2016
DOI: 10.1109/tip.2015.2509249
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Variational Phase Imaging Using the Transport-of-Intensity Equation

Abstract: Abstract-We introduce a variational phase retrieval algorithm for the imaging of transparent objects. Our formalism is based on the transport-of-intensity equation (TIE), which relates the phase of an optical field to the variation of its intensity along the direction of propagation. TIE practically requires one to record a set of defocus images to measure the variation of intensity. We first investigate the effect of the defocus distance on the retrieved phase map. Based on our analysis, we propose a weighted… Show more

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Cited by 30 publications
(24 citation statements)
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“…This seminal work launched a new field known as quantitative phase imaging (QPI), which aims at determining the optical phase delay induced by the refractive index distribution. The phase differences can be assessed with various techniques 19 such as measurement of the interference of the scattered field with a reference field (off-axis holography, HPM) [20][21][22][23] , controlled phase-shift of the reference field (FPM, SLIM) 24,25 or by measuring defocused image planes (TIE) [26][27][28][29] .…”
Section: Introductionmentioning
confidence: 99%
“…This seminal work launched a new field known as quantitative phase imaging (QPI), which aims at determining the optical phase delay induced by the refractive index distribution. The phase differences can be assessed with various techniques 19 such as measurement of the interference of the scattered field with a reference field (off-axis holography, HPM) [20][21][22][23] , controlled phase-shift of the reference field (FPM, SLIM) 24,25 or by measuring defocused image planes (TIE) [26][27][28][29] .…”
Section: Introductionmentioning
confidence: 99%
“…This effect is also present in transport of intensity experiments that share similar experimental conditions (i.e. sample-camera distance < 900μm) [29,30] and other quantitative phase imaging techniques [31,32]. However, lensless phase imagers are mainly used to image biological samples like cells [4][5][6][7][8][9][10] which sizes are typically less than 20μm for which the phase can be correctly computed.…”
Section: Phase Recoverymentioning
confidence: 99%
“…The absence of low spatial frequencies is not uncommon to phase reconstructions obtained from throughfocus image stacks. Methods based on solving the TIE [34][35][36][37] need to invert the Laplacian in the lateral coordinates. The Laplacian has a transfer function that depends quadratically on the (lateral) spatial frequency components, i.e., it has (near) zero transfer at low spatial frequencies.…”
Section: Quantitative Phase Tomography Of Unstained Tissue Layers a mentioning
confidence: 99%
“…Quantitative phase imaging forms a non-invasive and labelfree imaging platform in cell biology and pathology [33]. Algorithms are available for phase retrieval from a through-focus image stack to obtain a 2D phase contrast image of a thin layer, usually based on solving the transport of intensity equation (TIE) [34][35][36][37], as well as for a full 3D tomographic reconstruction of a thicker specimen [38][39][40]. Application of such computational phase contrast modalities based on multi-focal image stacks can broaden the application of WSI systems to unstained samples.…”
Section: Introductionmentioning
confidence: 99%