Zernike-polynomial description of the deformation of a known surface profile with a noncircularly symmetric shape

Zavgorodnyi, D.S., Ivanova, T.V.

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Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Иванова Т.В., Завгородний Д.С. Описание деформации детали некруглой формы полиномами Цернике по известному профилю поверхности // Оптический журнал. 2021. Т. 88. № 1. С. 14–21. http://doi.org/10.17586/1023-5086-2021-88-01-14-21

Ivanova T.V., Zavgorodnyi D.S. Zernike-polynomial description of the deformation of a known surface profile with a noncircularly symmetric shape [in Russian] // Opticheskii Zhurnal. 2021. V. 88. № 1. P. 14–21. http://doi.org/10.17586/1023-5086-2021-88-01-14-21

For citation (Journal of Optical Technology):

T. V. Ivanova and D. S. Zavgorodniĭ, "Zernike-polynomial description of the deformation of a known surface profile with a noncircularly symmetric shape," Journal of Optical Technology. 88(1), 8-13 (2021). https://doi.org/10.1364/JOT.88.000008

Abstract:

We analyze the errors in a Zernike-polynomial description of the deformation over a noncircularly symmetric portion of the overall input pupil of an optical system. Analysis reveals that Zernike polynomials can be used for such description, provided certain restrictions are observed. In this paper, we describe an example where Zernike polynomials are used to describe and assess the adverse effect of primary-mirror deformation on image quality in a three-mirror off-axis anastigmat.

Keywords:

Zernike polynomials, approximation, three-mirror off-axis anastigmat, Earth observing systems

OCIS codes: 080.1753, 080.3620, 220.3620

References:

1. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon Press, 1965; Nauka, Moscow, 1970).
2. S. N. Bezdidko, “New principles of synthesis and optimization of optical systems using a computer,” in OSA Proceedings of the International Optical Design Conference (1994), pp. 16–22.
3. V. N. Mahajan, “Zernike polynomials and aberration balancing,” Proc. SPIE 5173, 517302 (2003).
4. S. N. Bezdidko, “Theory of orthogonal aberrations and its use in lens design,” Opt. Rev. 21, 632–638 (2014).
5. S. N. Bezdidko, “Determination of the Zernike polynomial expansion coefficients of the wave aberration,” Opt.-Mekh. Prom-st. (7), 75–77 (1975).
6. S. N. Bezdidko, “Orthogonal aberrations: theory, methods, and practical applications in computational optics,” J. Opt. Technol. 83(6), 351–359 (2016) [Opt. Zh. 83, 32–43 (2016)].
7. V. N. Mahajan, “Zernike annular polynomials for imaging systems with annular pupils,” J. Opt. Soc. Am. 71, 75–85 (1981).
8. N. D. Tolstoba, “Gram-Schmidt technique for aberration analysis in telescope mirror testing,” Proc. SPIE 3785, 140–151 (1999).
9. N. D. Tolstoba, “Analysis of Hartmann testing techniques for large-sized optics,” Proc. SPIE 4451, 406–413 (2001).
10. S. A. Rodionov, B. B. Usoskin, and L. I. Przhevalinski˘ı, “Computation of Zernike polynomials orthogonal over the circle,” in Optical System Research and Design (Tr. LITMO, 1979), pp. 61–71.
11. E. R. Melamed, Design of Space-Based Optical Instruments (St. Petersburg, SPb ITMO (TU), 2002).
12. B. Singaravelu and R. A. Cabanac, “Obstructed telescopes versus unobstructed telescopes for wide field survey—a quantitative analysis,” Publ. Astron. Soc. Pac. 126(938), 386 (2014).
13. K. M. Weiß, E. Kammann, S. Fray, P. Gille, and M. Mol, “Alignment concept for the three mirror anastigmat telescope assembly of the Meteosat third generation flexible combined imager,” Proc. SPIE 10562, 105624R (2014).
14. V. Costes, G. Cassar, and L. Escarrat, “Optical design of a compact telescope for the next generation Earth observation system,” Proc. SPIE 10564, 1056416 (2017).
15. E. Hugot, X. Wang, D. Valls-Gabaud, G. Lemaître, T. Agocs, R. Shu, and J. Wang, “A freeform-based, fast, wide-field, and distortion-free camera for ultralow surface brightness surveys,” Proc. SPIE 9143, 91434X (2014).