Flexible phase error compensation based on Hilbert transform in phase shifting profilometry

Cai, Zewei; Liu, Xiaoli; Jiang, Hao; He, Dong; Peng, Xiang; Huang, Shujun; Zhang, Zonghua

doi:10.1364/oe.23.025171

Cited by 97 publications

(17 citation statements)

References 34 publications

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“…All the display and imaging devices possess a nonlinear response to adjust to human vision. However, a nonlinear response will change the standard shape of a sinusoidal fringe pattern into a non-sinusoidal shape, so that the calculated phase is incorrect [ 106 , 107 , 108 ]. Some researchers have used a binary fringe pattern to replace the sinusoidal fringe pattern on the side of the display screen [ 109 ].…”

Section: Influential Factors On Measurement Resultsmentioning

confidence: 99%

Three-Dimensional Shape Measurements of Specular Objects Using Phase-Measuring Deflectometry

Zhang

Wang

Huang

et al. 2017

Sensors

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The fast development in the fields of integrated circuits, photovoltaics, the automobile industry, advanced manufacturing, and astronomy have led to the importance and necessity of quickly and accurately obtaining three-dimensional (3D) shape data of specular surfaces for quality control and function evaluation. Owing to the advantages of a large dynamic range, non-contact operation, full-field and fast acquisition, high accuracy, and automatic data processing, phase-measuring deflectometry (PMD, also called fringe reflection profilometry) has been widely studied and applied in many fields. Phase information coded in the reflected fringe patterns relates to the local slope and height of the measured specular objects. The 3D shape is obtained by integrating the local gradient data or directly calculating the depth data from the phase information. We present a review of the relevant techniques regarding classical PMD. The improved PMD technique is then used to measure specular objects having discontinuous and/or isolated surfaces. Some influential factors on the measured results are presented. The challenges and future research directions are discussed to further advance PMD techniques. Finally, the application fields of PMD are briefly introduced.

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Section: Influential Factors On Measurement Resultsmentioning

confidence: 99%

Three-Dimensional Shape Measurements of Specular Objects Using Phase-Measuring Deflectometry

Zhang

Wang

Huang

et al. 2017

Sensors

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“…In Figure 3, it can be seen that the environment noise before compensation will cause the "jump points" of the last phase unwrapping. First, the root-meansquare error (RMSE) of the noise is calculated as σ φ , which is the constraint condition of Equations (13) and (15) in this , and 4(c), respectively, correspond to the phase compensation front curve of functions φ 1 , φ 2 , and φ 3 . The initial noise also exists in these three principal value functions.…”

Section: Simulation Analysis Of 3d Reconstruction Before and Aftermentioning

confidence: 99%

“…Zhang et al proposed a look-up table method to build a preestablished storage table between the input gray and the output gray to compensate for the nonlinear phase error in the projection and acquisition system, but this method took a lot of time to calculate [12]. Cai et al used the Hilbert algorithm to compensate the reverse error, but this method was unable to measure the profile of complex objects, and the measurement speed was slow [13].…”

Section: Introductionmentioning

confidence: 99%

A Multifrequency Heterodyne Phase Error Compensation Method for 3D Reconstruction

Liu

Yang

et al. 2020

Journal of Sensors

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In view of the problem of “jumping points” in the phase unwrapping of the multifrequency heterodyne principle, this paper proposes a novel method to improve the multifrequency heterodyne. By solving the root-mean-square error of the original frequency function, it includes the relationship between the error and the adjacent phase in the condition of constrained phase unwrapping, and it compensates phase ±2π of the skip point. To ensure the accuracy of phase unwrapping, the function with a “jump point” after each phase unwrapping and the absolute phase curve of the principal value function are used to establish the threshold judgment model of the least square method, and the initial phase unwrapping of the principal value function with different frequencies is carried out continuously. The simulation analysis of phase compensation with the four-step phase-shifting method shows that the error is reduced to 36% under the set environment. The experimental result of 3D reconstruction by measuring the flatness of the plate shows that the error decreases by 41% after phase compensation compared with before phase compensation. The three-dimensional reconstruction experiment of pitch measurement with a nut shows that the nut after phase compensation is smooth without noise, and the pitch error is 0.033 mm, which verified the method is workable and effective.

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“…Many phase-error compensation methods have been proposed to overcome this nonlinear response. These methods can be categorized in two main types: a) calibration based methods and b) defocusing based methods [4]. As the name suggests, calibration based compensation methods depend on a calibration procedure to quantify the nonlinearity of system response by using techniques like response curve fitting [5], phase benchmark building [6,7], and gamma model derivation [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Generic exponential fringe model for alleviating phase error in phase measuring profilometry

Chen

Gao

Wang

et al. 2018

Optics and Lasers in Engineering

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Phase measuring profilometry (PMP) is susceptible to phase error caused by gamma distortion that leads to the captured fringe patterns deviating from ideal sinusoidal waveforms. Existing phase-error compensation methods are generally complex and require significant computational resources for implementation. This paper proposes a generic exponential fringe model expressed as an exponential function of the generated fringe patterns. Based on this model, a straightforward gamma correction method is presented to alleviate phase error without the need for any estimation of nonlinear coefficients or complex calibration. Experimental results demonstrate that the proposed method improves the quality of measurements by suppressing phase error.

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Flexible phase error compensation based on Hilbert transform in phase shifting profilometry

Cited by 97 publications

References 34 publications

Three-Dimensional Shape Measurements of Specular Objects Using Phase-Measuring Deflectometry

Three-Dimensional Shape Measurements of Specular Objects Using Phase-Measuring Deflectometry

A Multifrequency Heterodyne Phase Error Compensation Method for 3D Reconstruction

Generic exponential fringe model for alleviating phase error in phase measuring profilometry

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