Skip to main content
Log in

Comparative Analysis of the Interferogram Sensitivity to Wavefront Aberrations Recorded with Plane and Cylindrical Reference Beams

  • Published:
Optical Memory and Neural Networks Aims and scope Submit manuscript

Abstract

The paper investigates the sensitivity of interferograms formed using the structured reference beams. The parameters of the reference beam are selected to improve the visualization of aberrations in the interferograms. A study carried out on the use of reference beams with cylindrical wavefronts in the interferograms formation to improve the aberrations recognition using a convolutional neural network. The applying of a cylindrical reference beam instead of a plane one in the interference method for recognition of wave aberrations based on neural networks with Xception architecture makes it possible to reduce the mean absolute error by more than 30%. In this work, for each type of interferogram, the model was trained for 80 epochs, which took about 1.8 hours using GeForce RTX 2070 graphics card. However, after completing this training once, we obtain a model that allows us to make forecasts in 0.055 s for every new interferogram of the same type.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

Similar content being viewed by others

REFERENCES

  1. Park, J.H. and Lee, B., Holographic techniques for augmented reality and virtual reality near-eye displays, Light: Adv. Manuf., 2022, vol. 3, no. 1, pp. 1–14.

    Google Scholar 

  2. Booth, M., Andrade, D., Burke, D., Patton, B., and Zurauskas, M., Aberrations and adaptive optics in super-resolution microscopy, Microscopy, 2015, vol. 64, no. 4, pp. 251–261.

    Article  Google Scholar 

  3. Klebanov, I.M., et al., Wavefront aberration compensation of space telescopes with telescope temperature field adjustment, Comput. Opt., 2017, vol. 41, no. 1, pp. 30–36. https://doi.org/10.18287/0134-2452-2017-41-1-30-36

    Article  Google Scholar 

  4. Golub, M.A., Kazanskiy, N.L., Sisakian, I.N., and Soifer, V.A., Computer-generated optical elements for optical testing, Proc. SPIE, 1990, vol. 1319. https://doi.org/10.1117/12.34894

  5. Lombardo, M. and Lombardo, G., Wave aberration of human eyes and new descriptors of image optical quality and visual performance, J. Cataract Refractive Surg., 2010, vol. 36, no. 2, pp. 313–331.

    Article  Google Scholar 

  6. Khorin, P.A., Khonina, S.N., Karsakov, A.V., and Branchevsky, S.L., Analysis of corneal aberration of the human eye, Comput. Opt., 2016, vol. 40, no. 6, pp. 810–817. https://doi.org/10.18287/0134-2452-2016-40-6-810-817

    Article  Google Scholar 

  7. Bisch, N., Guan, J., Booth, M.J., and Salter, P.S., Adaptive optics aberration correction for deep direct laser written waveguides in the heating regime, Appl. Phys. A, 2019, vol. 125, no. 5, pp. 1–6.

    Article  Google Scholar 

  8. Bian, Y., Li, Y., Li, W., Hong, X., Qiu, J., Chen, E., et el., The impact of optical system aberration and fiber positioning error on the FMF coupling efficiency for FSO receiver under atmospheric turbulence, J. Opt., 2022, vol. 24, pp. 085701.

    Article  Google Scholar 

  9. Cabriel, C., Bourg, N., Dupuis, G., and Lévêque-Fort, S., Aberration-accounting calibration for 3D single-molecule localization microscopy, Opt. Lett., 2018, vol. 43, no. 2, pp. 174–177.

    Article  Google Scholar 

  10. Kuschmierz, R., Scharf, E., Ortegón-González, D.F., Glosemeyer, T., and Czarske, J.W., Ultra-thin 3D lensless fiber endoscopy using diffractive optical elements and deep neural networks, Light: Adv. Manuf., 2021, vol. 2, no. 4, pp. 415–424.

    Google Scholar 

  11. Ellerbroek, B.L. and Vogel, C.R., Inverse problems in astronomical adaptive optics, Inverse Probl., 2009, vol. 25, no. 6, pp. 063001.

    Article  MathSciNet  MATH  Google Scholar 

  12. Ji, N., Adaptive optical fluorescence microscopy, Nat. Methods, vol. 14, no. 4, 2017, pp. 374–380.

    Article  Google Scholar 

  13. Bouchez, A.H., Angeli, G.Z., Ashby, D.S., Bernier, R., Conan, R., McLeod, B.A., et al., An overview and status of GMT active and adaptive optics, Adapt. Opt. Syst. VI, 2018, vol. 10703, pp. 284–299. https://doi.org/10.1117/12.2314255

    Article  Google Scholar 

  14. Khorin, P.A., Porfirev, A.P., and Khonina, S.N., Adaptive detection of wave aberrations based on the multichannel filter, Photonics, 2022, vol. 9, no. 3, pp. 204. https://doi.org/10.3390/photonics9030204

    Article  Google Scholar 

  15. Georgieva, A.O., Belashov, A.V., and Petrov, N.V., Complex wavefront manipulation and holographic correction based on digital micromirror device: A study of spatial resolution and discretisation, Proc. SPIE, 2020, vol. 11294, pp. 112940B.

