with two beam reflections, since the mirrors in this case are deployed relative to each other, and even more so compared to three-mirror lenses. This is especially important when using lenses on aircraft and space carriers. For example, for the purposes of remote sensing of the Earth. Lenses with a square field can be used in polychromatic cameras, and with a slit field in hyperspectral imaging devices together with a spectrometer.

Bazhanov Y.V., Perikov A.P. Design of two-mirror telescopes with three beam reflections. Information-measuring and Control Systems. 2023. V. 21. № 3. P. 34−43. DOI: https://doi.org/10.18127/j20700814-202303-06 (in Russian)

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