Abstract

The core problem of phase diversity phase retrieval (PDPR) is to find suitable optimization algorithms for wave-front sensing of different scales, especially for large-scale wavefront sensing. When dealing with large-scale wave-front sensing, existing gradient-based local optimization algorithms used in PDPR are easily trapped in local minimums near initial positions, and available global optimization algorithms possess low convergence efficiency. We construct a practicable optimization algorithm used in PDPR for large-scale wave-front sensing. This algorithm, named EPSO-BFGS, is a two-step hybrid global optimization algorithm based on the combination of evolutionary particle swarm optimization (EPSO) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Firstly, EPSO provides global search and obtains a rough global minimum position in limited search steps. Then, BFGS initialized by the rough global minimum position approaches the global minimum with high accuracy and fast convergence speed. Numerical examples testify to the feasibility and reliability of EPSO-BFGS for wave-front sensing of different scales. Two numerical cases also validate the ability of EPSO-BFGS for large-scale wave-front sensing. The effectiveness of EPSO-BFGS is further affirmed by performing a verification experiment.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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  1. D. J. Lee, B. M. Welsh, M. C. Roggemann, and B. L. Ellerbroek, “Diagnosing unknown aberrations in an adaptive optics system by use of phase diversity,” Opt. Lett. 22(13), 952–954 (1997).
    [Crossref] [PubMed]
  2. R. G. Paxman, B. J. Thelen, and J. H. Seldin, “Phase-diversity correction of turbulence-induced space-variant blur,” Opt. Lett. 19(16), 1231–1233 (1994).
    [Crossref] [PubMed]
  3. V. Korkiakoski, C. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint-optimization of phase-diversity and adaptive optics,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC5.
  4. J. J. Dolne, P. Menicucci, D. Miccolis, K. Widen, H. Seiden, F. Vachss, and H. Schall, “Real time phase diversity advanced image processing and wavefront sensing,” in Optical Engineering+ Applications (International Society for Optics and Photonics, 2007)
  5. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21(5), 829–832 (1982).
    [Crossref]
  6. D. J. Lee, M. C. Roggemann, B. M. Welsh, and E. R. Crosby, “Evaluation of least-squares phase-diversity technique for space telescope wave-front sensing,” Appl. Opt. 36(35), 9186–9197 (1997).
    [Crossref]
  7. N. Baba, H. Tomita, and N. Miura, “Iterative reconstruction method in phase-diversity imaging,” Appl. Opt. 33(20), 4428–4433 (1994).
    [Crossref] [PubMed]
  8. A. Wirth, R. Gonsalves, and A. Jankevics, “Adaptive optics enabled wavefront diversity sensing,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC4.
  9. V. Korkiakoski, C. U. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint optimization of phase diversity and adaptive optics: demonstration of potential,” Appl. Opt. 51(1), 102–113 (2012).
    [Crossref] [PubMed]
  10. I. Klapp and J. Rosen, “Phase diversity implementation in fresnel incoherent holography,” in Imaging and Applied Optics (Optical Society of America, 2013), p.CTh3C.3.
  11. N. Védrenne, L. M. Mugnier, V. Michau, M.-T. Velluet, and R. Bierent, “Laser beam complex amplitude measurement by phase diversity,” Opt. Express 22(4), 4575–4589 (2014).
    [Crossref] [PubMed]
  12. N. Védrenne, F. Cassaing, L. M. Mugnier, V. Michau, G. Iaquaniello, L. Blanco, and G. Chériaux, “Design and performance of an integrated phase and amplitude diversity sensor,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2015), paper STu2N.2
  13. P. Kner, “Phase diversity for three-dimensional imaging,” J. Opt. Soc. Am. A 30(10), 1980–1987 (2013).
    [Crossref]
  14. R. G. Paxman and J. R. Fienup, “Optical misalignment sensing and image reconstruction using phase diversity,” J. Opt. Soc. Am. A 5(6), 914–923 (1988).
    [Crossref]
  15. M. F. Fodslette, “A scaled conjugate gradient algorithm for fast supervised learning,” Neural. Netw. 6(4),525–533 (1993).
    [Crossref]
  16. X. Rondeau, E. Thiébaut, M. Tallon, and R. Foy, “Phase retrieval from speckle images,” J. Opt. Soc. Am. A 24(10), 3354–3365 (1988).
    [Crossref]
  17. P. M. Johnson, M. E. Goda, and V. L. Gamiz, “Multiframe phase-diversity algorithm for active imaging,” J. Opt. Soc. Am. A 24(7), 1894–1900 (2007).
    [Crossref]
  18. J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” in Proceedings of IEEE Transactions on Computational Imaging (IEEE, 2016), pp. 99
  19. L. Yeh, L. Tian, Z. Liu, M. Chen, J. Zhong, and L. Waller, “Experimental robustness of Fourier Ptychographic phase retrieval algorithms,” in Imaging and Applied Optics 2015 (Optical Society of America, 2015), paper CW4E.2
    [Crossref]
  20. Y. Huizhen and L. Yaoqiu, “Genetic algorithm for phase retrieval of generalized phase diversity,” Energy Procedia 13, 4806–4811 (2011).
  21. K. James, “Particle swarm optimization,” in Encyclopedia of Machine Learning (Springer, 2010)
  22. F. Van Den Bergh, “An analysis of particle swarm optimizers,” Ph.D. thesis, University of Pretoria, (2006).
  23. R. C. Eberhart and K. James, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (New York, 1995), pp. 39–43.
  24. J. W. Goodman and S. C. Gustafson, “Introduction to fourier optics,” Opt. Eng. 35(5), 1513 (1996).
    [Crossref]
  25. A. Blanc, L. M. Mugnier, and J. Idier, “Marginal estimation of aberrations and image restoration by use of phase diversity,” J. Opt. Soc. Am. A 20(6), 1035–1045 (2003).
    [Crossref]
  26. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207–211 (1976).
    [Crossref]
  27. M. Clerc, “The swarm and the queen: towards a deterministic and adaptive particle swarm optimization,” in Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress (IEEE, 1999).
  28. L. Meynadier, V. Michau, M.-T. Velluet, J.-M. Conan, L. M. Mugnier, and G. Rousset, “Noise propagation in wave-front sensing with phase diversity,” Appl. Opt. 38(23), 4967–4979 (1999).
    [Crossref]
  29. N. Baba and K. Mutoh, “Measurement of telescope aberrations through atmospheric turbulence by use of phase diversity,” Appl. Opt. 40(4), 544–552 (2001).
    [Crossref]
  30. L. M. Mugnier, A. Blanc, and J. Idier, “Phase diversity: a technique for wave-front sensing and for diffraction-limited imaging,” in Advances in Imaging and Electron Physics (Elsevier, 2006)
    [Crossref]
  31. N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990).
    [Crossref]
  32. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55(11), 1427–1435 (1965).
    [Crossref]