    Google Scholar 

  16. Venkanna, M. and Sagar, K.D., Edge imaging characteristics of aberrated coherent optical systems by edge masking of circular apertures, Comput. Opt., 2022, vol. 46, no. 3, pp. 388–394. https://doi.org/10.18287/2412-6179-CO-940

    Article  Google Scholar 

  17. Greisukh, G.I., Ezhov, E.G., and Antonov, A.I., Correction of chromatism of dual-infrared zoom lenses, Comput. Opt., 2020, vol. 44, no. 2, pp. 177–182. https://doi.org/10.18287/2412-6179-CO-623

    Article  Google Scholar 

  18. Zepp, A., Gladysz, S., Stein, K., and Osten, W., Simulation-based design optimization of the holographic wavefront sensor in closed-loop adaptive optics, Light: Adv. Manuf., 2022, vol. 3, no. 3, pp. 384–399. https://doi.org/10.37188/lam.2022.027

    Article  Google Scholar 

  19. Platt, B.C. and Shack, R., History and principles of Shack-Hartmann wavefront sensing, J. Refract. Surg., 2001, vol. 17, no. 5, pp. S573–S577.

    Article  Google Scholar 

  20. Hongbin, Y., Guangya, Z., Siong, C. F., Feiwen, L., and Shouhua, W., A tunable Shack–Hartmann wavefront sensor based on a liquid-filled microlens array, J. Micromech. Microeng., 2008, vol. 18, no. 10, pp. 105017.

    Article  Google Scholar 

  21. Fauvarque, O., Neichel, B., Fusco, T., Sauvage, J.F., and Girault, O., General formalism for Fourier-based wavefront sensing: application to the pyramid wavefront sensors, J. Astron. Telesc. Instrum. Syst., 2017, vol. 3, no. 1, pp. 019001.

    Article  Google Scholar 

  22. Hutterer, V., Ramlau, R., and Shatokhina, I., Real-time adaptive optics with pyramid wavefront sensors. Part I: A theoretical analysis of the pyramid sensor model, Inverse Probl., 2019, vol. 35, no. 4, pp. 045007.

    Article  MathSciNet  MATH  Google Scholar 

  23. Karpeev, S.V., Pavelyev, V.S., Khonina, S.N., and Kazanskiy, N.L., High-effective fiber sensors based on transversal mode selection, Proc. SPIE, 2005, vol. 5854, pp. 163–169.

    Article  Google Scholar 

  24. Fang, Z., Chin, K., Qu, R., and Cai, H., Hoboken, N.J.: Wiley, 2012. ISBN: 978-0-470-57540-6.

  25. Khonina, S.N., Karpeev, S.V., and Paranin, V.D., Birefringence detection of a gradient-index lens based on astigmatic transformation of a Bessel beam, Optik, 2018, vol. 164, pp. 679–685. https://doi.org/10.1016/j.ijleo.2018.03.086

    Article  Google Scholar 

  26. Booth, M.J., Direct measurement of Zernike aberration modes with a modal wavefront sensor, Proc. SPIE, 2003, vol. 5162, pp. 79–90.

    Article  Google Scholar 

  27. Porfirev, A.P. and Khonina, S.N., Experimental investigation of multi-order diffractive optical elements matched with two types of Zernike functions, Proc. SPIE, 2016, vol. 9807, pp. 98070E. https://doi.org/10.1117/12.2231378

    Article  Google Scholar 

  28. Khonina, S.N., Karpeev, S.V., and Porfirev, A.P., Wavefront aberration sensor based on a multichannel diffractive optical element, Sensors, 2020, vol. 20, no. 14, pp. 3850.

    Article  Google Scholar 

  29. Khorin, P.A., Volotovsky, S.G., and Khonina, S.N., Optical detection of values of separate aberrations using a multi-channel filter matched with phase Zernike functions, Comput. Opt., 2021, vol. 45, no. 4, pp. 525–533. https://doi.org/10.18287/2412-6179-CO-906

    Article  Google Scholar 

  30. Malacara, D., Optical Shop Testing, Hoboken, NJ, USA: Wiley, 2007.

    Book  Google Scholar 

  31. Gao, W., Huyen, N.T.T., Loi, H.S., and Kemao, Q., Real-time 2D parallel windowed Fourier transform for fringe pattern analysis using Graphics Processing Unit, Opt. Express, 2009, vol. 17, no. 25, pp. 23147–23152.

