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Phase retrieval by iterated projections
Open accessAbstract
Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and three real parameters. For the standard application in optics, where the two projections implement Fourier modulus and object support constraints, respectively, the difference map reproduces the "hybrid" form of Fienup's input-output map when a particular choice is made for two of the parameters. The geometric construction of the difference map illuminates the distinction between its fixed points and the recovered object, as well as the mechanism whereby the form of stagnation encountered by alternating projection schemes is avoided. When support constraints are replaced by object histogram or atomicity constraints, the difference map lends itself to crystallographic phase retrieval. Numerical experiments with synthetic data suggest that structures with hundreds of atoms can be solved.
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Cited by
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Thibault, P., Dierolf, M., Bunk, O., Menzel, A., & Pfeiffer, F. (2009) · Ultramicroscopy · doi:10.1016/j.ultramic.2008.12.011 · Cited by 717
High-resolution ab initio three-dimensional x-ray diffraction microscopy
Chapman, H. N., Barty, A., Marchesini, S., Noy, A., Hau-Riege, S. P., Cui, C., Howells, M. R., Rosen, R., He, H., Spence, J. C. H., et al. (2006) · Journal of the Optical Society of America A · doi:10.1364/josaa.23.001179 · Cited by 592
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Chapman, H. N., & Nugent, K. A. (2010) · Nature Photonics · doi:10.1038/nphoton.2010.240 · Cited by 591
Invited Article: A unified evaluation of iterative projection algorithms for phase retrieval
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Metadata
- Authors
- Elser, V.
- Venue
- Journal of the Optical Society of America A
- Publisher
- Optica Publishing Group
- Published
- 2003-01-01
- Volume
- 20
- Issue
- 1
- Pages
- 40
- ISSN
- 1084-7529 (ISSN-L)
- 1520-8532
- OpenAlex
- W2052552885
- Cited by
- 737
- References
- 0
- FWCI
- 11.29
- Type
- journal article
- Language
- en
- Open access
- green
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