2014 (1)

2013 (1)

2012 (1)

2011 (1)

Y. Huizhen and L. Yaoqiu, “Genetic algorithm for phase retrieval of generalized phase diversity,” Energy Procedia 13, 4806–4811 (2011).

2007 (1)

2003 (1)

2001 (1)

1999 (1)

1997 (2)

1996 (1)

J. W. Goodman and S. C. Gustafson, “Introduction to fourier optics,” Opt. Eng. 35(5), 1513 (1996).
[Crossref]

1994 (2)

1993 (1)

M. F. Fodslette, “A scaled conjugate gradient algorithm for fast supervised learning,” Neural. Netw. 6(4),525–533 (1993).
[Crossref]

1990 (1)

N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990).
[Crossref]

1988 (2)

1982 (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21(5), 829–832 (1982).
[Crossref]

1976 (1)

1965 (1)

Baba, N.

Bierent, R.

Blanc, A.

A. Blanc, L. M. Mugnier, and J. Idier, “Marginal estimation of aberrations and image restoration by use of phase diversity,” J. Opt. Soc. Am. A 20(6), 1035–1045 (2003).
[Crossref]

L. M. Mugnier, A. Blanc, and J. Idier, “Phase diversity: a technique for wave-front sensing and for diffraction-limited imaging,” in Advances in Imaging and Electron Physics (Elsevier, 2006)
[Crossref]

Blanco, L.

N. Védrenne, F. Cassaing, L. M. Mugnier, V. Michau, G. Iaquaniello, L. Blanco, and G. Chériaux, “Design and performance of an integrated phase and amplitude diversity sensor,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2015), paper STu2N.2

Cassaing, F.

