Iterative phase-shifting algorithm immune to random phase shifts and tilts

Chen, Yi Chun; Lin, Po Chih; Lee, Chung Min; Liang, Chao Wen

doi:10.1364/ao.52.003381

Cited by 51 publications

(20 citation statements)

References 12 publications

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“…To calculate the phase shift, the nonlinearity involved by tilt shifting is the key problem to solve. Taylor series expansion [9], subregion division [10], and nonlinear leastsquares fittings [11,13] have been applied to solve the problem. In TIA, we have decoupled the phase shifts in orthogonal directions and determined the tilt factors with linear regressions [12].…”

Section: Algorithm Descriptionsmentioning

confidence: 99%

“…Considering the fact that the wavefront is invariable during the measuring period, researchers have developed many algorithms to extract wavefront phase from interferograms subjected to vibration. These algorithms include detecting phase shifts from spatial-carrier interferograms [6][7][8], calculating wavefront phase by iteration [9][10][11][12][13] and some other methods [14,15]. These algorithms compensate the relative tilt between the test and reference wavefronts and have better performance than those algorithms that only consider the piston phase shifting.…”

Section: Introductionmentioning

confidence: 99%

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Modified three-step iterative algorithm for phase-shifting interferometry in the presence of vibration

Liu

Wang

et al. 2015

Appl. Opt.

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To suppress the sensitivity of phase-shifting interferometry to mechanical vibration, a modified three-step iteration algorithm (MTIA) is proposed. The wavefront phase, x- and y-directional phase shifts are calculated in three individual steps in an iteration cycle. MTIA solves the tilt factors of phase shift through orthogonal decomposition and linear regression, avoiding the nonlinear optimization. The advantage of MTIA lies in its ability of calculating and compensating tilt-shifting error and fringe contrast variation caused by vibration. The simulations show that MTIA could provide more accurate results than an algorithm without contrast compensation. The superiority of MTIA is demonstrated experimentally. The experiment results show that MTIA could suppress the effect of vibration on surface measurement, which is of amplitude larger than the wavelength and of frequency over a large range. MTIA manifests good insensitivity to exposure time increase as well.

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Section: Algorithm Descriptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modified three-step iterative algorithm for phase-shifting interferometry in the presence of vibration

Liu

Wang

et al. 2015

Appl. Opt.

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“…The nonlinear response functions of the LCD screen and CCD camera will introduce nonlinear error to the captured fringe pattern [9][10][11][12]20 and cause error in the demodulated phase. The nontelecentric imaging of the CCD camera will introduce another kind of nonlinear error (aberration) to the measurement.…”

Section: Phase Error Sources In Phase Measuring Deflectometrymentioning

confidence: 99%

“…The errors in the FPP systems are namely electronic noise, nonlinearity, phase-shifting error, and vibration, among which the electronic noise and nonlinearity are the two main errors. Nonlinear error-reduction methods include high-step phaseshifting method, 9,10 the error compensation technique, 11 phase iterative method, 12 Zernike polynomials method, 13 and so on. Random error-reduction methods such as least-square temporal phase unwrapping (TPU) 7 and phase averaging method 8 make use of a leastsquare method or averaging several unwrapped phase maps.…”

Section: Introductionmentioning

confidence: 99%

Phase error analysis and reduction in phase measuring deflectometry

Wu¹,

Yue²,

Yi³

et al. 2015

Opt. Eng

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In phase measuring deflectometry (PMD), the inspection accuracy of the defects and height of the specular surface are related to the level of phase errors. The usage of numeric integration in reconstructing the shape and the defocusing capture of the fringe pattern, which will amplify the phase errors, make error discussion more significant in PMD than other shape measurement techniques. Phase error analysis and reduction in PMD are presented. The random noises, nonlinear response function, the nontelecentric imaging of the charge-coupled device camera, and the nonlinear response function of the liquid crystal display screen are the main phase error sources in PMD. The analytical relation between the random phase error and its influence factors in PMD is deduced. From the relation formulation, the influence factors of random phase error are analyzed, and the results are proven by the simulation and experiment. A possible phase error-reduction method, which integrates several methods for congeneric errors in fringe projection profilometry, is investigated to reduce phase errors in PMD. This composite method is proven to have a good performance by a plane mirror experiment.

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“…1(b). The random vibration-modulated phase shifted interferograms are then calculated to retrieve the interference phase of each interferogram [11]. At least three interferograms are required for each subaperture for calculation of the interference phase.…”

Section: Vibration-modulated Subaperture Stitching Interferometrymentioning

confidence: 99%

Measurement improvement by high overlapping density subaperture stitching interferometry

et al. 2014

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The vibration-modulated subaperture stitching interferometer acquires the interferogram on the fly dynamically. With its highly improved measurement throughput, we applied the device for high overlapping density subaperture stitching interferometry to acquire hundreds of overlapping subapertures in a single phase stitching measurement. The averaging effect of the high overlapping density stitching interferometer is discussed. In the experiment, the proposed high overlapping density stitching interferometer is also proved to reduce measurement uncertainty and improve measurement quality effectively.

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Iterative phase-shifting algorithm immune to random phase shifts and tilts

Cited by 51 publications

References 12 publications

Modified three-step iterative algorithm for phase-shifting interferometry in the presence of vibration

Modified three-step iterative algorithm for phase-shifting interferometry in the presence of vibration

Phase error analysis and reduction in phase measuring deflectometry

Measurement improvement by high overlapping density subaperture stitching interferometry

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