A practical way to resolve ambiguities in wavefront reconstructions by the transport of intensity equation

Parvizi, Amin; Müller, Johannes; Funken, Stefan A.; Koch, Christoph T.

doi:10.1016/j.ultramic.2015.02.015

Cited by 9 publications

(3 citation statements)

References 25 publications

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“…However, using discrete Fourier transforms periodic boundary conditions are implicitly imposed. Also for iterative approaches, such as finite element [12,13] or multigrid [27] methods the boundary conditions…”

Section: ∂I( R)mentioning

confidence: 99%

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Recovering low spatial frequencies in wavefront sensing based on intensity measurements

Parvizi

Broek

Koch

2016

Adv Struct Chem Imag

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The transport of intensity equation (TIE) offers a convenient method to retrieve the phase of a wave function from maps of the irradiance (images) recorded at different planes along the optic axis of an optical system. However, being a second-order partial differential equation, even for noise-free data a unique solution of the TIE requires boundary conditions to be specified which are generally not accessible experimentally, jeopardizing retrieval of the low-frequency information in particular. Here we introduce an iterative algorithm which forgoes the need for explicit boundary conditions and combines the well-known reciprocal space solution of the TIE with the charge-flipping algorithm that has originally been developed to solve the crystallographic phase problem in X-ray diffraction. Application of this algorithm to experimental data and comparison with conventionally used algorithms demonstrates an improved retrieval of the low spatial frequencies of the phase.

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Section: ∂I( R)mentioning

confidence: 99%

“…Many algorithms such as the fast Fourier transform [6], the finite element method [12,13], multigrid methods [14], a special symmetrization approach [15], each requiring Neumann, Dirichlet, or periodic boundary conditions have been proposed and applied for solving the TIE.…”

Section: Introductionmentioning

confidence: 99%

Recovering low spatial frequencies in wavefront sensing based on intensity measurements

Parvizi

Broek

Koch

2016

Adv Struct Chem Imag

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“…The advantage of the TIE is that it is computationally efficient and experimentally cost-effective because it requires the acquisition of the intensity across only two transverse planes separated along the axis of propagation [26][27][28]. The TIE has been applicable in various fields due to its simple experimental setup and computational efficiency, such as wavefront sensing [29,30], phase unwrapping [31,32], microscopy [33][34][35][36], optical metrology [37], and optical information processing [38][39][40]. Zuo et al [32] described the applicability of the TIE to unwrap phase discontinuities.…”

Section: Introductionmentioning

confidence: 99%

Low-light phase imaging using in-line digital holography and the transport of intensity equation

Gupta

Nishchal

2021

J. Opt.

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In one of our recent studies, we have shown that a large defocusing distance in the transport of intensity equation (TIE) is required to retrieve the phase information in low-light conditions (OSA Continuum 3 (2020) 236). It has been found that image misalignment issues come into the picture due to translation of the camera for large distances, which creates artifacts in phase recovery. The issue of misalignment can be overcome if, instead of the object, we use the digital hologram of the object for the required defocused intensities and then apply the TIE. In this paper, we demonstrate low-light phase imaging by combining digital holography with the TIE. We reconstruct the required multiple intensity distributions from the captured in-line digital hologram. To implement the low-level light illumination, a variable neutral density filter has been used while recording the in-line digital hologram. Simulation and experimental results with different objects (United States air-force chart and glue drop) are presented. To simulate the low-light conditions, a Poisson distribution based photon-counting imaging technique has been applied.

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Non-interferometric Quantitative Optical Phase Imaging

Liu

Wang

Veetil

2022

Computational Optical Phase Imaging

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A practical way to resolve ambiguities in wavefront reconstructions by the transport of intensity equation

Cited by 9 publications

References 25 publications

Recovering low spatial frequencies in wavefront sensing based on intensity measurements

Recovering low spatial frequencies in wavefront sensing based on intensity measurements

Low-light phase imaging using in-line digital holography and the transport of intensity equation

Non-interferometric Quantitative Optical Phase Imaging

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