N. Védrenne, F. Cassaing, L. M. Mugnier, V. Michau, G. Iaquaniello, L. Blanco, and G. Chériaux, “Design and performance of an integrated phase and amplitude diversity sensor,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2015), paper STu2N.2

Chen, M.

L. Yeh, L. Tian, Z. Liu, M. Chen, J. Zhong, and L. Waller, “Experimental robustness of Fourier Ptychographic phase retrieval algorithms,” in Imaging and Applied Optics 2015 (Optical Society of America, 2015), paper CW4E.2
[Crossref]

Chériaux, G.

N. Védrenne, F. Cassaing, L. M. Mugnier, V. Michau, G. Iaquaniello, L. Blanco, and G. Chériaux, “Design and performance of an integrated phase and amplitude diversity sensor,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2015), paper STu2N.2

Clerc, M.

M. Clerc, “The swarm and the queen: towards a deterministic and adaptive particle swarm optimization,” in Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress (IEEE, 1999).

Conan, J.-M.

Crosby, E. R.

Doelman, N.

V. Korkiakoski, C. U. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint optimization of phase diversity and adaptive optics: demonstration of potential,” Appl. Opt. 51(1), 102–113 (2012).
[Crossref] [PubMed]

V. Korkiakoski, C. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint-optimization of phase-diversity and adaptive optics,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC5.

Dolne, J. J.

J. J. Dolne, P. Menicucci, D. Miccolis, K. Widen, H. Seiden, F. Vachss, and H. Schall, “Real time phase diversity advanced image processing and wavefront sensing,” in Optical Engineering+ Applications (International Society for Optics and Photonics, 2007)

Eberhart, R. C.

R. C. Eberhart and K. James, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (New York, 1995), pp. 39–43.

Ellerbroek, B. L.

Fienup, J. R.

Fodslette, M. F.

M. F. Fodslette, “A scaled conjugate gradient algorithm for fast supervised learning,” Neural. Netw. 6(4),525–533 (1993).
[Crossref]

Foy, R.

Fraanje, R.

V. Korkiakoski, C. U. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint optimization of phase diversity and adaptive optics: demonstration of potential,” Appl. Opt. 51(1), 102–113 (2012).
[Crossref] [PubMed]

V. Korkiakoski, C. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint-optimization of phase-diversity and adaptive optics,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC5.

Fried, D. L.

Gamiz, V. L.

Goda, M. E.

Gonsalves, R.

A. Wirth, R. Gonsalves, and A. Jankevics, “Adaptive optics enabled wavefront diversity sensing,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC4.

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21(5), 829–832 (1982).
[Crossref]

Goodman, J. W.

J. W. Goodman and S. C. Gustafson, “Introduction to fourier optics,” Opt. Eng. 35(5), 1513 (1996).
[Crossref]

Gustafson, S. C.

J. W. Goodman and S. C. Gustafson, “Introduction to fourier optics,” Opt. Eng. 35(5), 1513 (1996).
[Crossref]

Huizhen, Y.

Y. Huizhen and L. Yaoqiu, “Genetic algorithm for phase retrieval of generalized phase diversity,” Energy Procedia 13, 4806–4811 (2011).

Iaquaniello, G.

N. Védrenne, F. Cassaing, L. M. Mugnier, V. Michau, G. Iaquaniello, L. Blanco, and G. Chériaux, “Design and performance of an integrated phase and amplitude diversity sensor,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2015), paper STu2N.2

Idier, J.

A. Blanc, L. M. Mugnier, and J. Idier, “Marginal estimation of aberrations and image restoration by use of phase diversity,” J. Opt. Soc. Am. A 20(6), 1035–1045 (2003).
[Crossref]

L. M. Mugnier, A. Blanc, and J. Idier, “Phase diversity: a technique for wave-front sensing and for diffraction-limited imaging,” in Advances in Imaging and Electron Physics (Elsevier, 2006)
[Crossref]

James, K.

R. C. Eberhart and K. James, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (New York, 1995), pp. 39–43.

K. James, “Particle swarm optimization,” in Encyclopedia of Machine Learning (Springer, 2010)

Jankevics, A.

A. Wirth, R. Gonsalves, and A. Jankevics, “Adaptive optics enabled wavefront diversity sensing,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC4.

Johnson, P. M.

Keller, C.

