OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 4 — Apr. 1, 2012
  • pp: 585–592

Focal-plane detection and object reconstruction in the noninterferometric phase imaging

Wen Chen and Xudong Chen  »View Author Affiliations

JOSA A, Vol. 29, Issue 4, pp. 585-592 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1198 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In this paper, we propose effective methods to detect focal planes and recover objects in the noninterferometric phase imaging. A strategy using different aberration coefficients is developed, and a series of diffraction intensity maps is sequentially recorded by a charge-coupled device. During numerical reconstruction, a phase retrieval algorithm is applied to extract object wavefront from diffraction intensity maps. Subsequently, numerical methods are proposed to detect focal planes, and high-quality phase maps are recovered by using the detected focal distances. Theoretical results are presented to demonstrate feasibility and effectiveness of the proposed methods.

© 2012 Optical Society of America

OCIS Codes
(100.2000) Image processing : Digital image processing
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Image Processing

Original Manuscript: July 26, 2011
Revised Manuscript: January 9, 2012
Manuscript Accepted: January 13, 2012
Published: March 26, 2012

Wen Chen and Xudong Chen, "Focal-plane detection and object reconstruction in the noninterferometric phase imaging," J. Opt. Soc. Am. A 29, 585-592 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400, 342–344 (1999). [CrossRef]
  2. J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003). [CrossRef]
  3. M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006). [CrossRef]
  4. J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998). [CrossRef]
  5. J. Miao, T. Ishikawa, E. H. Anderson, and K. O. Hodgson, “Phase retrieval of diffraction patterns from noncrystalline samples using the oversampling method,” Phys. Rev. B 67, 174104 (2003). [CrossRef]
  6. M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994). [CrossRef]
  7. F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007). [CrossRef]
  8. P. Almoro, G. Pedrini, and W. Osten, “Aperture synthesis in phase retrieval using a volume-speckle field,” Opt. Lett. 32, 733–735 (2007). [CrossRef]
  9. W. Chen and X. Chen, “Quantitative phase retrieval of complex-valued specimens based on noninterferometric imaging,” Appl. Opt. 50, 2008–2015 (2011). [CrossRef]
  10. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40–55 (2003). [CrossRef]
  11. H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. H. Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006). [CrossRef]
  12. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  13. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef]
  14. J. R. Fienup, “Phase retrieval using boundary conditions,” J. Opt. Soc. Am. A 3, 284–288 (1986). [CrossRef]
  15. J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986). [CrossRef]
  16. A. N. Simonov and M. C. Rombach, “Sharp-focus image restoration from defocused images,” Opt. Lett. 34, 2111–2113 (2009). [CrossRef]
  17. A. N. Simonov and M. C. Rombach, “Asymptotic behavior of the spatial frequency response of an optical system with defocus and spherical aberration,” J. Opt. Soc. Am. A 27, 2563–2573 (2010). [CrossRef]
  18. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]
  19. T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A 13, 1670–1682 (1996). [CrossRef]
  20. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009). [CrossRef]
  21. G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006). [CrossRef]
  22. G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Fresnel coherent diffractive imaging: treatment and analysis of data,” New J. Phys. 12, 035020 (2010). [CrossRef]
  23. W. Chen and X. Chen, “Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain,” Opt. Express 18, 13536–13541 (2010). [CrossRef]
  24. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  25. T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).
  26. M. V. Klein and T. E. Furtak, Optics, 2nd ed. (Wiley, 1986).
  27. Y. M. Engelberg and S. Ruschin, “Fast method for physical optics propagation of high-numerical-aperture beams,” J. Opt. Soc. Am. A 21, 2135–2145 (2004). [CrossRef]
  28. 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). [CrossRef]
  29. W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13, 075404 (2011). [CrossRef]
  30. C. Wu, T. W. Ng, and A. Neild, “Phase and amplitude retrieval of objects embedded in a sinusoidal background from its diffraction pattern,” Appl. Opt. 49, 1831–1837 (2010). [CrossRef]
  31. H. Shioya, Y. Maehara, and K. Gohara, “Spherical shell structure of distribution of images reconstructed by diffractive imaging,” J. Opt. Soc. Am. A 27, 1214–1218 (2010). [CrossRef]
  32. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).
  33. F. C. A. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81–91 (1985). [CrossRef]
  34. M. Bravo-Zanoguera, B. V. Massenbach, A. L. Kellner, and J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instrum. 69, 3966–3977 (1998). [CrossRef]
  35. F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 5895–5908 (2006). [CrossRef]
  36. W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009). [CrossRef]
  37. A. Hermerschmidt, S. Osten, J. Frank, and S. Krüger, “New liquid crystal microdisplays permit phase-only light modulation,” SPIE Newsroom (2006), http://spie.org/x8714.xml?highlight=x2408&ArticleID=x8714 . [CrossRef]
  38. D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948). [CrossRef]
  39. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997). [CrossRef]
  40. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). [CrossRef]
  41. J. Hua, L. Liu, and G. Li, “Extended fractional Fourier transforms,” J. Opt. Soc. Am. A 14, 3316–3322 (1997). [CrossRef]
  42. W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010). [CrossRef]
  43. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform With Applications in Optics and Signal Processing (Wiley, 2001).
  44. I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008). [CrossRef]
  45. W. McBride, N. L. O. Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr. Sect. A 61, 321–324 (2005).
  46. C. A. Henderson, G. J. Williams, A. G. Peele, H. M. Quiney, and K. A. Nugent, “Astigmatic phase retrieval: an experimental demonstration,” Opt. Express 17, 11905–11915 (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited