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Image of Discontinuity, Nonlinearity and Complexity
ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Wavefront Sensing using GMM Clustering for Initialization of L-BFGS Optimization

Discontinuity, Nonlinearity, and Complexity 14(3) (2025) 537--547 | DOI:10.5890/DNC.2025.09.007

Neha Goel, Dinesh Ganotra

Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University for Women, Delhi, 110006, India

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Abstract

This paper introduces a method for correcting wavefront aberrations using intensity images obtained under varying phase diversities. The proposed methodology integrates Gaussian mixture model (GMM) clustering and employs the resulting cluster centers as initial positions for a Limited memory Broyden Fletcher Goldfarb Shanno (L-BFGS) optimization process. The study evaluates the performance of this method using simulated data. The dataset consists of 500 distinct aberrations characterized by root mean square (RMS) errors ranging from 0.2$\lambda$ to 0.3$\lambda$. The analysis focuses on assessing the accuracy achieved, particularly emphasizing the effectiveness of wavefront reconstruction. The obtained RMS residual errors range from 0.017$\lambda$ (lowest) to 0.066$\lambda$ (highest), with an average of 0.039$\lambda$. Notably, 89.6\% of the RMS residual errors fall below 0.05$\lambda$. These results demonstrate the reliability and practicality of the proposed approach in wavefront aberration correction, as confirmed through numerical experimentation. Results can improve applications requiring precise wavefront correction for clear and detailed observations, such as astronomical imaging or high-resolution microscopy.