V. Korkiakoski, C. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint-optimization of phase-diversity and adaptive optics,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC5.

Keller, C. U.

Klapp, I.

I. Klapp and J. Rosen, “Phase diversity implementation in fresnel incoherent holography,” in Imaging and Applied Optics (Optical Society of America, 2013), p.CTh3C.3.

Kner, P.

Korkiakoski, V.

V. Korkiakoski, C. U. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint optimization of phase diversity and adaptive optics: demonstration of potential,” Appl. Opt. 51(1), 102–113 (2012).
[Crossref] [PubMed]

V. Korkiakoski, C. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint-optimization of phase-diversity and adaptive optics,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC5.

Lee, D. J.

Liu, Z.

L. Yeh, L. Tian, Z. Liu, M. Chen, J. Zhong, and L. Waller, “Experimental robustness of Fourier Ptychographic phase retrieval algorithms,” in Imaging and Applied Optics 2015 (Optical Society of America, 2015), paper CW4E.2
[Crossref]

Menicucci, P.

J. J. Dolne, P. Menicucci, D. Miccolis, K. Widen, H. Seiden, F. Vachss, and H. Schall, “Real time phase diversity advanced image processing and wavefront sensing,” in Optical Engineering+ Applications (International Society for Optics and Photonics, 2007)

Meynadier, L.

Miccolis, D.

J. J. Dolne, P. Menicucci, D. Miccolis, K. Widen, H. Seiden, F. Vachss, and H. Schall, “Real time phase diversity advanced image processing and wavefront sensing,” in Optical Engineering+ Applications (International Society for Optics and Photonics, 2007)

Michau, V.

N. Védrenne, L. M. Mugnier, V. Michau, M.-T. Velluet, and R. Bierent, “Laser beam complex amplitude measurement by phase diversity,” Opt. Express 22(4), 4575–4589 (2014).
[Crossref] [PubMed]

L. Meynadier, V. Michau, M.-T. Velluet, J.-M. Conan, L. M. Mugnier, and G. Rousset, “Noise propagation in wave-front sensing with phase diversity,” Appl. Opt. 38(23), 4967–4979 (1999).
[Crossref]

N. Védrenne, F. Cassaing, L. M. Mugnier, V. Michau, G. Iaquaniello, L. Blanco, and G. Chériaux, “Design and performance of an integrated phase and amplitude diversity sensor,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2015), paper STu2N.2

Miura, N.

Mugnier, L. M.

N. Védrenne, L. M. Mugnier, V. Michau, M.-T. Velluet, and R. Bierent, “Laser beam complex amplitude measurement by phase diversity,” Opt. Express 22(4), 4575–4589 (2014).
[Crossref] [PubMed]

A. Blanc, L. M. Mugnier, and J. Idier, “Marginal estimation of aberrations and image restoration by use of phase diversity,” J. Opt. Soc. Am. A 20(6), 1035–1045 (2003).
[Crossref]

L. Meynadier, V. Michau, M.-T. Velluet, J.-M. Conan, L. M. Mugnier, and G. Rousset, “Noise propagation in wave-front sensing with phase diversity,” Appl. Opt. 38(23), 4967–4979 (1999).
[Crossref]

N. Védrenne, F. Cassaing, L. M. Mugnier, V. Michau, G. Iaquaniello, L. Blanco, and G. Chériaux, “Design and performance of an integrated phase and amplitude diversity sensor,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2015), paper STu2N.2

L. M. Mugnier, A. Blanc, and J. Idier, “Phase diversity: a technique for wave-front sensing and for diffraction-limited imaging,” in Advances in Imaging and Electron Physics (Elsevier, 2006)
[Crossref]

Mutoh, K.

Noll, R. J.

Paxman, R. G.

Roddier, N. A.

N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990).
[Crossref]

Roggemann, M. C.

Rondeau, X.

Rosen, J.

I. Klapp and J. Rosen, “Phase diversity implementation in fresnel incoherent holography,” in Imaging and Applied Optics (Optical Society of America, 2013), p.CTh3C.3.

Rousset, G.

Schall, H.

J. J. Dolne, P. Menicucci, D. Miccolis, K. Widen, H. Seiden, F. Vachss, and H. Schall, “Real time phase diversity advanced image processing and wavefront sensing,” in Optical Engineering+ Applications (International Society for Optics and Photonics, 2007)

Seiden, H.

