Fringe phase extraction using windowed Fourier transform guided by principal component analysis

A hybrid algorithm is proposed in this study for demodulating a single spatial carrier fringe pattern (FP) of interferometric measurement, which essentially combines the spatial carrier phase shift (SCPS) method and Fourier transform (FT) method. It firstly extracts three phase-shifted FPs from a single spatial carrier FP, then employs the FT method and a subtraction operation to determine the phase shift of three phase-shifted FPs, and finally retrieves the phase map using a least-square phase shift algorithm. The subtraction operation could considerably mitigate the inherent edge error of the FT method, resulting in an increase of accuracy compared with the FT method. It also does not require the background and modulation amplitude of the spatial carrier FP to be constant; thus it is robust and quite suitable for engineering. The factors that may influence the performance of the proposed algorithm are analyzed, including the random and speckle noise, carrier frequency, shape of the background, and modulation amplitude. The feasibility of the proposed algorithm is validated by two experiments, comparing them with the temporal phase-shifted method. The proposed algorithm is expected to be used in interferometric measurement under adverse environments.

This letter introduces a new approach for the demodulation of fringe patterns recorded in holographic interferometry using high-order ambiguity function (HAF). The proposed approach is capable of retrieving the phase from a single fringe pattern. The main advantage of this approach is that it directly provides an estimation of the continuous phase distribution and thereby avoids the necessity of using a cumbersome 2D phase unwrapping procedure. This method first computes the discrete-time analytic signal of the recorded fringe pattern. Then, by modelling this analytic signal as a polynomial phase signal embedded in additive complex white Gaussian noise, a parametric estimation procedure based on HAF is employed to directly estimate the unwrapped phase distribution. Numerical simulations and experimental results demonstrate the potential of the proposed approach.

In this paper, a novel technique for quantitative vibration analysis using time-average electronic speckle pattern interferometry is proposed. An amplitude-varied time-average refreshing reference frame method is used to capture a fringe pattern with a better fringe contrast than the conventional reference frame technique. The recorded fringe patterns with improved contrast provide better mode shape visibility and are easier to process. A derivative-based regularized phase tracker model is used to retrieve vibration amplitudes from a single fringe pattern. The method does not require a phase shifter to obtain the mode shape or amplitude. The method provides unwrapped amplitude and amplitude derivatives maps directly, so a separate phase unwrapping process is not required. Experimental work is carried out using a circular aluminum plate test specimen and the results are compared with a finite element method modal analysis. Both experimental and numerical results show that the proposed method is robust and accurate.

Phase shifting profilometry (PSP) shifts the phase by projecting multiple fringe patterns with different initial phase values. Errors will be introduced when the dynamic object moves among the multiple fringe patterns. This paper presents a new 3D reconstruction method of moving object based on PSP by projecting single fringe pattern. The phase shift is caused by the object movement. Multiple images of the object with movement are captured. The object movement is tracked first; then, the phase variation caused by the movement in the single projected fringe pattern is analyzed and the reconstruction model describing the fringe pattern with movement is given; at last, the phase value is retrieved by utilizing the phase variation caused by the movement. The effectiveness of the proposed method is verified by the simulations and the experiment.

Windowed Fourier transform (WFT) is used to analyze fringe patterns observed from optical measurements. The space-frequency resolution of the WFT is limited, which affects the analyzing performance. In this Letter, we propose to apply the two-dimensional synchrosqueezing transform (SST) for analyzing fringe patterns. The SST is a technique used to overcome the limitation of the space-frequency resolution of the WFT, which sharpens the WFT representation using the derivative of the WFT phase. Numerical experiments confirm the effectiveness of the SST in denoising the fringe pattern and estimating the local frequency from the observed fringe pattern.

The quality enhancement of a single fringe pattern is a challenging task in speckle interferometry. Fringe patterns suffer greatly from three adverse variations (nonuniform background, speckle noise, and intensity modulation). In this Letter, we propose a three-layer filtering strategy for noisy fringe patterns. The first layer is aimed at high-frequency speckle noises and low-frequency background. The second layer is for remaining speckle noises distributed in the middle-frequency band. The third layer will further implement quality enhancement by a phase-recovery technique. The proposed strategy is quantitatively evaluated by different indexes and verified to be effective through numerous comparative experiments.

Series of thermodiffusion experiments using optical digital interferometry (ODI) have been conducted onboard the International Space Station. Conventionally, the two-dimensional (2D) fast Fourier transform (FFT) fringe analysis technique has been applied as a fast and reliable technique to extract data. In this study, for the first time, the windowed Fourier transform (WFT) method is used to analyse the same experiments. In this method, a Fourier transformation is applied on the fringes at two different stages: initially, during the filtration of the non-zero peaks and then on the wrapped phase image. We provide a detailed comparison between FFT and WFT results of binary and ternary mixtures for ODI thermodiffusion experiments. The substantial enhancements of this method are presented and discussed for different experiments conducted for both binary and ternary mixtures. We show that while disturbances in the phase fringe pattern can cause significant error in FFT techniques, if the windowed Fourier filtration (WFF) parameters are properly chosen this type of noise can be eliminated during WFF analysis. The importance of replacing the FFT method becomes more pronounced for the ternary system, as this method fails to reconcile reliable concentration profiles. The results of this chapter can show that the application of the windowed Fourier transform in optical digital interferometry investigations show improved results over the same experiments analysed using FFT methods, especially for experiments involving very small heat and mass fluxes such as the Soret effect in multicomponent mixtures.

