Regularized Phase-tracking Research Articles

DeepDensity: Convolutional neural network based estimation of local fringe pattern density

Fringe pattern based measurement techniques are crucial both in macroscale, e.g., fringe projection profilometry, and microscale, e.g., label-free quantitative phase microscopy. Accurate estimation of the local fringe density map can significantly facilitate almost all stages of fringe pattern analysis process. Example includes: (1) using density map as a determinant for the selection of the proper window size in windowed Fourier transform method, (2) guiding the decomposition process in empirical mode decomposition, (3) improving the phase unwrapping accuracy by providing additional reliability indicators, (4) guiding phase estimation process in regularized phase tracking. For these reasons, the accurate and robust estimation of local fringe density map is of high importance and can boost fringe pattern analysis on different stages of processing path, resulting in increased capacity of the full-field noncontact/noninvasive optical measurement system. In this paper, we propose a new, accurate, robust, and fast numerical solution for local fringe density map estimation called DeepDensity. DeepDensity is based on the convolutional neural network and deep learning, making it significantly outperform other conventional solutions to this problem. Numerical simulations and experimental results corroborate the effectiveness of the proposed DeepDensity.

可用于单幅闭合干涉图相位恢复的正则化相位跟随技术

可用于单幅闭合干涉图相位恢复的正则化相位跟随技术

Adaptive Unscented Kalman Filter Phase Unwrapping Method and Its Application on Gaofen-3 Interferometric SAR Data.

Phase unwrapping (PU) is a key step in the reconstruction of digital elevation models (DEMs) and the monitoring of surface deformation from interferometric synthetic aperture radar (SAR, InSAR) data. In this paper, an improved PU method that combines an amended matrix pencil model, an adaptive unscented kalman filter (AUKF), an efficient quality-guided strategy based on heapsort, and a circular median filter is proposed. PU theory and the existing UKFPU method are covered. Then, the improved method is presented with emphasis on the AUKF and the circular median filter. AUKF has been well used in other fields, but it is for the first time applied to interferometric images PU, to the best of our knowledge. First, the amended matrix pencil model is used to estimate the phase gradient. Then, an AUKF model is used to unwrap the interferometric phase based on an efficient quality-guided strategy based on heapsort. Finally, the key results are obtained by filtering the results using a circular median. The proposed method is compared with the minimum cost network flow (MCF), statistical cost network flow (SNAPHU), regularized phase tracking technique (RPTPU), and UKFPU methods using two sets of simulated data and two sets of experimental GF-3 SAR data. The improved method is shown to yield the greatest accuracy in the interferometric phase maps compared to the methods considered in this paper. Furthermore, the improved method is shown to be the most robust to noise and is thus most suitable for PU of GF-3 SAR data in high-noise and low-coherence regions.

Demodulation of a single complex fringe interferogram with a path-independent regularized phase-tracking technique

The two-dimensional regularized phase-tracking (RPT) technique is one of the most powerful approaches to demodulate a single interferogram with either open or closed fringes. However, it often fails in the cases of complex interferograms and needs well-defined scanning strategies. An improved algorithm based on the RPT is presented in this paper. We use a paraboloid phase model to approximate the phase function and modify the cost functional to search the smoothest phase solutions in the function space C(2). With these modifications, the phase tracker preserves the robustness of the RPT while at the same time it is no more sensitive to stationary points and is capable of demodulating complex interferograms with arbitrary scanning schemes. Moreover, the phase reconstructed by the proposed algorithm is normally more accurate than that of the RPT both for noiseless and noisy interferograms under the same conditions. Computer simulations and experimental results are both presented.