    Article  Google Scholar 

  32. Firsov, N.A., Podlipnov, V.V., Ivliev, N.A., Nikolaev, P.P., Mashkov, S.V., Ishkin, P.A., Skidanov, R.V., and Nikonorov, A.V., Neural network-aided classification of hyperspectral vegetation images with a training sample generated using an adaptive vegetation index, Comput. Optics, 2021, vol. 45, no. 6, pp. 887–896. https://doi.org/10.18287/2412-6179-CO-1038l

    Article  Google Scholar 

  33. Abdulkadirov, R.I. and Lyakhov, P.A., A new approach to training neural networks using natural gradient descent with momentum based on Dirichlet distributions, Comput. Opt., 2023, vol. 47, no. 1, pp. 160–169. https://doi.org/10.18287/2412-6179-CO-1147

    Article  Google Scholar 

  34. Evdokimova, V.V., Petrov, M.V., Klyueva, M.A., Zybin, E.Y., and Kosianchuk, V.V., Deep learning-based video stream reconstruction in mass production diffractive optical systems, Comput. Opt., 2021, vol. 45, no. 1, pp. 130–141. https://doi.org/10.18287/2412-6179-CO-834

    Article  Google Scholar 

  35. Rivenson, Y., Zhang, Y., Günaydın, H., Teng, D., and Ozcan, A., Phase recovery and holographic image reconstruction using deep learning in neural networks, Light: Sci. Appl., 2018, vol. 7, no. 2, pp. 17141–17141. https://doi.org/10.1038/lsa.2017.141

    Article  Google Scholar 

  36. Andersen, T., Owner-Petersen, M., and Enmark, A., Neural networks for image-based wavefront sensing for astronomy, Opt. Lett., 2019, vol. 44, no. 18, pp. 4618–4621.

    Article  Google Scholar 

  37. Jia, P., Wu, X., Yang, X., Huang, Y., Cai, B., and Cai, D., Astronomical image restoration and point spread function estimation with deep neural networks, SPIE Astron. J., 2020, vol. 11203, pp. 42–45.

    Google Scholar 

  38. Rodin, I.A., Khonina, S.N., Serafimovich, P.G., and Popov, S.B., Recognition of wavefront aberrations types corresponding to single Zernike functions from the pattern of the point spread function in the focal plane using neural networks, Comput. Opt., 2020, vol. 44, no. 6, pp. 923–930. https://doi.org/10.18287/2412-6179-CO-810

    Article  Google Scholar 

  39. Khorin, P.A., Dzyuba, A.P., Serafimovich, P.G., and Khonina, S.N., Neural networks application to determine the types and magnitude of aberrations from the pattern of the point spread function out of the focal plane, J. Phys.: Conf. Ser., 2021, vol. 2086, pp. 012148-7. https://doi.org/10.1088/1742-6596/2086/1/012148

    Article  Google Scholar 

  40. Liu, X., Yang, Z., Dou, J., and Liu, Z., Fast demodulation of single-shot interferogram via convolutional neural network, Opt. Commun., 2021, vol. 487, pp. 126813.

    Article  Google Scholar 

  41. Khonina, S.N., Khorin, P.A., Serafimovich, P.G., Dzyuba, A.P., Georgieva, A.O., and Petrov, N.V., Analysis of the wavefront aberrations based on neural networks processing of the interferograms with a conical reference beam, Appl. Phys. B, 2022, vol. 128, no. 3, pp. 60.

    Article  Google Scholar 

  42. Born, M. and Wolf, E., Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed., Cambridge: Cambridge Univ. Press, 1999.

    Book  MATH  Google Scholar 

  43. Sherif, S.S., Cathey, W.T., and Dowski, E.R., Phase plate to extend the depth of field of incoherent hybrid imaging systems, Appl. Opt., 2004, vol. 43, no. 13, pp. 2709–2721.

    Article  MATH  Google Scholar 

  44. Khonina, S.N. and Ustinov, A.V., Generalized apodization of an incoherent imaging system aimed for extending the depth of focus, Pattern Recognit. Image Anal., 2015, vol. 25, no. 4, pp. 626–631. https://doi.org/10.1134/S1054661815040100

    Article  Google Scholar 

  45. Khonina, S.N., Volotovskiy, S.G., Dzyuba, A.P., Serafimovich, P.G., Popov, S.B., and Butt, M.A., Power phase apodization study on compensation defocusing and chromatic aberration in the imaging system, Electronics, 2021, vol. 10, no. 11, pp. 1327. https://doi.org/10.3390/electronics10111327

    Article  Google Scholar 

  46. Khorin, P.A. and Volotovskiy, S.G., Analysis of the threshold sensitivity of a wavefront aberration sensor based on a multi-channel diffraction optical element, Proc. SPIE, 2021, vol. 11793, pp. 117930B.

    Google Scholar 

  47. Chollet, F., Xception: Deep learning with depthwise separable convolutions, in Proceedings of the IEEE Conference on Computer Vision and Pattern recognition, 2017, pp. 1251–1258.

Download references

Funding

This work was supported by the grant of the President of the Russian Federation, no. MD-6101.2021.1.2.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. A. Khorin.

Ethics declarations

The authors declare that they have no conflicts of interest.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khorin, P.A., Dzyuba, A.P. & Petrov, N.V. Comparative Analysis of the Interferogram Sensitivity to Wavefront Aberrations Recorded with Plane and Cylindrical Reference Beams. Opt. Mem. Neural Networks 32 (Suppl 1), S27–S37 (2023). https://doi.org/10.3103/S1060992X23050090

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1060992X23050090

Keywords:

Navigation