Frequency guided methods for demodulation of a single fringe pattern with quadratic phase matching

Phase demodulation from a single fringe pattern is a challenging task but of interest. A quadratic phase matching and frequency-guided regularized phase tracker (QFGRPT) and a quadratic phase matching and frequency-guided sequential demodulation (QFSD) for demodulation of a single fringe pattern are proposed. The algorithms are characterized by their improvements on both robustness and accuracy, which are realized by quadratic phase matching and frequency guided scanning strategy, respectively. Quadratic phase matching improves accuracy compared with the existing regularized phase tracker techniques and the frequency-guided sequential demodulation technique using linear phase matching. Frequency guidance ensures high robustness compared with the recently published path-independent regularized phase-tracking technique. Demodulation results from computer-simulated and experimental fringe patterns using the proposed methods are demonstrated and analyzed.     

Fast frequency-guided sequential demodulation of a single fringe pattern

Fast frequency-guided sequential demodulation (FFSD) for demodulating a single closed-fringe pattern is proposed as an improvement of frequency-guided sequential demodulation (FSD). Instead of using optimization to estimate the local frequencies for determining the sign of the phase, the FFSD estimates the local frequencies by directly calculating the gradient of the obtained phase with an undetermined sign. This improvement considerably reduces the computational complexity of the FSD and leads to a faster and simpler method. Simulated and experimental fringe patterns are used to test the proposed method and show that the demodulation speed of FFSD is about 150 times faster than that of the FSD, while the robustness and accuracy remain almost the same.     

A derivative based simplified phase tracker for a single fringe pattern demodulation

In this paper, a novel fringe demodulation method for the estimation of phase and its first-order derivative from a closed-fringe interferogram is proposed. The proposed method determines the phase derivatives in both x&y directions from fringe orientation and density. The phase derivatives are subsequently used to determine phase values using a novel simplified phase tracker. In the phase tracking model, the complexity of the cost function is reduced using predetermined derivatives so computation time required for phase tracking is reduced considerably. The proposed model is more robust while dealing with saddle points in fringes than the conventional phase tracker model. Hence it does not require any specialized scanning strategy. The proposed method is validated with simulated and experimental fringe patterns (obtained using electronic speckle pattern interferometry and optical holographic interferometry) and a comparison study is carried out with conventional regularized phase tracker. The simulation results show that the proposed method has good accuracy and requires less computation time than existing phase-tracking algorithms. The experimental results demonstrate the robustness of the proposed method against speckle noise and its practical applicability for static and dynamic applications.     

Window fringe pattern demodulation by multi-functional fitting using a genetic algorithm

We present a new way to demodulate complicated fringe patterns containing closed fringes using a genetic algorithm (GA). The entire fringe pattern is divided into a set of partially overlapping smaller sub-image windows. Each of these has a lower dimensionality and as a consequence is faster and can be demodulated more reliably. The demodulation process proceeds row-by-row way passing from one sub-image in a neighborhood until the whole interferogram is processed. The modulating phase of each sub-image is modeled as a parametric analytic function whose parameters are optimized using a GA. The technique is demonstrated demodulating some normalized fringe patterns that have two main difficulties: closed fringes within the interferogram and regions of under-sampled fringes. These fringe images cannot be demodulated by techniques such as the regularized phase tracker (RPT).     

Noisy fringe pattern demodulation by an iterative phase locked loop

The phase locked loop (PLL) technique applied to demodulate two-dimensional carrier-frequency fringe patterns has been developed recently. Here we present an extension to the basic PLL scheme to demodulate noisy fringe patterns. This modified technique estimates the phase in the fringe pattern iteratively; that is, the first wavefront estimation is done using a flat reference phase and the second iteration takes the demodulated phase found in the first iteration as the new reference. The third demodulating iteration uses the second phase estimation as the reference and so on, until further changes in the detected wavefront fall below a predefined threshold. During the iterative process the bandwidth of the iterative PLL system is gradually decreased to improve the signal-to-noise ratio of the detected phase as well as to resolve noise-generated phase inconsistencies.     