Isotropic n-dimensional fringe pattern normalization

In the field of optical measurement, phase always represents the physical quantity to be measured. Thus, phase retrieval from a fringe pattern is a key step for quantitative measurement and evaluation. Much research work has been conducted to develop phase evaluation methods such as fringe tracking and fringe skeletons in earlier, and the more precise methods of phase-shifting and Fourier transform more recently. For phase evaluation, the phase-shifting method requires three or more phase-shifted speckle patterns at each deformed stage; thus, it is not suitable for measurement of continuous deformation. The Fourier transform, on the other hand, requires a high-frequency carrier for phase separation in the spectral domain, which places an additional requirement on experimental arrangement. Thus, it would be desirable to develop a convenient method that can retrieve the modulated phase from a single fringe pattern. We propose an approach that utilizes the phase-clustering property to extract phase information from a single interference specklegram. To explore the ability and limitation for the proposed technique, typical shearographic fringe patterns are used for phase evaluation. Results obtained are similar to those from the standard four-step phase-shifting method. Nonrepeatable continuous movement is also measured by the proposed method, and the results confirm the robustness and accuracy of the clustering method.

Phase-shifting interferometry is a highly accurate technique for obtaining phase distribution from the recorded fringe patterns. Generally, phase-shifting interferometry requires recording several fringe patterns with varying phase shifts experimentally and during the acquisition, the object must be stable. Also, the atmospheric turbulence and mechanical conditions should also remain constant during this time. These requirements limit the use of these phase-shifting interferometric techniques in dynamic event studies. In the present work, we introduce Riesz transformed based digital four-step phase-shifting interferometer to obtain phase distribution from a single recorded fringe pattern. All the experimental phase-shifting setups necessary to realize the phase-shifting are removed. The idea is based on the recording of a single fringe pattern, and computes its Riesz transform at first, second and third-orders. The obtained Riesz transform components are combined to generate three π/2 phase-shifted fringe patterns, and then, the phase distribution is obtained from these phase-shifted fringe patterns. The performance of this method is demonstrated first by using numerical simulation and the quantitative appraisal is given by using image quality index. Further, we apply this technique on a real fringe pattern recorded in digital speckle pattern interferometry (DSPI). The obtained results reveal that our method provides a simple and accurate solution for phase evaluation, therefore, makes it suitable for real-time measurements.

Fringe projection profilometry is widely used for three-dimensional measurements. Sinusoidal patterns are commonly used; those patterns are modulated by the object’s topography, raising the necessity to relate this modulation with the object’s shape. Several approaches have been proposed and can be classified as spatial or temporal algorithms, making them suitable for dynamic or static objects. In this paper, an improvement of a different approach to analyze the modulated fringe pattern is proposed; from a single fringe pattern, the object’s shape can be found with the determination of maximums and minimums of the signal, avoiding the use of Fourier transform, wavelet transform, and Riez transform techniques.

We describe a method of obtaining optically scanned fluorescence images in a widefield conventional microscope by interfering two beams on an object so as to illuminate it with a single spatial frequency fringe pattern. Images taken at three spatial positions of the fringe pattern are processed in real time to produce optically sectioned images which are substantially similar to those obtained with confocal microscopes.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Parallel computing for fringe pattern processing: A multicore CPU approach in MATLAB ® environment

This study presents a simple and reliable method for numerical evaluation of the sensitivity of SPR systems. A Windowed Fourier Transform (WFT) based method is applied to extract shifts of SPR interferogram. By applying the WFT, the frequencies consisting of SPR interferogram are extracted, and phase shifts of relevant frequencies are also obtained. The normalized amplitude of the frequencies larger than 0.35 is regarded as the most prominent frequency. The summation of the phase shifts of the most prominent frequencies is regarded as an index to numerically analyzing phase shifts of SPR sensors. Through this method, the small change in the sensing surface can be monitored. By using a homemade SPR system with the proposed calculation method, it can detect the NaCl solutions ranging from 0.00003% to 0.03% (wt%), indicating its great promise for applications in fields such as medicine, food safety, and biotechnology.

Phase unwrapping is an important and challenging process in optical interferometry. Difficulties in phase unwrapping are usually caused by either noise (“bad” pixels) or invalid areas (“bad” regions). If the “bad” pixels can be removed, the problems due to the noise are solved. Further, if the “bad” regions can be identified, they can be avoided in phase unwrapping. In our previous work the noise can be successfully removed using a windowed Fourier transform [Optics and Lasers Technology, 37:458-462 (2005)]. In this paper we will show that the invalid areas can be identified by the same windowed Fourier transform. Thus a single windowed Fourier transform is able to process both “bad” pixels and “bad” regions simultaneously, which makes the phase unwrapping simple and effective.