Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain

Optics Express

Volumn 18, Issue 13, 2010, Pages 13536-13541

  Chen, Wen ^a   Chen, Xudong ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; WAVELET TRANSFORMS;

DIFFRACTION INTENSITY; FRACTIONAL FOURIER DOMAINS; FRACTIONAL FOURIER TRANSFORMS; PHASE RETRIEVAL; PHASE RETRIEVAL ALGORITHM; PROOF OF PRINCIPLES; VARIABLE FUNCTIONS;

FOURIER TRANSFORMS;

ALGORITHM; ARTICLE; ARTIFACT; FEASIBILITY STUDY; FOURIER ANALYSIS; HOLOGRAPHY; METHODOLOGY; PHASE CONTRAST MICROSCOPY; THEORETICAL MODEL;

ALGORITHMS; ARTIFACTS; FEASIBILITY STUDIES; FOURIER ANALYSIS; HOLOGRAPHY; MICROSCOPY, PHASE-CONTRAST; MODELS, THEORETICAL;

EID: 77953864162     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.18.013536     Document Type: Article

References (17)

1. J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, "Atomic resolution imaging of a carbon nanotube from diffraction intensities," Science 300(5624), 1419-1421 (2003).
2. 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(7098), 63-66 (2006).
3. D. Gabor, "A new microscopic principle," Nature 161(4098), 777-778 (1948).
4. C. J. Mann, L. Yu, C. Lo, and M. K. Kim, "High-resolution quantitative phase-contrast microscopy by digital holography," Opt. Express 13, 8693-8698 (2005), http://www.opticsi.nfobase.org/oe/abstract.cfm? URI = oe-13-22-8693.
5. W. Chen, C. Quan, and C. J. Tay, "Extended depth, of focus in a particle field measurement using a single-shot digital hologram," Appl. Phys. Lett. 95(20), 201103 (2009).
6. W. Chen, C. Quan, and C. J. Tay, "Measurement of curvature and twist of a deformed object using digital holography," Appl. Opt. 47(15), 2874-2881 (2008).
7. I. Yamaguchi, and T. Zhang, "Phase-shifting digital, holography," Opt. Lett. 22(16), 1268-1270 (1997).
8. R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 237-246 (1972).
9. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21(15), 2758-2769 (1982).
10. 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(6742), 342-344 (1999).
11. Y. J. Uu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, "Phase retrieval in X-ray imaging based on using structured illumination," Phys. Rev. A 78(2), 023817 (2008).
12. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
13. A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Am. A. 10(10), 2181-2186 (1993).
14. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).
15. M. G. Ertosun, H. Atli, H. M. Ozaktas, and B. Barshan, "Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence," Opt. Commun. 244(1-6), 61-70 (2005).
16. M. G. Ertosun, H. Atli, H. M. Ozaktas, and B. Barshan, "Complex signal recovery from multiple fractional Fourier-transform intensities," Appl. Opt. 44(23), 4902-4908 (2005).
17. J. Hua, L. Liu, and G. Li, "Extended fractional Fourier transforms," J. Opt. Soc. Am. A 14(12), 3316-3322 (1997).