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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)orcid ; Paganin, David (author); Pavlov, Konstantin M  (author)orcid 
Publication Date: 2011
DOI: 10.1103/PhysRevA.84.023808
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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
Field of Research (FOR): 020599 Optical Physics not elsewhere classified
020402 Condensed Matter Imaging
029999 Physical Sciences not elsewhere classified
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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Appears in Collections:Journal Article
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