J. J. Dolne, P. Menicucci, D. Miccolis, K. Widen, H. Seiden, F. Vachss, and H. Schall, “Real time phase diversity advanced image processing and wavefront sensing,” in Optical Engineering+ Applications (International Society for Optics and Photonics, 2007)

Seldin, J. H.

Tallon, M.

Thelen, B. J.

Thiébaut, E.

Tian, L.

L. Yeh, L. Tian, Z. Liu, M. Chen, J. Zhong, and L. Waller, “Experimental robustness of Fourier Ptychographic phase retrieval algorithms,” in Imaging and Applied Optics 2015 (Optical Society of America, 2015), paper CW4E.2
[Crossref]

J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” in Proceedings of IEEE Transactions on Computational Imaging (IEEE, 2016), pp. 99

Tomita, H.

Vachss, F.

J. J. Dolne, P. Menicucci, D. Miccolis, K. Widen, H. Seiden, F. Vachss, and H. Schall, “Real time phase diversity advanced image processing and wavefront sensing,” in Optical Engineering+ Applications (International Society for Optics and Photonics, 2007)

Van Den Bergh, F.

F. Van Den Bergh, “An analysis of particle swarm optimizers,” Ph.D. thesis, University of Pretoria, (2006).

Varma, P.

J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” in Proceedings of IEEE Transactions on Computational Imaging (IEEE, 2016), pp. 99

Védrenne, N.

N. Védrenne, L. M. Mugnier, V. Michau, M.-T. Velluet, and R. Bierent, “Laser beam complex amplitude measurement by phase diversity,” Opt. Express 22(4), 4575–4589 (2014).
[Crossref] [PubMed]

N. Védrenne, F. Cassaing, L. M. Mugnier, V. Michau, G. Iaquaniello, L. Blanco, and G. Chériaux, “Design and performance of an integrated phase and amplitude diversity sensor,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2015), paper STu2N.2

Velluet, M.-T.

Verhaegen, M.

V. Korkiakoski, C. U. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint optimization of phase diversity and adaptive optics: demonstration of potential,” Appl. Opt. 51(1), 102–113 (2012).
[Crossref] [PubMed]

V. Korkiakoski, C. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint-optimization of phase-diversity and adaptive optics,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC5.

Waller, L.

J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” in Proceedings of IEEE Transactions on Computational Imaging (IEEE, 2016), pp. 99

L. Yeh, L. Tian, Z. Liu, M. Chen, J. Zhong, and L. Waller, “Experimental robustness of Fourier Ptychographic phase retrieval algorithms,” in Imaging and Applied Optics 2015 (Optical Society of America, 2015), paper CW4E.2
[Crossref]

Welsh, B. M.

Widen, K.

J. J. Dolne, P. Menicucci, D. Miccolis, K. Widen, H. Seiden, F. Vachss, and H. Schall, “Real time phase diversity advanced image processing and wavefront sensing,” in Optical Engineering+ Applications (International Society for Optics and Photonics, 2007)

Wirth, A.

A. Wirth, R. Gonsalves, and A. Jankevics, “Adaptive optics enabled wavefront diversity sensing,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC4.

Yaoqiu, L.

Y. Huizhen and L. Yaoqiu, “Genetic algorithm for phase retrieval of generalized phase diversity,” Energy Procedia 13, 4806–4811 (2011).

Yeh, L.

L. Yeh, L. Tian, Z. Liu, M. Chen, J. Zhong, and L. Waller, “Experimental robustness of Fourier Ptychographic phase retrieval algorithms,” in Imaging and Applied Optics 2015 (Optical Society of America, 2015), paper CW4E.2
[Crossref]

Zhong, J.

L. Yeh, L. Tian, Z. Liu, M. Chen, J. Zhong, and L. Waller, “Experimental robustness of Fourier Ptychographic phase retrieval algorithms,” in Imaging and Applied Optics 2015 (Optical Society of America, 2015), paper CW4E.2
[Crossref]

J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” in Proceedings of IEEE Transactions on Computational Imaging (IEEE, 2016), pp. 99

Appl. Opt. (5)

Energy Procedia (1)

Y. Huizhen and L. Yaoqiu, “Genetic algorithm for phase retrieval of generalized phase diversity,” Energy Procedia 13, 4806–4811 (2011).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

Neural. Netw. (1)

M. F. Fodslette, “A scaled conjugate gradient algorithm for fast supervised learning,” Neural. Netw. 6(4),525–533 (1993).
[Crossref]

Opt. Eng. (3)

N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990).
[Crossref]

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21(5), 829–832 (1982).
[Crossref]

J. W. Goodman and S. C. Gustafson, “Introduction to fourier optics,” Opt. Eng. 35(5), 1513 (1996).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Other (12)

V. Korkiakoski, C. Keller, N. Doelman, R. Fraanje, and M. Verhaegen, “Joint-optimization of phase-diversity and adaptive optics,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC5.

J. J. Dolne, P. Menicucci, D. Miccolis, K. Widen, H. Seiden, F. Vachss, and H. Schall, “Real time phase diversity advanced image processing and wavefront sensing,” in Optical Engineering+ Applications (International Society for Optics and Photonics, 2007)

I. Klapp and J. Rosen, “Phase diversity implementation in fresnel incoherent holography,” in Imaging and Applied Optics (Optical Society of America, 2013), p.CTh3C.3.

A. Wirth, R. Gonsalves, and A. Jankevics, “Adaptive optics enabled wavefront diversity sensing,” in Imaging and Applied Optics, (Optical Society of America, 2011), p.JTuC4.

N. Védrenne, F. Cassaing, L. M. Mugnier, V. Michau, G. Iaquaniello, L. Blanco, and G. Chériaux, “Design and performance of an integrated phase and amplitude diversity sensor,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2015), paper STu2N.2

J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” in Proceedings of IEEE Transactions on Computational Imaging (IEEE, 2016), pp. 99

L. Yeh, L. Tian, Z. Liu, M. Chen, J. Zhong, and L. Waller, “Experimental robustness of Fourier Ptychographic phase retrieval algorithms,” in Imaging and Applied Optics 2015 (Optical Society of America, 2015), paper CW4E.2
[Crossref]

M. Clerc, “The swarm and the queen: towards a deterministic and adaptive particle swarm optimization,” in Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress (IEEE, 1999).

K. James, “Particle swarm optimization,” in Encyclopedia of Machine Learning (Springer, 2010)

F. Van Den Bergh, “An analysis of particle swarm optimizers,” Ph.D. thesis, University of Pretoria, (2006).

R. C. Eberhart and K. James, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (New York, 1995), pp. 39–43.

L. M. Mugnier, A. Blanc, and J. Idier, “Phase diversity: a technique for wave-front sensing and for diffraction-limited imaging,” in Advances in Imaging and Electron Physics (Elsevier, 2006)
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Flow chart of EPSO-BFGS algorithm.
Fig. 2
Fig. 2 Sketch map of EPSO-BFGS algorithm.
Fig. 3
Fig. 3 RMS errors chart with SD, CG, BFGS and EPSO-BFGS algorithms for wave-front aberrations of different RMS.
Fig. 4
Fig. 4 Simulation results of phase retrieval and reconstructed for the phase aberration of RMS=1.0λ, PV=5.8325λ. (a) and (d) are the simulated and reconstructed phases respectively, where the RMS phase error is 0.01092λ. (b) and (c) are the simulated focused and defocused images, respectively. (e) is the reconstructed object.
Fig. 5
Fig. 5 Simulation results of phase retrieval and reconstructed for the phase aberration of RMS=1.2λ, PV=8.6304λ. (a) and (d) are the simulated and reconstructed phases respectively, where the RMS phase error is 0.00096λ. (b) and (c) are the simulated focused and defocused images, respectively. (e) is the reconstructed object.
Fig. 6
Fig. 6 Simplified block diagram of the verification experiment system of PDPR.
Fig. 7
Fig. 7 Experimental results of PDPR for a 2λ(PV) defocus wave-front aberration. (a) contains the focal image(left) and the defocused image(right) collected by the CCD. (b),(c),(d) and (e) show the phases and images reconstructed by SD, CG, BFGS and EPSO-BFGS,respectively.
Fig. 8
Fig. 8 Experimental results of PDPR for three different wave-front aberrations by EPSO-BFGS. (a),(b) and (c) contain the the focal image, the defocused image, reconstructed phase and images, respectively.

