An advanced phase retrieval algorithm in N-step phase-shifting interferometry with unknown phase shifts

Li, Jiaosheng; Zhong, Liu; Liu, Shengde; Zhou, Yunfei; Xu, Jie; Tian, Jing; Liu, Xiaoxu

doi:10.1038/srep44307

Cited by 24 publications

(13 citation statements)

References 26 publications

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“…Finally, the noisy experimental wrapping phase map shown in Fig. 5(a) is generated, and then, phase extraction is performed using the eight-image four-step phase shift method 25 – 27 to obtain a shear fringe phase map that can represent object defects. After obtaining the wrapping phase, the traditional DCT unwrapping algorithm and the proposed DCT unwrapping algorithm based on phase gradient smoothing correction are used for testing.…”

Section: Algorithm Simulation and Experimental Resultsmentioning

confidence: 99%

Discrete cosine transformation unwrapping algorithm based on phase gradient smoothing correction

et al. 2023

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At present, in the shear speckle interference technique for vehicle tire defect detection, the key is to accurately reflect the real phase of object motion when there are interference factors. Thus, this study proposes a discrete cosine transformation (DCT) unwrapping algorithm based on phase gradient smoothing correction, and analyzes the feasibility of the proposed method through several experiments and numerical simulation calculations. The proposed method replaces abnormal phase gradients caused by noise with calculated weighted moving average phase gradients, bringing phases closer to real values. Finally, the DCT unwrapping method is used to obtain the final solution of phase. A phase recovered using the proposed method is closer to the real value than that recovered using the traditional DCT unwrapping algorithm. Compared to the traditional DCT unwrapping algorithm, the root mean square error accuracy of the proposed method is improved by 10 to 100 times. And after many experiments to record the average running speed, it can be obtained that the time-consumption of the two algorithms only differs by ∼0.1 to 0.3 s.

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Section: Algorithm Simulation and Experimental Resultsmentioning

confidence: 99%

Discrete cosine transformation unwrapping algorithm based on phase gradient smoothing correction

et al. 2023

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“…Where m and n can be determined by tan α ≈ n/m (m, n = 0, 1 or 2). Also, by using equations (6), (7), and (8), the measured phase will be obtained with unknown phase-shifting algorithms, such as the normalized and orthogonal phase-shifting algorithm (NOPSA) [17], diamond diagonal vectors (DDV) algorithm [18], principal component analysis (PCA) [19] and advanced iterative algorithm (AIA) [20]. The specific steps of phase extraction with SCFPS-G algorithm are as follows: 1) Perform the differential operation in one-frame SCFI to obtain the direction of phase-shifting gradient.…”

Section: Theory and Methodsmentioning

confidence: 99%

Phase Extraction Algorithm Based on the Spatial Carrier-Frequency Phase-Shifting Gradient

Zou

Zhong

et al. 2019

IEEE Photonics J.

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For improving the accuracy and processing speed of phase extraction, a new phase extraction algorithm based on the spatial carrier-frequency phase-shifting gradient (SCFPS-G) is proposed. First, three-frame sub-interferograms along the direction of spatial carrier-frequency phase-shifting gradient (SCFPS-G), which can be constructed by the differential method from only one-frame spatial carrier-frequency interferogram (SCFI). And then, the measured phase will be extracted by unknown phase-shifting algorithms. Compared with the existing spatial carrier-frequency phase-shifting (SCFPS) algorithms, the proposed SCFPS-G algorithm not only can improve the efficiency of constructing sub-interferograms, but also decrease one-frame sub-interferogram requirement for phase extraction, so the data redundancy of interferogram and the influence of noise will be reduced. Specially, it is found even if the carrier frequency becomes very small, corresponding to the large spatial bandwidth utilization of image sensor, the proposed SCFPS-G algorithm still can work well. And the obvious advantages of the SCFPS-G algorithm in accuracy, processing time and feasibility of phase extraction can be demonstrated by the numerical simulations and the experimental results.

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“…Another, advantage of the proposed approach is that it can be implemented for any number of step, for example, 3-step, 4-step,………, N-step PSI depending upon the speed of recording device. This is advantageous as the phase measurement accuracy increases with the increase in phase steps [14,31]. In the present study, we will discuss advantages, results and opportunities associated with our present method.…”

Section: Introductionmentioning

confidence: 99%

“…Even a small amount of error in PZT calibration, which occurs due to the backlash and hysteresis, can lead to the nonlinear phase shift between data frames resulting in phase measurement errors, such as background modulation errors in the reconstructed phase maps of the target, see results of Refs. [5,[14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Sub-nanometer height sensitivity by phase shifting interference microscopy under environmental fluctuations

et al. 2020

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Phase shifting interferometric (PSI) techniques are among the most sensitive phase measurement methods. Owing to its high sensitivity, any minute phase change caused due to environmental instability results into, inaccurate phase measurement. Consequently, a well calibrated piezo electric transducer (PZT) and highly-stable environment is mandatory for measuring accurate phase map using PSI implementation. Here, we present a new method of recording temporal phase shifted interferograms and a numerical algorithm, which can retrieve phase maps of the samples with negligible errors under the ambient environmental fluctuations. The method is implemented by recording a video of continuous temporally phase shifted interferograms and phase shifts were calculated between all the data frames using newly developed algorithm with a high accuracy ≤ 5.5 × 10 -4 π rad. To demonstrate the robustness of the proposed method, a manual translation of the stage was employed to introduce continuous temporal phase shift between data frames. The developed algorithm is first verified by performing quantitative phase imaging of optical waveguide and red blood cells using uncalibrated PZT under the influence of vibrations/air turbulence and compared with the well calibrated PZT results. Furthermore, we demonstrated the potential of the proposed approach by acquiring the quantitative phase imaging of an optical waveguide with a rib height of only 2 nm. By using 12-bit CMOS camera the height of shallow rib waveguide is measured with a height sensitivity of 4 Å without using PZT and in presence of environmental fluctuations.

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An advanced phase retrieval algorithm in N-step phase-shifting interferometry with unknown phase shifts

Cited by 24 publications

References 26 publications

Discrete cosine transformation unwrapping algorithm based on phase gradient smoothing correction

Discrete cosine transformation unwrapping algorithm based on phase gradient smoothing correction

Phase Extraction Algorithm Based on the Spatial Carrier-Frequency Phase-Shifting Gradient

Sub-nanometer height sensitivity by phase shifting interference microscopy under environmental fluctuations

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