Analysis on fringe pattern demodulation by use of 2-D CWT

We discuss the wavelet transform profilometry based on the continuous wavelet transform technique as viewed from frequency analysis. We deduce the expression of one-dimensional (1-D) and two-dimensional (2-D) wavelet transform in frequency domain and analyze their characteristics in the application of demodulating the fringe patterns. We also compare 1-D CWT and 2-D CWT in demodulating the oblique fringe patterns with dual carrier frequency components. When oblique fringe patterns are processed, the direction normal to the grating line and x axis or y axis is not identical. By 1-D CWT, in which wavelet transform is carried out row by row, we cannot obtain the most similarity between local signal and the wavelet functions with different dilation values. While a fan 2-D continuous wavelet transformation can deal with the fringe pattern as a 2-D unit as well as has multi-directions, its advantage is that it can be used to exact the information in the spatial direction. However, its spatial localization ability is not very good, which leads that it is not suitable for demodulating the fringe patterns with high phase variation. Computer simulations and experiments have verified our analysis.     

High-speed fringe analysis by using stair-shaped virtual grating demodulation

This article describes a novel fringe analysis technique using stair-shaped virtual grating demodulation algorithm for extracting the phase information from a single fringe pattern. In contrast to the Fourier transform technique and quadrature multiplicative moire method, the new method processes a fringe pattern in the integer signal domain instead of the frequency domain and real-signal domain. The spatial carrier of fringe image is not limited to any particular frequency as long as it fulfills the sampling theorem. The errors analysis of this technique is conducted by computer simulation and experiments.     

Real-time determination of fringe pattern frequencies: An application to pressure measurement

Retrieving information in real time from fringe patterns is a topic of a great deal of interest in scientific and engineering applications of optical methods. This paper presents a method for fringe frequency determination based on the capability of neural networks to recognize signals that are similar but not identical to signals used to train the neural network. Sampled patterns are generated by calibration and stored in memory. Incoming patterns are analyzed by a back-propagation neural network at the speed of the recording device, a CCD camera. This method of information retrieval is utilized to measure pressures on a boundary layer flow. The sensor combines optics and electronics to analyze dynamic pressure distributions and to feed information to a control system that is capable to preserve the stability of the flow.     

Two-dimensional multiscale windowed Fourier transform based on two-dimensional wavelet transform for fringe pattern demodulation

A two-dimensional multiscale windowed Fourier transform (2D-MWFT), based on two-dimensional Gabor wavelet transform (2D-GWT), for the phase extraction from a spatial fringe pattern in fringe projection profilometry is presented. First, the instantaneous frequencies on x and y direction of the modulated fringe pattern are determined by 2D-GWT, and then the local stationary lengths are obtained. The 2D-MWFT with different two-dimensional Gaussian windows whose width is set according to the local stationary length is preformed for each section of the modulated fringe pattern to achieve multiresolution analysis and phase demodulation. Comparing the result of the phase demodulated by 2D-GWT and two-dimensional windowed Fourier transform (2D-WFT) with that by 2D-MWFT in a numerical simulation, we show that the 2D-MWFT method is superior to these methods, especially for the local non-stationary signal with low frequency. The theory and the results of a simulation and experiment are shown.     

Phase demodulation in the space domain without a fringe carrier

It is demonstrated that interference phase can be obtained from a fringe pattern using the spatial domain method known as spatial synchronous detection (direct interferometry) but without the usual fringe carrier (e.g. tilt) introduced into the interferometer. This is particularly useful in the study of transient events, where it is not always straightforward to introduce these carrier fringes. Spatial domain analysis is considerably faster than frequency domain (Fourier) methods, and could enable phase to be calculated in real time on relatively cheap personal computers. The main disadvantage of the new technique is that the sign of the recovered phase is lost, and must be inferred from object constraints.     

