Phase retrieval algorithm for wavefront reconstruction by four scattering spots

Ivanova, T.V., Kalinkina, O.S., Letova E.Y.

Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Иванова Т.В, Калинкина О.С., Летова Е.Ю. Алгоритм восстановления фазы для определения волнового фронта по четырём функциям рассеяния точки // Оптический журнал. 2023. Т. 90. № 8. С. 77-86. http://doi.org/10.17586/1023-5086-2023-90-08-77-86

Ivanova T.V., Kalinkina O.S., Letova E.U. Phase retrieval algorithm for wavefront reconstruction by four scattering spots [In Russian] // Opticheskii Zhurnal. 2023. V. 90. № 8. P. 77–86. http://doi.org/10.17586/1023-5086-2023-90-08-77-86

For citation (Journal of Optical Technology):

Tatiana Ivanova, Olga Kalinkina, and Elizaveta Letova, "Phase retrieval algorithm for wavefront reconstruction using four scattering spots," Journal of Optical Technology. 90(8), 464-469 (2023). https://doi.org/10.1364/JOT.90.000464

Abstract:

Subject of research. A method of wavefront reconstruction by known intensity distribution of several scattering spots with extended iterative Misell algorithm was considered. The input data for wavefront recovery are the intensity distribution in four scattering spots with various defocusing values. The analysis of the recovery error and the convergence criterion for wavefronts with different peak-to-valley was carried out. The purpose of this work is to analyze the numerical parameters of the Misel algorithm, namely, the convergence criterion of the method and the effect of the error in determining the center of the scattering spot on the result of restoring the telescope wavefront from four known intensity distributions in defocused scattering spots. The analysis of the influence of the scattering spot center determination error on the result of the reconstruction was performed. Method. Wavefronts with peak-to-valley up to 5 were modeled by arbitrary sets of Zernike polynomials coefficients, and then the known defocusing was added to these wavefronts and the scattering spots were calculated. The wavefronts were reconstructed by known scattering spots with the extended Misell algorithm, and then they were approximated by Zernike polynomials. The coefficients obtained as a result of the algorithm application were compared with those where were given when simulating the spots, and the error was estimated. The analysis of the influence of the numerical parameters of the algorithm on the error of the wavefront reconstruction is carried out. Main results. The extended Misell algorithm allows to successfully reconstruct the wavefront by known intensity distribution in four defocused scattering spots. The convergence criterion 10–6 is optimal and allows to provide the root-mean-square relative error of less than 0,0005%, and the error of the Zernike polynomials approximation is no more than 10–6 for the wavefront with peak-to-valley up to 5. The error of the scattering spot center determination does not affect the recovery result for the wavefront with peak-to-valley up to 3,5. For the wavefront with peak-to-valley from 3.5 to 5 the acceptable scattering spot center error is up to 4 pixels. Practical relevance. Wavefront reconstruction by four defocused scattering spots can be efficiently applied for the wavefronts with peak-to-valley up to 5 and can be used for telescope alignment during operation, when other methods are difficult to implement.

Keywords:

scattering spot, wavefront, phase retrieval methods, Zernike polinomials, Misell algorithm

OCIS codes: 080.1753, 080.3620, 220.3620

References:

1. Optical production control / Ed. by Malacara D. M: Mashinostroenie, 2007. 400 p.
2. Krist J.E., Burrows C.J. Phase-retrieval analysis of pre- and post-repair Hubble Space Telescope images // Applied Optics. 1995. V. 34. № 22. P. 4951-–4964.
3. Klebanov Y.M., Karsakov A.V., Khonina S.N., Davydov A.N., Polyakov K.A. Compensation of wavefront aberrations in spacecraft telescopes with adjustment of the telescope’s temperature field // Computer Optics. 2017. V. 41. №. 1. P. 30–36. http://doi.org/10.18287/0134-2452-2017-41-1-30-36
4. Inochkin F.M., Belashenkov N.R. Digital image aberration correction technique for structured illumination microscopy // Scientific and Technical Journal of Information Technologies, Mechanics and Optics. 2019. V. 19. №. 6. P. 1004–1012 (in Russian). https://doi.org/10.17586/2226-1494-2019-19-6-1004-1012
5. Joachim W., Joachim H., Thomas S. Reconstructing the pupil function of microscope objectives from the intensity PSF // Proceedings of SPIE. 2002. V. 4767. P. 32–43. http://doi.org/10.1117/12.451320
6. Nalegaev S.S., Petrov N.V., Bespalov V.G. Iterative methods for solving the phase problem in optics and their features // Scientific and technical bulletin of
information technologies, mechanics and optics. 2012. №. 6 (82). P. 30–35.
7. Gladysz S. Adaptive optics point spread function reconstruction directly from target data // Proceedings of Imaging and Applied Optics Congress OSA. 2016. P. AOT2C.1. http://doi.org/10.1364/AOMS.2016.AOT2C.1
8. Gerchberg R.W., Saxton W.O. A practical algorithm for the determination of phase from image and diffraction plane pictures // Optik. 1972. V. 35. № 2. P. 237–246.
9. Fienup J.R. Reconstruction of an object from the modulus of its Fourier transform // Optics Letters. 1978. V. 3. № 1. P. 27–29. http://doi.org/10.1364/OL.3.000027

10. Misell D.L. A method for the solution of the phase problem in electron microscopy // Journal of Physics D: Applied Physics. 1973. V. 6. № 1. P. L6–L9.
11. Misell D.L. An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations // Journal of Physics D. 1973. V. 6. P. 2200–2216. http://doi.org/10.1088/0022-3727/6/18/305
12. Gur E., Zalevsky Z. Image deblurring through static or time-varying random perturbation medium // Journal of Electronic Imaging. 2009. V. 18(3). P. 033016. http://doi.org/10.1117/1.3224953
13. Aviv M., Gur E., Zalevsky Z. Experimental results of revised Misell algorithm for imaging through weakly scattering biological tissue // Applied Optics. 2013. V. 52. № 11. P. 2300–2305. http://doi.org/10.1364/AO.52.002300
14. Itoh K. Analysis of the phase unwrapping algorithm // Applied Optics. 1982. V. 21. № 14. P. 2470–2470. http://doi.org/10.1364/AO.21.002470
15. Navarro M.A., Estrada J.C. Servin M., Quiroga J.A., Vargas J. Fast two-dimensional simultaneous phase unwrapping and low-pass filtering // Optics Express. 2012. V. 20. № 3. P. 2556–2561. http://doi.org/10.1364/OE.20.002556
16. Ivanova T.V., Letova E.Y., Kalinkina O.S., Nikiforova D.V., Strigalev V.E. An analysis of methods for aberrated spot diagram center evaluation // Scientific and Technical Journal of Information Technologies, Mechanics and Optics. 2021. V. 21. № 3. P. 334–341. http://doi.org/0.17586/2226-1494-2021-21-3