DOI: 10.17586/2226-1494-2018-18-1-9-14


T. V. Ivanova , D. I. Anoshchenkov

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For citation: Ivanova T.V., Anoshchenkov D.I. Distribution analysis of real ray coordinates on optical system entrance pupil for wave aberration approximation by Zernike polynomials. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2018, vol. 18, no. 1, pp. 9–14 (in Russian). doi: 10.17586/2226-1494-2018-18-1-9-14

 Subject of Research.The paper deals with description of optical system wave aberration by Zernike polynomials. We perform the search of suitable point distribution (real ray coordinates on optical system entrance pupil) for the least squares method approximation. Six possible types of distribution are considered. The conclusion on their advantages and disadvantages is drawn. Method. The method essence lies in various types of distribution research for real rays on entrance pupil that allow for necessary accuracy with minimum rays number. Main Results. We compare standard deviation between the reference wave front and result wave front after approximation by Zernike polynomials by the least squares method for several types of point distribution (real ray coordinates) on optical system entrance pupil. The best types of distribution with maximum convergence are determined. Practical Relevance. The discussed distribution of points can be useful for ray tracing calculation through optical system for the further wave front reconstruction by Zernike polynomials. The usage of optimal point distribution can reduce the number of rays necessary for wave front reconstruction that increases drastically calculation speed.

Keywords: Zernike polynomials, wave aberration, aberration computation, approximation, point distribution

 1.      Tolstoba N.D. Gram-Schmidt technique for aberration analysis in telescope mirror testing. Proceedings of SPIE, 1999, vol. 3785, pp. 140–151.
2.      Smirnov A.J., Utkin A.B. On relation between the wave aberration function and the phase transfer function in an adaptive optical system for Earth observation. Proceedings of SPIE, 2001, vol. 4353, pp. 256–265. doi: 10.1117/12.417744
3.      Zhao Q., Fan H., Hu S., Zhong M., Baida L. Effect of optical aberration of telescopes to the laser radar. Proceedings of SPIE, 2010, vol. 7656, art. 76565Z. doi: 10.1117/12.867716
4.      Zhang W., Liu P., Wei X., Zhuang S., Yang B. The analysis of the wavefront aberration caused by the gravity of the tunable-focus liquid-filled membrane lens. Proceedings of SPIE, 2010, vol. 7849, art. 78491W. doi: 10.1117/12.869866
5.      Romanova G., Ivanova T., Korotkova N. Automation design of cemented doublet. Proceedings of SPIE, 2015, vol. 9626, art. 96262S. doi: 10.1117/12.2191115
6.      Ivanova T.V., Romanova G.E., Zhukova T.I., Kalinkina O.S. Method for calculation and analysis of a cemented component with achromatic and aplanatic correction. Journal of Optical Technology, 2017, vol. 84, no. 8, pp. 548–551. doi:10.1364/JOT.84.000548
7.      Born M., Wolf E. Principles of Optics. NY, Pergamon, 1959.
8.      Sheppard C.J.R., Campbell S., Hirschhorn M.D. Zernike expansion of separable functions of Cartesian coordinates. Applied Optics, 2004, vol. 43, no. 20, pp. 3963–3966. doi: 10.1364/AO.43.003963
9.      Bezdidko S.N. New principles of synthesis and optimization of optical systems using a computer. OSA Proc.Int. Optical Design Conference, 1994, vol. 22, pp. 16–22.
10.   Mahajan V.N. Zernike polynomials and aberration balancing. Proceedings of SPIE, 2003, vol. 5173, pp. 1–17. doi: 10.1117/12.511384
11.   Bezdidko S.N. Theory of orthogonal aberrations and its use in lens design. Optical Review, 2014, vol. 21, no. 5, pp. 632–638. doi: 10.1007/s10043-014-0101-2
12.   Bezdidko S.N. Determination of the coefficients of wave aberration expansion in Zernike polynomials. Journal of Optical Technology, 1975, no. 7, pp. 75–77. (In Russian)
13.   Bezdidko S.N. Orthogonal aberrations: theory, methods, and practical applications in computational optics. Journal of Optical Technology, 2016, vol. 83, no. 6, pp. 351–359. doi: 10.1364/JOT.83.000351
14.   Ezhova K.V. Expansion of photogrammetric distortion in orthogonal Zernike polynomials. Journal of Optical Technology, 2012, vol. 79, no. 5, pp. 299–301.
15.   Rodionov S.A. Automation of Optical Systems Design. Leningrad, Mashinostroenie Publ., 1982, 270 p. (In Russian)
16.   Masset L., Bruls O., Kerschen G. Partition of the circle in cells of equal area and shape. Technical Report. University of Liege. 2012. Available at: (accessed 14.09.2017).
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