References

  1. [1]  Wyant, J.C. and Creath, K. (1992), Basic wavefront aberration theory for optical metrology, Applied Optics and optical engineering, 11(2), 28-39.
  2. [2]  Booth, M.J. and Creath, K. (2007), Wavefront sensorless adaptive optics for large aberrations, Optics Letters, 32(1), 5-7.
  3. [3]  Gerchberg, R.W. and Saxton, W.O. (1972), A practical algorithm for the determination of plane from image and diffraction pictures, Optik, 35(2), 237-246.
  4. [4]  Gonsalves, R.A. (1982), Phase retrieval and diversity in adaptive optics, Optical Engineering, 21(5), 19-22.
  5. [5]  Mugnier, L.M., Blanc, A., and Idier, J. (2006), Phase diversity: A technique for wavefront sensing and for diffraction-limited imaging, Advances in Imaging and Electron Physics, 141(5), 1-76.
  6. [6]  Zhao, L., Wang, K., and Bai, J. (2021), Large-scale phase retrieval method for wavefront reconstruction with multi-stage random phase modulation, Optics Communications, 498(2021), 127115-1-5.
  7. [7]  Yang, H., Soloviev, O., and Verhaegen, M. (2015), Model-based wavefront sensorless adaptive optics system for large aberrations and extended objects, Optics Express, 23(19), 24587-24601.
  8. [8]  Zhang, C., Wang, M., Chen, Q., Wang, D., and Wei, S. (2018), Two-step phase retrieval algorithm using single-intensity measurement, International Journal of Optics, 2018, Article ID 8643819.
  9. [9]  Allen, L.J. and Oxley, M.P. (2001), Phase retrieval from series of images obtained by defocus variation, Optics Communications, 199, 65-75.
  10. [10]  L\"{o}fdahl, M.G. and Scharmer, G.B. (1994), Wavefront sensing and image restoration from focused and defocused solar images, Astronomy $\&$ Astrophysics Supplement Series, 107, 243-264.
  11. [11]  Blanc, A., Mugnier, L.M., and Idier, J. (2003), Marginal estimation of aberrations and image restoration by use of phase diversity, Journal of Optical Society of America A, 20(6), 1035-1045.
  12. [12]  Fern{a}ndez, E.J., Hermann, B., Povazay, B., Unterhuber, A., Sattmann, H., Hofer, B., Ahnelt, P.K., and Drexler, W. (2008), Ultrahigh resolution optical coherence tomography and pancorrection for cellular imaging of the living human retina, Optics Express, 16(15), 11083-11094.
  13. [13]  Andersen, T.E., Owner-Petersen, M., and Enmark, A. (2020), Image-based wavefront sensing for astronomy using neural networks, Journal of Astronomical Telescopes, Instruments, and Systems, 6(3), 034002-1--15.
  14. [14]  M{\o}ller, M.F. (1993), A scaled conjugate gradient algorithm for fast supervised learning, Neural Networks, 6(4), 525-533.
  15. [15]  Zhong, J., Tian, L., Varma, P., and Waller, L. (2016), Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery, IEEE Transactions on Computational Imaging, 2(3), 310--322.
  16. [16]  Zhang, P.G., Yang, C.L., Xu, Z.H., Cao, Z.L., Mu, Q.Q., and Xuan, L. (2016), Hybrid particle swarm global optimization algorithm for phase diversity phase retrieval, Optics Express, 24(22), 25704-25717.
  17. [17]  Li, Z. and Zhao, X. (2017), BP artificial neural network based wavefront correction for sensorless free space optics communication, Optics Communications, 385, 219-228.
  18. [18]  White, J., Wang, S., Eschen, W., and Rothhardt, J. (2021), Real-time phase retrieval and wavefront sensing enabled by an artificial neural network, Optics Express, 29(6), 9283-9293.
  19. [19]  Lohani, S. and Glasser, R.T. (2018), Turbulence correction with artificial neural networks, Optics Letters, 43(11), 2611-2614.
  20. [20]  Ju, G., Qi, X., Ma, H., and Yan, C. (2018), Feature-based phase retrieval wavefront sensing approach using machine learning, Optics Express, 26(24), 31767-31783.
  21. [21]  Xin, Q., Ju, G., Zhang, C., and Xu, S. (2019), Object independent image-based wavefront sensing approach using phase diversity images and deep learning, Optics Express, 27(18), 26102-26119.
  22. [22]  Li, Y., Yue, D., and He, Y. (2022), Prediction of wavefront distortion for wavefront sensorless adaptive optics based on deep learning, Applied Optics, 61(14), 4168-4176.
  23. [23]  Paxman, R.G., Schulz, T.J., and Fienup, J.R. (1992), Joint estimation of object and aberrations by using phase diversity, Journal of the Optical Society of America A, 9(7), 1072-1085.
  24. [24]  Lee, D.J., Roggemann, M.C., and Welsh, B.M. (1999), Cramér-Rao analysis of phase-diverse wavefront sensing, Journal of the Optical Society of America A, 16(5), 1005-1015.
  25. [25]  Zhou, Z., Nie, Y., Fu, Q., Liu, Q., and Zhang, J. (2021), Robust statistical phase-diversity method for high-accuracy wavefront sensing, Optics and Lasers in Engineering, 137, 106335-1-9.
  26. [26]  Zhao, B., Zhong, Y., Ma, A., and Zhang, L. (2016), A spatial Gaussian mixture model for optical remote sensing image clustering, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 9(12), 5748-5759.
  27. [27]  Vogel, C.R. (2000), A limited memory BFGS method for an inverse problem in atmospheric imaging, Lecturer Notes in Earth Sciences (LNEARTH), 92(1), 292-304.
  28. [28]  Goodman, J.W. (2005), Introduction to Fourier optics (2nd ed.), McGraw-Hill Book Company: New York.
  29. [29]  Zhang, P., Yang, C., Xu, Z., Cao, Z., Mu, Q., and Xuan, L. (2017), High-accuracy wavefront sensing by phase diversity technique with bisymmetric defocuses diversity phase, Scientific Reports, 7(1), 1-10.
  30. [30]  Noll, R.J. (1976), Zernike polynomials and atmospheric turbulence, Journal of Optical Society of America, 63(3), 207-211.
  31. [31]  Bergkoetter, M.D. and Fienup, J.R. (2015), Increasing capture range of phase retrieval on a large scale laser system, Imaging and Applied Optics, paper CW4E-3.
  32. [32]  Moore, D.B. and Fienup, J.R. (2014), Extending the capture range of phase retrieval through random starting parameters, Frontier in Optics, OSA Technical Digest (Optical Publishing Group), paper FTu2C.2.
  33. [33]  Yue, D., Xu, S., and Nie, H. (2015), Co-phasing of the segmented mirror and image retrieval based on phase diversity using a modified algorithm, Applied Optics, 54(26), 7917-7924.
  34. [34]  Qureshi, S. and Jan, R. (2021), Modeling of measles epidemic with optimized fractional order under Caputo differential operator, Chaos Solitons $\&$ Fractals, 145, 110766-1-1.
  35. [35]  Qureshi, S., Chicharro, F. I., Argyros, I. K., Soomro, A., Alahmadi, J., and Hincal, E. (2024), A new optimal numerical root-solver for solving systems of nonlinear equations using local semi-local and stability analysis, Axioms, 13(6), 341-1-26.

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