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https://hdl.handle.net/1959.11/8396
Title: | Phase retrieval using radiation and matter-wave fields: Validity of Teague's method for solution of the transport-of-intensity equation | Contributor(s): | Schmalz, Jelena (author); Gureyev, Timur (author) ; Paganin, David (author); Pavlov, Konstantin M (author) | Publication Date: | 2011 | DOI: | 10.1103/PhysRevA.84.023808 | Handle Link: | https://hdl.handle.net/1959.11/8396 | Abstract: | Although originally developed for coherent paraxial scalar electromagnetic radiation in the visible-light regime, phase retrieval using the transport-of-intensity equation has been successfully applied to a range of paraxial radiation and matter-wave fields. Such applications include using electron wave fields to quantitatively image magnetic skyrmions and spin ices, propagation-based phase-contrast imaging using cold neutrons and hard x-rays, and visible-light refractive imaging of the projected column density of cold-atom clouds. Teague's method for phase retrieval using the transport-of-intensity equation, which renders the phase of a paraxial complex wave indirectly measurable via the existence of a conserved current, has been applied to a broad variety of situations which include all of the experiments described above. However, these applications have been undertaken without a thorough analysis of the underlying validity of the method. Here we derive sufficient conditions for the phase-retrieval solution provided by Teague's method to coincide with the true phase of the paraxial radiation or matter-wave field. We also present a sufficient condition guaranteeing that the discrepancy between the true phase function and that reconstructed using Teague's solution is small. These conditions demonstrate that, in most practical cases, for phase-amplitude retrieval using the transport-of-intensity equation, the Teague solution is very close to the exact solution. However, we also describe a counter example in the context of phase-amplitude retrieval using hard x-rays, in which the relative root-mean-square difference between the exact solution and that obtained using Teague's method is 9%. These findings clarify the foundations of one of the most widely applied methods for propagation-based phase retrieval of both paraxial matter and radiation wave fields and define a region for its applicability. | Publication Type: | Journal Article | Source of Publication: | Physical Review A (Atomic, Molecular and Optical Physics), 84(2), p. 023808-1-023808-10 | Publisher: | American Physical Society | Place of Publication: | United States of America | ISSN: | 1094-1622 1050-2947 2469-9934 2469-9926 |
Fields of Research (FoR) 2008: | 020599 Optical Physics not elsewhere classified 020402 Condensed Matter Imaging 029999 Physical Sciences not elsewhere classified |
Socio-Economic Objective (SEO) 2008: | 861502 Medical Instruments 861503 Scientific Instruments |
Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal |
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Appears in Collections: | Journal Article School of Science and Technology |
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