TY - JOUR

T1 - Phase retrieval using radiation and matter-wave fields: Validity of Teague's method for solution of the transport-of-intensity equation

AU - Schmalz, Jelena

AU - Gureyev, Timur

AU - Paganin, David

AU - Pavlov, Konstantin

PY - 2011

Y1 - 2011

N2 - lthough 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.

AB - lthough 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.

UR - http://pra.aps.org.ezproxy.lib.monash.edu.au/abstract/PRA/v84/i2/p023808_1

U2 - 10.1103/PhysRevA.84.023808

DO - 10.1103/PhysRevA.84.023808

M3 - Article

VL - 84

SP - 1

EP - 10

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

ER -