![]() ![]() With the development of generalized PSA in temporal PSI, especially the advanced iterative algorithm (AIA) 7 and the principle component analysis method (PCA) 18, the CFI can now be demodulated without pre-calibrating the carrier frequency 19, 20, 21, 22. Hereafter, the classic SCPS demodulates the phase using conventional PSAs with the predetermined carrier frequency of π/2 rad/pixel 17. Based on this approximation, which also assumes that the background intensities and modulation amplitudes of adjacent pixels are equal, the single CFI can be decomposed into a series of temporal phase shifted interferograms. It uses the phase increment of adjacent pixels in intra-frame to approximate the carrier frequency. The TPS technique is well known for single-point-level spatial localization, and it is possible to transfer the TPS concept to spatial CFI analysis, which is called the spatial carrier-frequency phase shifting (SCPS) technique 16. The windowed FT(WFT) method 15 was therefore suggested as a way of improving spatial localization, but the automatic selection of a window remains a major problem for dynamic measurement. Due to the global operation mechanism in the frequency domain, a lack of spatial localization might lead to spectral overlapping, rendering it almost impossible to extract the first-order component accurately 14. ![]() 13 is a mainstay technique used to perform phase demodulation. For a carrier-frequency interferogram (CFI), the FT method, first proposed in 1982 by Takeda M. The retrace error is the main disadvantage of SCFI but can be calibrated out in advance. The spatial carrier-frequency (SCF) method is a good choice since implementation of spatial carrier-frequency interferometry (SCFI) is relatively easily accomplished on most advanced laser interferometers. With the exception of simultaneous phase shifting interferometry (SPSI) 12, which is not our concern in this contribution, demodulation of a single shot fringe pattern is an attractive option. visual monitoring of cell culture in the biomedical domain 11. ![]() high-aperture and long-distance primary mirror testing 10 but also in many other phase-demodulation operations, e.g. Dynamic measurement is an attractive option not only in optical shop testing, e.g. Though various kinds of generalized PSI have been put forward in recent years as a means of coping with random phase shift error caused by vibration 5, 6, 7, 8, 9, it remains difficult to achieve real time phase demodulation in dynamic measurement operations since at least three interferograms are usually required in order to record and process data. A well-calibrated phase shifter and stable environment are crucial factors to TPS due to equal steps conventionally used in phase-shifting algorithms (PSA) 3, 4. Phase shifting interferometry (PSI), for example, has already become a standard configuration of a modern high accuracy interferometer 2. ![]() Temporal phase shifting (TPS) is a phase demodulation method, which has been used extensively in optical metrology since its introduction 1. Since the relevant physical information is usually encoded in the fringe phase, phase demodulation always plays a very critical role in fringe analysis. Interferometry, deflectometry and profilometry are diagnostic tools frequently used in optical metrology to achieve highly accurate, non-contact and full-field measurements. variations of background/modulation, phase amplitude, carrier frequency, additive noise that may affect the precision of PLEF are discussed in detail. In conclusion, various influencing factors, e.g. Experiments further corroborate the effectiveness of the proposed method. Theoretical phase extraction error is as low as 10 −4 rad. The mathematic demodulation model is of interest and has been demonstrated via simulation. Based on a more adaptable approach, account is taken of variations in illumination and phase distribution over a few neighboring pixels. Local demodulation in the spatial domain makes PLEF more flexible than the FT method, without spectral leakage. A novel demodulation method based on pixel-level Lissajous figure and ellipse fitting (PLEF) is presented in this paper. However FT has the drawback of significant edge errors because of the Gibbs effect, whilst detuning errors for the local phase shift occur when SCPS is applied. The Fourier transform (FT) method and the spatial-carrier phase-shifting technique (SCPS) are two popular and well-established approaches to demodulation. Phase demodulation from a single carrier-frequency fringe pattern is becoming increasingly important particularly in areas of optical metrology such as dynamic interferometry, deflectometry and profilometry. ![]()
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