Tables (4)

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Table 1 RMS errors(λ) achieved by SD, CG, BFGS and EPSO-BFGS algorithms for wavefront aberrations of different D/r0.

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Table 2 RMS errors(λ) achieved by SD, CG, BFGS and EPSO-BFGS algorithms for wavefront aberrations of different RMS.

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Table 3 RMS errors(λ) achieved by EPSO and EPSO-BFGS algorithms for different particle number N and iteration number M.

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Table 4 Coefficients of three cases used for simulations. Case1 is used for the simulations in Tab. 3. Case2 and case3 are large-scale phases for the simulations of Fig. 4 and Fig. 5.

Equations (25)

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i ( r ) = o ( r ) h ( r ) + n ( r ) ,
h ( r ) = | F T 1 { P ( v ) exp [ j ϕ ( v ) ] } | 2 ,
i d ( r ) = o ( r ) h d ( r ) + n d ( r ) ,
h d ( r ) = | F T 1 { P ( v ) exp [ j ( ϕ ( v ) + ϕ d ( v ) ) ] } | 2 ,
E = u E ˜ ( u ) = u { [ I ( u ) O ( u ) H ( u ) ] 2 + [ I d ( u ) O ( u ) H d ( u ) ] 2 }
O ( u ) = F T { o ( r ) } ,   I ( u ) = F T { i ( r ) } , I d ( u ) = F T { i d ( r ) } , H ( u ) = F T { h ( r ) } , H d ( u ) = F T { h d ( r ) } ,
E ˜ ( u ) O = 0 ,
O ( u ) = H ( u ) I ( u ) + H d ( u ) I d ( u ) | H ( u ) | 2 + | H d ( u ) | 2 .
E = u | I ( u ) H d ( u ) I d ( u ) H ( u ) | 2 | H ( u ) | 2 + | H d ( u ) | 2 .
ϕ ( v ) = j = 4 K a j Z j ( v ) .
a = [ a 4 , a 5 , , a K ] .
x ( 0 ) = x ( 0 ) ( i , j )
v ( 0 ) = v ( 0 ) ( i , j ) i = 1 , , N j = 4 , , K
v i , j ( n + 1 ) = φ { v i , j ( n ) + c 1 r 1 [ p i , l ( n ) x i , j ( n ) ] + c 2 r 2 [ p i , g ( n ) x i , j ( n ) ] } ,
x i , j ( n + 1 ) = x i , j ( n ) + v i , j ( n + 1 ) i = 1 , , N , j = 4 , , K ,
φ = 2 | 2 C C 2 4 C | , C = c 1 + c 2 , C > 4 .
p i , l ( n + 1 ) = { p i , l ( n ) , E ( x i , j ( n + 1 ) ) E ( p i , l ( n ) ) , x i , j ( n + 1 ) , E ( x i , j ( n + 1 ) ) < E ( p i , l ( n ) ) .
p i , g ( n + 1 ) = p , l ( n + 1 ) , p , l ( n + 1 ) { p i , g ( n ) , p i , l ( n + 1 ) } , E ( p , l ( n + 1 ) ) = min { E ( p i , g ( n ) ) , E ( p i , l ( n + 1 ) ) } .
p i , g ( n + 1 ) = p , l ( n + 1 ) , p , l ( n + 1 ) { p i , g ( n ) , p i , l ( n + 1 ) } , E ( p , l ( n + 1 ) ) = min { E ( p i , g ( n ) ) , E ( p i , l ( n + 1 ) ) } .
x i + N / 2 , j ( n + 1 ) = x i , j ( n + 1 ) , v i + N / 2 , j ( n + 1 ) = v i , j ( n + 1 ) i = 1 , , N / 2 , j = 4 , , K .
a = [ a 4 , a 5 , , a 15 ] .
R M S { ϕ t r u e } ( λ ) = 1 2 π [ v ( ϕ t r u e ( v ) ϕ a v e r ( v ) ) 2 / N T ] 1 2 ,
R M S error ( λ ) = 1 2 π [ v ( ϕ ( v ) ϕ t r u e ( v ) ) 2 / N T ] 1 2 .
Δ = d 8 ( F / D ) 2 .
O ( u ) = H ( u ) I ( u ) + H d ( u ) I d ( u ) | H ( u ) | 2 + | H d ( u ) | 2 + P n ( u ) / P f ( u ) .

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