Non-iterative solution of the phase retrieval problem using a single diffraction measurement
Optics Express, Vol. 16, Issue 10, pp. 6896-6903 (2008)
http://dx.doi.org/10.1364/OE.16.006896
Enhanced HTML 
Acrobat PDF (322 KB)
Abstract
Coherent diffractive imaging is a method by which iterative methods are employed to recover image information about a finite object from its coherent diffraction pattern. We employ methods borrowed from density functional theory to show that an image can be recovered in a single non-iterative step for a finite sample subject to phase-curved illumination. The result also yields a new approach to quantitative x-ray phase-contrast imaging.
© 2008 Optical Society of America
OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(100.3010) Image processing : Image reconstruction techniques
(100.5070) Image processing : Phase retrieval
(110.7440) Imaging systems : X-ray imaging
ToC Category:
Image Processing
History
Original Manuscript: February 11, 2008
Revised Manuscript: March 18, 2008
Manuscript Accepted: April 20, 2008
Published: April 30, 2008
Citation
H. M. Quiney, G. J. Williams, and K. A. Nugent, "Non-iterative solution of the phase retrieval problem using a single diffraction measurement," Opt. Express 16, 6896-6903 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-6896
Sort: Year | Journal | Reset
References
- J. W. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature 400, 342-344 (1999). [CrossRef]
- J. R. Fienup, "Phase retrieval algorithms- a comparison," Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]
- V. Elser, "Phase retrieval by iterated projections," J. Opt. Soc. A. 20, 40-55 (2003). [CrossRef]
- S. Marchesini, H. He, H. N. Chapman, S. P Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B. 68, 140101 (2003). [CrossRef]
- D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005). [CrossRef] [PubMed]
- I. K. Robinson, I. A. Vartanyants, G. J. Williams, M. A. Pfeifer, and J. A. Pitney, "Reconstruction of the shapes of gold nanocrystals using coherent X-ray diffraction," Phys. Rev. Lett. 87, 195505 (2001). [CrossRef] [PubMed]
- 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] [PubMed]
- R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, "Potential for biomolecular imaging with femtosecond X-ray pulses," Nature 406, 752-757 (2000). [CrossRef] [PubMed]
- H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006). [CrossRef]
- A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995). [CrossRef]
- M. W. Westneat, O. Betz, R. W. Blob, K. Fezzaa, W. J. Cooper, and W. K. Lee, "Tracheal respiration in insects visualized with synchrotron X-ray imaging," Science 299, 558-560 (2003). [CrossRef] [PubMed]
- D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997). [CrossRef] [PubMed]
- P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M Schlenker, "Holotomography: quantitative phase tomographywith micrometre resolution using hard synchrotron radiation X-rays," Appl. Phys. Lett. 75, 2912-2914 (1999). [CrossRef]
- K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard X-rays," Phys. Rev. Lett. 77, 2961-2964 (1996). [CrossRef] [PubMed]
- K. A. Nugent, D. Paganin, and T. E. Gureyev, "A phase odyssey," Physics Today 54, 27-32 (2001). [CrossRef]
- G. J. Williams, H. M. Quiney, B. B. Dhal, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, "Fresnel coherent diffractive imaging," Phys. Rev. Lett. 97, 025506 (2006). [CrossRef] [PubMed]
- D. Sayre, "Some implications of a theorem due to Shannon," Acta. Cryst. 5, 843 (1952). [CrossRef]
- 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]
- K. A. Nugent, "X-ray non-interferometric phase imaging: a unified picture," J. Opt. Soc. Am. A 24, 536-547 (2007). [CrossRef]
- M. R. Teague, "Deterministic phase retrieval: a Green�??s function solution," J. Opt. Soc. Am. 73, 1434-1441 (1983). [CrossRef]
- D. Paganin, Coherent X-ray Optics (Oxford University Press, 2005).
- K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, "Unique phase recovery for nonperiodic objects," Phys. Rev. Lett. 91, 203902 (2003). [CrossRef] [PubMed]
- T. E. Gureyev, A. Roberts, and K. A. Nugent, "Partially coherent fields, the transport of intensity equation, and phase uniqueness," J.Opt. Soc. Am. A. 12, 1942-1946 (1995). [CrossRef]
- R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension. 1: Underlying theory," Optik 61, 247-262 (1982).
- M. Abramowitz and I. Stegun (eds), Handbook of Mathematical Functions, Dover Publications, New York (1970).
- H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focussed X-ray fields," Nature Physics 2, 101-104 (2006). [CrossRef]
- P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Phys. Rev. B 136, B864 (1964). [CrossRef]
- D. Paganin and K. A. Nugent, "Noninterferometric phase imaging with partially coherent light," Phys. Rev. Lett. 802586-2589 (1998). [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.
Related Journal Articles 
- Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field (AO)
- Aperture synthesis in phase retrieval using a volume-speckle field (OL)
- Wavefront sensing with random amplitude mask and phase retrieval (OL)
- Phase retrieval with transverse translation diversity: a nonlinear optimization approach (OE)
- Wavefront sensing using speckles with fringe compensation (OE)
Related Conference Papers
- Coherent imaging with illumination optics designed for the reconstruction algorithm
- Transport of Intensity Imaging with Higher Order Derivatives
- Schulz-Snyder Phase Retrieval Algorithm as an Alternating Minimization Algorithm
- Methods and Applications of X-ray Phase Nanotomography
- Low-complexity noise-resilient recovery of phase and amplitude from defocused intensity images
« Previous Article | Next Article »
OSA is a member of 