Two-dimensional phase unwrapping using the transport of intensity equation

Pandey, Neeraj; Ghosh, Amitava; Khare, Kedar

doi:10.1364/ao.55.002418

Cited by 63 publications

(29 citation statements)

References 37 publications

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“…As shown in Figs. 6(a2)-6(f2), after the unwrapping operation [46], in GS1 algorithm, a serious cloud-like phase distortion appears (Fig. 6(e2)) while the phase retrieved by the proposed QSF algorithm reveals high accuracy (Fig.…”

Section: Experimental Researchmentioning

confidence: 99%

Two-Step Phase-Shifting Algorithm Based on the Quadratic Spatial Filtering of Interferograms

et al. 2020

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By using the quadratic spatial filtering (QSF) operation of interferograms, we propose a fast and accurate phase retrieval algorithm in 2-step phase-shifting interferometry (PSI), in which both the interference signal separation and blind phase shift estimation can be realized. Compared with the existed 2-step PSI algorithms, the proposed QSF algorithm reveals two advantages: First, when the background intensity is not accurately estimated, which is a serious problem in 2-step PSI, the distortion of the retrieved phase can be released. Second, there is no requirement about the fringe density of interference pattern, reflecting the phase shift estimation can be realized even if the fringes density is sparse. The former is a valuable solution to reduce most significant errors in 2-step PSI, and the latter makes the accuracy robust against different fringe patterns. Both the simulation and experimental results demonstrate the excellent performance of the proposed QSF algorithm.

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Section: Experimental Researchmentioning

confidence: 99%

Two-Step Phase-Shifting Algorithm Based on the Quadratic Spatial Filtering of Interferograms

et al. 2020

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“…One essential step in 3D imaging with fringe projection method is to unwrap the wrapped phase. Various phase unwrapping approaches have been developed in past few decades to improve the speed and accuracy [ 6 , 7 , 8 , 9 , 10 , 11 , 12 ].…”

Section: Introductionmentioning

confidence: 99%

Deep Convolutional Neural Network Phase Unwrapping for Fringe Projection 3D Imaging

Liang

Zhang

Shao

et al. 2020

Sensors

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Phase unwrapping is a very important step in fringe projection 3D imaging. In this paper, we propose a new neural network for accurate phase unwrapping to address the special needs in fringe projection 3D imaging. Instead of labeling the wrapped phase with integers directly, a two-step training process with the same network configuration is proposed. In the first step, the network (network I) is trained to label only four key features in the wrapped phase. In the second step, another network with same configuration (network II) is trained to label the wrapped phase segments. The advantages are that the dimension of the wrapped phase can be much larger from that of the training data, and the phase with serious Gaussian noise can be correctly unwrapped. We demonstrate the performance and key features of the neural network trained with the simulation data for the experimental data.

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“…However, by an inverse trigonometric computation, the measured phase is normally wrapped onto the range of (−π, +π], which does not reflect the true phase values. To address this problem, lots of phase unwrapping approaches [1][2][3][4][5][6][7][8][9][10][11] have been proposed. The discontinuity arisen at residues is firstly identified in the Goldstein's branch-cut algorithm [1] and it is identified based on that the closed-path integral of phase gradient is not zero.…”

Section: Introductionmentioning

confidence: 99%

“…For methods [7,8], the phase unwrapping problem is formulated as a generalized minimum-norm sense to minimize the difference of local derivatives between true and measured phases. Unwrapping algorithms [9][10][11] based on the transport of intensity equation (TIE) were proposed to obtain the absolute phase map directly from intensity information. The TIE unwrapping method is easy to implement and path independent.…”

Section: Introductionmentioning

confidence: 99%

Phase unwrapping in optical metrology via denoised and convolutional segmentation networks

et al. 2019

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The interferometry technique is commonly used to obtain the phase information of an object in optical metrology. The obtained wrapped phase is subject to a 2π ambiguity. To remove the ambiguity and obtain the correct phase, phase unwrapping is essential. Conventional phase unwrapping approaches are time-consuming and noise sensitive. To address those issues, we propose a new approach, where we transfer the task of phase unwrapping into a multi-class classification problem and introduce an efficient segmentation network to identify classes. Moreover, a noise-to-noise denoised network is integrated to preprocess noisy wrapped phase. We have demonstrated the proposed method with simulated data and in a real interferometric system.

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Two-dimensional phase unwrapping using the transport of intensity equation

Cited by 63 publications

References 37 publications

Two-Step Phase-Shifting Algorithm Based on the Quadratic Spatial Filtering of Interferograms

Two-Step Phase-Shifting Algorithm Based on the Quadratic Spatial Filtering of Interferograms

Deep Convolutional Neural Network Phase Unwrapping for Fringe Projection 3D Imaging

Phase unwrapping in optical metrology via denoised and convolutional segmentation networks

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