Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection

Zhang, Minliang; Chen, Qian; Tao, Tianyang; Feng, Shijie; Hu, Yan; Li, Hui; Zuo, Chao

doi:10.1364/oe.25.020381

Cited by 95 publications

(22 citation statements)

References 41 publications

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“…With Eqs. (8) and (9), we rescale φ and φ r intoφ ∈ [0, f r ] andφ r ∈ [0, f ], respectively. As the relationships among rescaled interceptb i and fringe orders listed in Table 2, we havê…”

Section: One-dimensional Look-up Tablementioning

confidence: 99%

See 1 more Smart Citation

Automatic look-up table based real-time phase unwrapping for phase measuring profilometry and optimal reference frequency selection

Song¹,

Lau²,

Ho³

et al. 2019

Opt. Express

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For temporal phase unwrapping in phase measuring profilometry, it has recently been reported that two phases with co-prime frequencies can be absolutely unwrapped using a look-up table; however, frequency selection and table construction has been performed manually without optimization. In this paper, a universal phase unwrapping method is proposed to unwrap phase flexibly and automatically by using geometric analysis, and thus we can programmatically build a one-dimensional or two-dimensional look-up table for arbitrary two co-prime frequencies to correctly unwrap phases in real time. Moreover, a phase error model related to the defocus effect is derived to figure out an optimal reference frequency co-prime to the principal frequency. Experimental results verify the correctness and computational efficiency of the proposed method.

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Section: One-dimensional Look-up Tablementioning

confidence: 99%

“…4, rescale them to obtainφ andφ r by using Eqs. (8) and 9; 3: Compute the difference betweenφ andφ r by using Eq. 10and then unify the difference by using Eq.…”

Section: Inputmentioning

confidence: 99%

Automatic look-up table based real-time phase unwrapping for phase measuring profilometry and optimal reference frequency selection

Song¹,

Lau²,

Ho³

et al. 2019

Opt. Express

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show abstract

“…where ‖•‖ 1 is the 1 norm, defined as the sum of the absolute values of the elements in E, ‖•‖ * is the nuclear norm, defined as the sum of all the singular values of K, and > 0 is a constant to balance low-rankness and sparsity. Different algorithms can be applied to approximately solve (6). We here adopt the alternating direction method (ADM), which minimizes the following augmented Lagrangian function:…”

Section: Fringe Order Errors In Temporal Phase Unwrappingmentioning

confidence: 99%

“…In order to eliminate the phase ambiguity, phase unwrapping is required to recover the absolute phase maps (which are continuous). Among many phase unwrapping methods, temporal phase unwrapping is commonly used, especially for applications with noise and discontinuities [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

A new method for fringe order error correction in fringe projection profilometry

Zhang

Duan

et al. 2019

Optical Metrology and Inspection for Industrial Applications VI

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© 2019 SPIE. Phase unwrapping is an essential step for 3D shape measurement based on fringe projection. Temporal phase unwrapping methods can be implemented by analyzing the multiple patterns that encode the fringe order information. They can retrieve the fringe orders on a pixel-by-pixel basis and are less prone to error propagation compared with spatial methods. However, fringe orders errors may still occur due to noise, reflectivity fluctuation and discontinuity of the object surface. Such errors may exhibit an impulsive nature and result in significant error to the recovered absolute phase map. This has been exploited by several methods to correct the fringe order errors, e.g., by filtering the fringe order sequences in a line-by-line manner. In this paper, a new method is proposed to correct the errors associated with fringe orders for the temporal phase unwrapping. The scheme first makes use of the lowrankness property of the fringe order map and sparse nature of the impulsive fringe order errors to more effectively remove the impulsive errors by applying robust principal component analysis (RPCA) algorithm. Then the smoothness of the two-dimensional unwrapped phase map is examined and the residual fringe order errors are detected based on a discontinuity measure of the phase map and corrected by comparing phase difference between two adjacent pixels in the unwrapped phase. The effectiveness of the proposed method is demonstrated via numerical experiments.

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“…Assembly line product inspection etc.). Fringe pattern profilometry (FPP) is one of the most used technologies for 3D surface profile measurement because of its advantages of non-contact, high speed and high accuracy [1][2][3][4][5][6]. Fourier transform profilometry (FTP) and phase shifting profilometry (PSP) are the typical and popular methods implementing FPP.…”

Section: Introductionmentioning

confidence: 99%

Automated approach for the surface profile measurement of moving objects based on PSP

Lü¹,

Ding²,

Luan³

et al. 2017

Opt. Express

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Phase shifting profilometry can achieve high accuracy for the 3D shape measurement of static object. Errors will be introduced when the object is moved during the movement. The fundamental reason causing the above issue is: PSP requires multiple fringe patterns but the reconstruction model does not include the object movement information. This paper proposes a new method to automatically measure the 3D shape of the rigid object with arbitrary 2D movement. Firstly, the object movement is tracked by the SIFT algorithm and the rotation matrix and translation vector describing the movement are estimated. Then, with the reconstruction model including movement information, a least-square algorithm is applied to retrieve the correct phase value. The proposed method can significantly reduce the errors caused by the object movement. The whole reconstruction process does not need human intervention and the proposed method has high potential to be applied in industrial applications. Experiments are presented to verify the effectiveness. Abstract: Phase shifting profilometry can achieve high accuracy for the 3D shape measurement of static object. Errors will be introduced when the object is moved during the movement. The fundamental reason causing the above issue is: PSP requires multiple fringe patterns but the reconstruction model does not include the object movement information. This paper proposes a new method to automatically measure the 3D shape of the rigid object with arbitrary 2D movement. Firstly, the object movement is tracked by the SIFT algorithm and the rotation matrix and translation vector describing the movement are estimated. Then, with the reconstruction model including movement information, a least-square algorithm is applied to retrieve the correct phase value. The proposed method can significantly reduce the errors caused by the object movement. The whole reconstruction process does not need human intervention and the proposed method has high potential to be applied in industrial applications. Experiments are presented to verify the effectiveness.

show abstract

Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection

Cited by 95 publications

References 41 publications

Automatic look-up table based real-time phase unwrapping for phase measuring profilometry and optimal reference frequency selection

Automatic look-up table based real-time phase unwrapping for phase measuring profilometry and optimal reference frequency selection

A new method for fringe order error correction in fringe projection profilometry

Automated approach for the surface profile measurement of moving objects based on PSP

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