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

In the process of measurements such as optical interferometry and fringe projection, an important stage is fringe pattern analysis. Many advanced fringe analysis algorithms have been proposed including regularized phase tracking (RPT), partial differential equation based methods, wavelet transform, Wigner–Ville distribution, and windowed Fourier transform. However, most of those algorithms are computationally expensive. MATLAB ® is a general algorithm development environment with powerful image processing and other supporting toolboxes. It is also commonly used in photomechanical data analysis. With rapid development of multicore CPU technique, using multicore computer and MATLAB ® is an intuitive and simple way to speed up the algorithms for fringe pattern analysis. The paper introduces two acceleration approaches for fringe pattern processing. The first approach is task parallelism using multicore computer and MATLAB ® parallel computing toolbox. Since some algorithms are embarrassing problems, our first approach makes use of this characteristic to parallelize these algorithms. For this approach, parallelized windowed Fourier filtering (WFF) algorithm serves as an example to show how parallel computing toolbox accelerates the algorithm. Second, data parallelism using multicore computer and MATLAB ® parallel computing toolbox is proposed. A high level parallel wrapping structure is designed, which can be used for speeding up any local processing algorithms. WFF, windowed Fourier ridges (WFR), and median filter are used as examples to illustrate the speedup. At last, the results show that the parallel versions of former sequential algorithm with simple modifications achieve the speedup up to 6.6 times.

Fast half-quadratic regularized phase tracking for nonnormalized fringe patterns

Although one of the simplest and powerful approaches for the demodulation of a single fringe pattern with closed fringes is the regularized phase-tracking (RPT) technique, this technique has two important drawbacks: its sensibility at the fringe-pattern modulation and the time employed in the estimation. We present modifications to the RPT technique that consist of the inclusion of a rough estimate of the fringe-pattern modulation and the linearization of the fringe-pattern model that allows the minimization of the cost function through stable numerical linear techniques. With these changes, the demodulation of nonnormalized fringe patterns is made with a significant reduction in the processing time, preserving the demodulation accuracy of the original RPT method.

Fast algorithm for estimation of the orientation term of a general quadrature transform with application to demodulation of an n-dimensional fringe pattern

The spatial orientation of fringes has been demonstrated to be a key point in reliable phase demodulation from a single n-dimensional fringe pattern, regardless of the frequency spectrum of the signal. Recent publications have shown a general method for determination of the orientation factor by use of a regularized phase-tracking (RPT) algorithm. We propose a generalization of a RPT algorithm for estimation of the spatial orientation in a general n-dimensional case. The proposed algorithm makes use of a simplified cost function that remains one dimensional regardless of the dimension of the problem. This makes the calculation faster than with a standard RPT algorithm, with which it is necessary to minimize an n + 1-dimensional cost function for each point of the sample space. We have applied the method to the three-dimensional demodulation of a time-evolving fringe pattern, with good results.

Phase unwrapping with regularized phase-tracking technique based on simulated annealing algorithm

We propose an improved regularized phase-tracking (RPT) technique for unwrapping two-dimensional principal phase maps. The size of the neighborhood selected for plane approximation at each pixel is adjustable according to local noise severity. In the area of low noise, the size is small to improve processing speed. On the contrary, a neighborhood with large size is selected to enhance the noise-reduced ability in the high-noisy area. Further, simulated annealing (SA) algorithm is applied to RPT technique for finding the global optimum solutions. Numerical simulation proves that this SA-based RPT phase unwrapping technique is highly robust to noise and experimental results also show its feasibility in practical applications.

Improvement of the regularized phase tracking technique for the processing of nonnormalized fringe patterns.

One of the powerful approaches to demodulate a single fringe pattern is the regularized phase tracking (RPT) technique. Here, a new improvement in the RPT technique is presented. This new improvement consists in the addition of one term that models the fringe-pattern modulation. With this new term, the RPT technique can be used for the demodulation of nonnormalized fringe patterns. The performance of the improved RPT technique is shown on examples of various fringe patterns.

Modulo 2pi fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm.

The fringe orientation angle provides useful information for many fringe-pattern-processing techniques. From a single normalized fringe pattern (background suppressed and modulation normalized), the fringe orientation angle can be obtained by computing the irradiance gradient and performing a further arctangent computation. Because of the 180 degrees ambiguity of the fringe direction, the orientation angle computed from the gradient of a single fringe pattern can be determined only modulo pi. Recently, several studies have shown that a reliable determination of the fringe orientation angle modulo 2pi is a key point for a robust demodulation of the phase from a single fringe pattern. We present an algorithm for the computation of the modulo 2pi fringe orientation angle by unwrapping the orientation angle obtained from the gradient computation with a regularized phase tracking method. Simulated as well as experimental results are presented.

