Shearographic phase retrieval using one single specklegram: a clustering approach

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.

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.

‘Ghosted’ fringe patterns simultaneously reflected from both the upper and lower sides of a transparent target in the fringe reflection technique are captured for transparent surface 3D shape measurement, but the phase retrieval from the captured ‘ghosted’ fringe patterns is still not solved. A novel method is proposed to solve this issue by using two sets of phase-shifted fringe patterns with slightly different frequencies. The nonlinear least-squares method is used to estimate the fringe phase and modulation from both front and rear interfaces. Several simulations are done to show the feasibility of the proposed method. The influence of fringe noise on the algorithm is studied as well, which indicates that the proposed method is able to retrieve the phase from double-sided reflective fringe patterns with fringe noise equivalent to that in practical measurements. The merits and limitations of the method are discussed and recommendations for future studies are made.

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.

Phase analysis of fringe pattern technique has been widely used for three-dimensional shape and deformation measurement by fringe projection method, precise inspection of optical components by various interferometry, etc. To analyze the phase distribution of fringe pattern, more than 80 phase analysis methods have been proposed by many researchers in this research field [1]. For instance, a Fourier transform [2], a wavelet transform, a windowed Fourier transform, and a sampling Moire method [3] have been developed from a single-shot image by using the intensity information in the spatial domain. In addition, the phase-shifting method (PSM) [4], which uses multi-frame phase-shifted fringe patterns is mostly used to analyze the phase distribution by using the intensity information in the temporal domain. However, these techniques only use one-dimensional intensity information in the spatial- or temporal-domains. For this reason, the analyzed phase distribution for noisy fringe pattern remains large measurement error due to the low reflectance of the object and the random noise of the camera.

Isotropic n-dimensional fringe pattern normalization

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.

The windowed Fourier transform (WFT) has been recognized as an effective tool for extracting phase map from a single fringe pattern. This paper presents a new WFT-based algorithm, which is guided by the principal component analysis (PCA) of the fringe pattern. With it, the principal direction of frequency at each pixel is determined first by using the PCA of the gradients of the fringe pattern, and then the windowed Fourier ridge for each pixel is detected by searching a one-dimensional space of frequency, so that the computational burden for phase extraction is alleviated significantly. In addition, this technique enables automatically identifying and excluding the regions of singular points from the fringe pattern by using the eigenvalues resulting from the PCA just mentioned. Numerical simulation and experiment are carried out to demonstrate the validity of this method.

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.

Fringe skeletonizing using an improved derivative sign binary method

In dynamic 3D measurements, the recovering carrier signal as well as phase retrieval are important issues for single fringe image analysis. Local mean decomposition is a powerful signal demodulation tool, but it usually encounters an obstacle, namely, the mode-mixing problem. Then different components, especially noise and carrier signals, are all probably mixed in one of the decomposition results, thus confusing its physical meaning. Utilizing the characteristics of original noise, we design a pair of differential signals based on the conditions that two mixed components should meet to be separated completely and then add them to the original signal. Re-decomposing the newly formed signal, the differential signal, along with the original noise, will be separated from the carrier signal, leaving very little negative impact due to the characteristics of the same amplitude and opposite polarity of the differential signal. With the mode-mixing problem of high-frequency components being resolved, the decomposition of the following low-frequency components becomes more reasonable, facilitating the fringe pattern analysis and further phase retrieval. The proposed method is suitably used for the signal, even though it is not stable. Experiments illustrate the efficiency of this novel adaptive method.

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.

The new VLTI/GRAVITY instrument is a four telescope beam combiner installed at the VLT Interferometer. The principal novelty of this instrument is the availability of a dual field mode enabling narrow-angle relative astrometry at micro-arcsecond accuracy between two objects separated by several arcseconds. The fringe tracker (FT) stabilizes the interference fringes at up to 1 kHz frequency, allowing for long exposures with the science combiner (SC) as well as phase referenced imaging and differential astrometry (in dual field mode). The FT and SC beam combiners are integrated optics (IO) components, whose 24 outputs are (optionally) polarization-split and spectrally dispersed. The processing of the photometric signals from the IO components is based on the pixel-to-visibility matrix (P2VM) formalism, that translates them into complex visibilities. The retrieval of the relative phase of the two objects subsequently relies on the combination of the phases measured from the FT, SC and the laser metrology. We will present the adopted algorithms, and an overview of the structure of the developed software. The calibration of the wavelength scales of the FT and SC at the required accuracy presents specific difficulties that we will briefly discuss. Examples of the reduction of on-sky data obtained during the commissioning will also be presented.

In the phase measuring deflectometry, two groups of fringe patterns in orthogonal directions are usually applied to establish the correspondences between the pixel pairs on the screen and camera. Usually, 16 phase-shifting fringe patterns with different spatial frequencies are required in order to calculate the absolute phases in the conventional temporal phase unwrapping algorithms. This requirement makes the measurement inefficient and not robust against environmental noise. In this paper, an efficient phase retrieval strategy is developed, which requires only six fringe patterns. The modulating information in one-direction is obtained by first using four fringe patterns, and then it is applied to assist the phase calculation in the other direction, so that only two extra fringe patterns are needed. Subsequently the phases are unwrapped by using the geometric constraints of the software configurable optical test system without additional image acquisition. The measurement time is saved by 5/8, compared to the conventional methods. In this way, the influence of the low-frequency disturbances can be suppressed in the workshop condition. Experiments demonstrate that the proposed method can reliably retrieve the absolute phases, and it is of significance to improve the measuring efficiency and stability of in situ deflectometry.

This paper will report on the methods of compound regions average (CRA) and the adaptive visual primitive elements matched (AWE). By CRA method, the high frequency noise of the digital speckle pattern interference (DSPI) fringe could be filtered. Further. the directions of the fringes were determined with AVPE method and the fringe skeleton could be obtained accurately by directional derivative. Results are presented for center determination from DSP! fringe patterns.