Synthesis and analysis of an aplanatic mirror-lens system with axial symmetry

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Abstract

The problems of synthesis and analysis of an axisymmetric aplanatic mirror-lens system that transforms the spherical front of a source into a flat one are considered. Two methods have been developed for solving the problem of synthesizing the system’s generatrices: using a numerical procedure and the Kelleher formula, and also by reducing it to a differential equation with a retarded argument. Formulas are obtained for the eikonal in the aperture of the system when the source is displaced from the focus. The dependence of the mean square aberration of the eikonal on the system parameters has been studied and their optimal values have been found.

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About the authors

A. S. Venetsky

Kotelnikov Institute of Radio Engineering and Electronics RAS

Author for correspondence.
Email: red@cplire.ru
Russian Federation, Mokhivaya Str. 11, build. 7, Moscow, 125009

V. A. Kaloshin

Kotelnikov Institute of Radio Engineering and Electronics RAS

Email: red@cplire.ru
Russian Federation, Mokhivaya Str. 11, build. 7, Moscow, 125009

Trinh Van Tuan

Moscow Institute of Physics and Technology (National Research University)

Email: red@cplire.ru
Russian Federation, Institutskii Lane 9, Dolgoprudny, Moscow region, 141700

References

  1. Schmidt B. //Centralzeitung fur Optik und Mechanik. 1931. V. 52. № 2. P. 25.
  2. Максутов Д. Д. Астрономическая оптика. 2-е изд. Л.: Наука, 1979.
  3. Михельсон Н. Н. Оптика астрономических телескопов и методы ее расчета. М.: Физматлит, 1995.
  4. Калошин В. А., Фролова Е. В. // Журн. радиоэлектроники. 2015. № 12. http://jre.cplire.ru/jre/dec15/19/text.pdf.
  5. Kelleher K. S.// J. Appl. Phys. 1950. V. 21. № 6. P. 573.

Supplementary files

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2. Fig. 1. Mirror-lens system: 1 and 2 – generators of the first and second surfaces.

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3. Fig. 2. Geometry of new sections and rays.

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4. Fig. 3. Generators of the first (1) and second (2) synthesized aplanatic mirror-lens systems for different sets of parameters: a) f = 1, q = 0.8, n = 1.2, k = 0.95, b1 = 0.4605; b) f = 1, q = 0.5, n = 1.1, k = 0.9, b1 = –0.1111; c) f = 1, q = 0.8, n = 1.049, k = 0.99, b1 = 0.4957; d) f = 0.5, q = 0.3, n = 1.3, k = 0.8, b1 = 0.2778.

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5. Fig. 4. Errors of the eikonal (a) and the mapping function (b): curve 1 – x0 = 10–3 and 18 partition sections; curve 2 – x0 = 10–5 and 23 partition sections.

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6. Fig. 5. Geometry of the problem for deriving a differential equation: 1 – generator of the first surface, 2 – generator of the second surface.

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7. Fig. 6. Errors in the synthesis of the eikonal (a) and the mapping function (b).

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8. Fig. 7. Rays with a shifted (to point O1) and unshifted source.

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9. Fig. 8. The difference between the eikonals in the meridional (a) and sagittal (b) planes for different values ​​of the source displacement in the meridional plane: 0(1), 0.05(2), 0.1(3), 0.15(4), 0.2(5), 0.25(6) and 0.3(7).

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10. Fig. 9. Geometry of rays in a mirror-lens system with a shifted source: 1, 2 – generators of the first and second surfaces, 3 – focal line, 4 – front corresponding to the reference beam.

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11. Fig. 10. Dependence of the root-mean-square aberration on the angle of view: a mirror-lens system optimized using ray tracing (1) and an approximate formula (2), a single-mirror system (3).

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