Phase retrieval using coherent imaging systems with linear transfer functions

Paganin, David; Gureyev, Timur; Pavlov, Konstantin M; Lewis, R A; Kitchen, M J

doi:10.1016/j.optcom.2004.02.015

Author(s)

Paganin, David

Gureyev, Timur

Pavlov, Konstantin M

Lewis, R A

Kitchen, M J

Publication Date

2004

Abstract

We consider the problem of quantitative phase retrieval from images obtained using a coherent shift-invariant linear imaging system whose associated transfer function (i.e., the Fourier transform of the complex point-spread function) is well approximated by a linear function of spatial frequency. This linear approximation to the transfer function is applicable when the spread of spatial frequencies, in a two-dimensional complex wavefield, is sufficiently narrow when compared to the characteristic length of variation of the transfer function for an imaging system taking such a wavefield as input. We give several algorithms for reconstructing both the phase and amplitude of a given two-dimensional coherent wavefield, given as input data one or more images of such a wavefield which may be formed by different states of the imaging system. When an object to be imaged consists of a single material, or of a single material embedded in a substrate of constant thickness, the phase-amplitude reconstruction can be performed using a single image (DEI) to obtain a quantitative reconstruction of the projected thickness of a single-material sample which is embedded within a substrate of approximately constant thickness. This algorithm is used to quantitatively map inclusions in a breast phantom, from a single synchrotron DEI image of the same. In particular, the reconstructed images quantitatively represent the projected thickness in the bulk of the sample, in contrast to raw DEI images which greatly emphasise sharp edges (high spatial frequencies). Lastly, we point out that the methods presented here are also applicable to the quantitative analysis of differential interference contrast (DIC) images, obtained using both visible-light and X-ray microscopy.

Citation

Optics Communications, 234(1-6), p. 87-105

ISSN

1873-0310

0030-4018

Link

https://hdl.handle.net/1959.11/4217

Language

en

Publisher

Elsevier BV

Title

Phase retrieval using coherent imaging systems with linear transfer functions

Type of document

Journal Article

Entity Type

Publication

Author(s)	Paganin, David Gureyev, Timur Pavlov, Konstantin M Lewis, R A Kitchen, M J
Publication Date	2004
Abstract	We consider the problem of quantitative phase retrieval from images obtained using a coherent shift-invariant linear imaging system whose associated transfer function (i.e., the Fourier transform of the complex point-spread function) is well approximated by a linear function of spatial frequency. This linear approximation to the transfer function is applicable when the spread of spatial frequencies, in a two-dimensional complex wavefield, is sufficiently narrow when compared to the characteristic length of variation of the transfer function for an imaging system taking such a wavefield as input. We give several algorithms for reconstructing both the phase and amplitude of a given two-dimensional coherent wavefield, given as input data one or more images of such a wavefield which may be formed by different states of the imaging system. When an object to be imaged consists of a single material, or of a single material embedded in a substrate of constant thickness, the phase-amplitude reconstruction can be performed using a single image (DEI) to obtain a quantitative reconstruction of the projected thickness of a single-material sample which is embedded within a substrate of approximately constant thickness. This algorithm is used to quantitatively map inclusions in a breast phantom, from a single synchrotron DEI image of the same. In particular, the reconstructed images quantitatively represent the projected thickness in the bulk of the sample, in contrast to raw DEI images which greatly emphasise sharp edges (high spatial frequencies). Lastly, we point out that the methods presented here are also applicable to the quantitative analysis of differential interference contrast (DIC) images, obtained using both visible-light and X-ray microscopy.
Citation	Optics Communications, 234(1-6), p. 87-105
ISSN	1873-0310 0030-4018
Link	https://hdl.handle.net/1959.11/4217
Language	en
Publisher	Elsevier BV
Title	Phase retrieval using coherent imaging systems with linear transfer functions
Type of document	Journal Article
Entity Type	Publication

Phase retrieval using coherent imaging systems with linear transfer functions

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