DOI QR코드

DOI QR Code

Fast-Converging Algorithm for Wavefront Reconstruction based on a Sequence of Diffracted Intensity Images

  • Chen, Ni (School of Electrical Engineering, Seoul National University) ;
  • Yeom, Jiwoon (School of Electrical Engineering, Seoul National University) ;
  • Hong, Keehoon (School of Electrical Engineering, Seoul National University) ;
  • Li, Gang (School of Electrical Engineering, Seoul National University) ;
  • Lee, Byoungho (School of Electrical Engineering, Seoul National University)
  • Received : 2014.02.12
  • Accepted : 2014.04.23
  • Published : 2014.06.25

Abstract

A major advantage of wavefront reconstruction based on a series of diffracted intensity images using only single-beam illumination is the simplicity of setup. Here we propose a fast-converging algorithm for wavefront calculation using single-beam illumination. The captured intensity images are resampled to a series of intensity images, ranging from highest to lowest resampling; each resampled image has half the number of pixels as the previous one. Phase calculation at a lower resolution is used as the initial solution phase at a higher resolution. This corresponds to separately calculating the phase for the lower- and higher-frequency components. Iterations on the low-frequency components do not need to be performed on the higher-frequency components, thus making the convergence of the phase retrieval faster than with the conventional method. The principle is verified by both simulation and optical experiments.