A numerical spatial carrier for single fringe pattern analysis algorithm

Hilbert transform and continuous wavelet transform are combined to form an algorithm for the analysis of a single fringe pattern with open or closed fringes. Only one recorded fringe pattern is needed to extract the phase information. A second π/2 phase shifted fringe pattern should first be generated from the other using Hilbert transform to superpose numerically the spatial carrier. Several phase extraction techniques are conceived to demodulate fringe patterns. In this paper, the wavelet technique is used to obtain the required phase distribution. The algorithm offers an advantage that it is appropriate when the spatial carrier is impossible to be added experimentally. Finally, a simulation was carried out to validate the algorithm, giving good results.     

Phase difference determination by fringe pattern matching

A method of phase difference determination in interferometry is presented. In this method, the phase difference between two interferograms is determined by fringe pattern matching with subpixel accuracy. The signal-to-noise ratio is significantly improved due to the region-based fringe pattern matching and its effect of averaging noise. The experiment shows that this method is useful for the determination of phase difference between two equi-spaced fringe patterns, and it has the advantages of high precision of measurement and high resistance to noise.     

Fluctuations of the fringe pattern generated by a partially developed speckle

The fluctuations of fringe pattern intensity are studied experimentally by means of Young's interference experiment. It is shown that the average contrast of the fringe intensity changes with the position in the fringe pattern. The characteristic values of the contrast are measured as a function of the separation of the pinholes. The experimental results are discussed qualitatively.     

The architecture of a multipurpose fringe pattern analysis system

A review of the advantages and disadvantages of analytical phase measurement methods of automatic fringe patterm analysis is given. The pros and cons for their applications due to the complexity of an interferogram, the accuracies required and the type of quantity measured are considered. The architecture of the system which enables a proper choice between the Fourier transform method, temporal and spatial phase-shifting methods is described. The modular structure of the software gives the possibility of getting the results in the most efficient way.     

Two-step fringe pattern analysis with a Gabor filter bank

We propose a two-shot fringe analysis method for Fringe Patterns (FPs) with random phase-shift and changes in illumination components. These conditions reduce the acquisition time and simplify the experimental setup. Our method builds upon a Gabor Filter (GF) bank that eliminates noise and estimates the phase from the FPs. The GF bank allows us to obtain two phase maps with a sign ambiguity between them. Due to the fact that the random sign map is common to both computed phases, we can correct the sign ambiguity. We estimate a local phase-shift from the absolute wrapped residual between the estimated phases. Next, we robustly compute the global phase-shift. In order to unwrap the phase, we propose a robust procedure that interpolates unreliable phase regions obtained after applying the GF bank. We present numerical experiments that demonstrate the performance of our method.     

A flexible new three-dimensional measurement technique by projected fringe pattern

Aimed at the problems of inferior precision and bad maneuverability for three-dimensional (3D) measurement by projected fringe pattern, a flexible new 3D technique for performing system calibration and measuring was proposed. First, we analyzed the principle of conventional 3D measurement with projected fringe pattern, and pointed out the shortcoming of measurement system. Then, the CCD camera calibration technique is analyzed and we set up the perspective projection model which transforms the computer image coordinate to 3D world coordinate, and we get the coordinate of the CCD camera image lens. Third, the position of projection lens optical center can be obtained using the above model. At last, some experiment results presented show that this technique is more simple and robust in engineering than conventional measurement method.     

Linear optical coherence tomography system with a downconverted fringe pattern

Linear optical coherence tomography (LOCT) systems are a simple and robust alternative to time-domain optical coherence tomography systems, but a detector with approximately 10(4) pixels is needed for an imaging depth of 2 mm. We present a new system for LOCT with a special mask attached to the image sensor. The mask essentially performs a downconversion of the spatial frequencies by multiplication with a second spatial frequency. This reduces the fringe frequency of the optical coherence tomography signal so that the signal can be sampled with fewer pixels.     

Binarization of scanning Moiré fringe pattern

This paper describes a digital picture processing method to obtain a binary scanning moiré pattern. In this method, a bias component due to the illumination light distribution is eliminated from the scanning moiré fringe pattern to detect the zero-crossing points of the moiré profile. The binary fringe pattern is then obtained from the zero-crossing points. Experiments indicate that the method is useful for facilitating three-dimensional automatic measurement using moiré topography.