Keywords

References

  1. W.-D. Joo, "Wavefront sensitivity analysis using global wavefront aberration in an unobscured optical system," J. Opt. Soc. Korea 16, 228-235 (2012). https://doi.org/10.3807/JOSK.2012.16.3.228
  2. C. M. Vest, Holographic Interferometry (Wiley, New York, USA, 1979).
  3. D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948). https://doi.org/10.1038/161777a0
  4. E. N. Leith and J. Upatnieks, "Wavefront reconstruction with continues-tone objects," J. Opt. Soc. Am. 53, 1377-1381 (1963). https://doi.org/10.1364/JOSA.53.001377
  5. T. Kreis and W. Juptner, "Suppression of the dc term in digital holography," Opt. Eng. 36, 2357-2360 (1997). https://doi.org/10.1117/1.601426
  6. M. R. Teague, "Irradiance moments: Their propagation and use for unique retrieval of phase," J. Opt. Soc. Am. 72, 1199-1209 (1982). https://doi.org/10.1364/JOSA.72.001199
  7. T. E. Gureyev, A. Roberts, and K. A. Nugenr, "Partially coherent fields, the transport of intensity equation, and the phase uniqueness," J. Opt. Soc. Am. A 12, 1942-1946 (1995).
  8. D. Paganin and K. A. Nugent, "Noninterferometric phase imaging with partially coherent light," Phys. Rev. Lett. 80, 2586-2589 (1998). https://doi.org/10.1103/PhysRevLett.80.2586
  9. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 227-246 (1972).
  10. J. R. Fienup, "Phase retrieval algorithms: A comparison," Appl. Opt. 21, 2758-2769 (1982). https://doi.org/10.1364/AO.21.002758
  11. G. Z. Yang, B. Z. Dong, B. Y. Gu, J. Y. Zhuang, and O. K. Ersoy, "Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: A comparison," Appl. Opt. 33, 209-218 (1994). https://doi.org/10.1364/AO.33.000209
  12. J. R. Fienup and A. M. Kowalczyk, "Phase retrieval for a complex-valued object by using a low-resolution image," J. Opt. Soc. Am. A 7, 450-458 (1990). https://doi.org/10.1364/JOSAA.7.000450
  13. J. R. Fienup, "Lensless coherent imaging by phase retrieval with an illumination pattern constraint," Opt. Express 14, 498-508 (2006). https://doi.org/10.1364/OPEX.14.000498
  14. W. O. Saxton, "Correction of artefacts in linear and nonlinear high resolution electron micrographs," J. Microsc. Spectrosc. Electron. 5, 661-670 (1980).
  15. D. L. Misell, "A method for the solution of the phase problem in electron microscopy," J. Phys. D: Appl. Phys. 6, L6-L9 (1973). https://doi.org/10.1088/0022-3727/6/1/102
  16. D. L. Misell, "An examination of an iterative method for the solution of the phase problem in optics and electron optics," J. Phys. D: Appl. Phys. 6, 2200-2225 (1973). https://doi.org/10.1088/0022-3727/6/18/305
  17. G. R. Brady, M. Guizar-Sicairos, and J. R. Fienup, "Optical wavefront measurement using phase retrieval with transverse translation diversity," Opt. Express 17, 624-639 (2009). https://doi.org/10.1364/OE.17.000624
  18. J. M. Rodenburg and H. M. L. Faulkner, "A phase retrieval algorithm for shifting illumination," Appl. Phys. Lett. 85, 4795-4797 (2004). https://doi.org/10.1063/1.1823034
  19. G. Pedrini, W. Osten, and Y. Zhang, "Wave-front reconstruction from a sequence of iterferograms recorded at different planes," Opt. Lett. 30, 833-835 (2005). https://doi.org/10.1364/OL.30.000833
  20. A. Anand, V. K. Chhaniwal, P. Almoro, G. Pedrini, and W. Osten, "Shape and deformation measurements of 3D objects using volume speckle field and phase retrieval," Opt. Lett. 34, 1522-1524 (2009). https://doi.org/10.1364/OL.34.001522
  21. P. F. Almoro, G. Pedrini, A. Anand, W. Osten, and S. G. Hanson, "Angular displacement and deformation analyses using a speckle-based wavefront sensor," Appl. Opt. 48, 932-940 (2009). https://doi.org/10.1364/AO.48.000932
  22. K. A. Nugent, "X-ray noninterferometric phase imaging: A unified picture," J. Opt. Soc. Am. A 24, 536-547 (2007). https://doi.org/10.1364/JOSAA.24.000536
  23. P. Almoro, G. Pedrini, and W. Osten, "Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field," Appl. Opt. 45, 8596-8605 (2006). https://doi.org/10.1364/AO.45.008596
  24. P. Almoro, A. M. S. Maallo, and S. G. Hanson, "Fastconvergent algorithm for speckle-based phase retrieval and a design for dynamic wavefront sensing," Appl. Opt. 48, 1485-1493 (2009). https://doi.org/10.1364/AO.48.001485
  25. L. Camacho, V. Mico, Z. Zalevsky, and J. Garcia, "Quantitative phase microscopy using defocusing by means of a spatial light modulator," Opt. Express 18, 6755-6766 (2010). https://doi.org/10.1364/OE.18.006755
  26. A. Agour, P. F. Almoro, and C. Falldorf, "Investigation of smooth wave fronts using SLM-based phase retrieval and a phase diffuser," J. Eur. Opt. Soc.-Rapid 7, 12046 (2012). https://doi.org/10.2971/jeos.2012.12046
  27. P. Almoro, J. Gluckstad, and S. G. Hanson, "Single-plane multiple speckle pattern phase retrieval using a deformable mirror," Opt. Express 18, 19304-19313 (2010). https://doi.org/10.1364/OE.18.019304
  28. A. Anand, G. Pedrini, W. Osten, and P. Almoro, "Wavefront sensing with random amplitude mask and phase retrieval," Opt. Lett. 32, 1584-1586 (2007). https://doi.org/10.1364/OL.32.001584
  29. P. F. Almoro and S. G. Hanson, "Random phase plate for wavefront sensing via phase retrieval and a volume speckle field," Appl. Opt. 47, 2979-2987 (2008). https://doi.org/10.1364/AO.47.002979
  30. J. L. Crowley and A. C. Sanderson, "Multiple resolution representation and probabilistic matching of 2-D gray-scale shape," IEEE Trans. Pattern Anal. Mach. Intel. 9, 113-121 (1987).
  31. T. Lindeberg, "Scale-space for discrete signals," IEEE Trans. Pattern Anal. Mach. Intel. 12, 234-254 (1990). https://doi.org/10.1109/34.49051
  32. B. E. A. Saleh and M. C. Teich, Fundamental of Photonics, 2nd ed. (John Wiley & Sons, Inc., Hoboken, United States, 2007).
  33. M. R. Teague, "Irradiance moments: Their propagation and use for unique retrieval of phase," J. Opt. Soc. Am. 72, 1199-1209 (1982). https://doi.org/10.1364/JOSA.72.001199
  34. T. Acharya and P. S. Tsai, "Computational foundations of image interpolation algorithms," ACM Ubiquity 8, page 4 (2007).
  35. F. P. Miller, A. F. Vandome, and J. McBrewster, Bicubic Interpolation (Alphascript Publishing, United States, 2010).
  36. D. Fraser, "Interpolation by the FFT revisited - An experimental investigation," IEEE Trans. Acoust. Speech Signal Process 37, 665-675 (1989). https://doi.org/10.1109/29.17559
  37. T. Smith, M. S. Smith, and S. T. Nichols, "Efficient sinc function interpolation technique for center padded data," IEEE Trans. Acoust. Speech Signal Process 38, 1512-1517 (1990). https://doi.org/10.1109/29.60071
  38. L. Yaroslavsky, "Efficient algorithm for discrete sinc interpolation," Appl. Opt. 36, 460-463 (1997). https://doi.org/10.1364/AO.36.000460
  39. A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, "Optical ptychography: A practical implementation with useful resolution," Opt. Lett. 35, 2585-2587 (2010). https://doi.org/10.1364/OL.35.002585
  40. K. Matsushima and T. Shimobaba, "Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields," Opt. Express 17, 19662-19673 (2009). https://doi.org/10.1364/OE.17.019662
  41. S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, "Diversity selection for phase-diverse phase retrieval," J. Microscopy 207, 79-96 (2002). https://doi.org/10.1046/j.1365-2818.2002.01046.x

Cited by

  1. Fast and robust misalignment correction of Fourier ptychographic microscopy for full field of view reconstruction vol.26, pp.18, 2018, https://doi.org/10.1364/OE.26.023661
  2. Analysis of Fourier ptychographic microscopy with half of the captured images vol.20, pp.9, 2018, https://doi.org/10.1088/2040-8986/aad453