Isochromatics demodulation from a single image using the regularized phase tracking technique

Isochromatics demodulation from a single image using the regularized phase tracking technique

Isochromatics demodulation from a single image using the regularized phase tracking technique

In this work we propose a robust fringe demodulation technique applied to the analysis of a single isochromatics fringe pattern produced in photoelasticity. The method used is a regularized phase tracking algorithm with a new sequential scanning technique specifically adapted for the characteristics of the isochromatic fringe patterns: possible apparition of closed fringes, large dynamic range in its spatial frequency content and low noise. The performance of the method is discussed and experimental results are presented.

Separation of isoclinics and isochromatics from photoelastic data with a regularized phase-tracking technique

We present the application of a regularization algorithm to the processing of photoelastic fringe patterns. The method used is a modified regularized phase-tracking (RPT) algorithm applied to phase-shifted images. In particular, we present an algorithm for isoclinic-isochromatic separation that uses only five images. In the case of isoclinics the method can deal with problems associated with modulation of isochromatics and with isotropic points by means of a modified cost functional. With respect to the isochromatics the problems associated with regions of high fringe density are solved in a robust way by the unmodified RPT algorithm by use of the modulation information. The performance of the method is discussed, and experimental results are presented.

Improved regularized phase-tracking technique for the processing of squared-grating deflectograms

We propose a robust procedure based on the regularized phase-tracking (RPT) technique to demodulate squared-grating deflectograms. The use of squared gratings, already reported, lets us multiplex the information of the deflections in two orthogonal directions in a single image, thus avoiding the necessity of rotating the gratings. The good noise-rejection characteristics of the RPT technique are improved by use of a quasi-Newton optimization algorithm and a quality-map-based algorithm for the crystal-growing process.

Direct ray aberration estimation in Hartmanngrams by use of a regularized phase-tracking system

The Hartmann test is a well-known technique for testing large telescope mirrors. The Hartmann technique samples the wave front under analysis by use of a screen of uniformly spaced array of holes located at the pupil plane. The traditional technique used to gather quantitative data requires the measurement of the centroid of these holes as imaged near the paraxial focus. The deviation from its unaberrated uniform position is proportional to the slope of the wave-front asphericity. The centroid estimation is normally done manually with the aid of a microscope or a densitometer; however, newer automatic fringe-processing techniques that use the synchronous detection technique or the Fourier phase-estimation method may also be used. Here we propose a new technique based on a regularized phase-tracking (RPT) system to detect the transverse aberration in Hartmanngrams in a direct way. That is, it takes the dotted pattern of the Hartmanngram as input, and as output the RPT system gives the unwrapped transverse ray aberration in just one step. Our RPT is compared with the synchronous and the Fourier methods, which may be regarded as its closest competitors.

Phase unwrapping through demodulation by use of the regularized phase-tracking technique

Most interferogram demodulation techniques give the detected phase wrapped owing to the arctangent function involved in the final step of the demodulation process. To obtain a continuous detected phase, an unwrapping process must be performed. Here we propose a phase-unwrapping technique based on a regularized phase-tracking (RPT) system. Phase unwrapping is achieved in two steps. First, we obtain two phase-shifted fringe patterns from the demodulated wrapped phase (the sine and the cosine), then demodulate them by using the RPT technique. In the RPT technique the unwrapping process is achieved simultaneously with the demodulation process so that the final goal of unwrapping is therefore achieved. The RPT method for unwrapping the phase is compared with the technique of least-squares integration of wrapped phase differences to outline the substantial noise robustness of the RPT technique.

Phase-shifting interferometry using a two-dimensional regularized phase-tracking technique

Phase-shifting interferometry is the most used method whenever the optical stability of the interferometer remain high when several phase-shifted interferograms are taken. In this work we present a two-dimensional regularized phase-tracking (RPT) technique applied to demodulate multiple phase-shifted interferograms. The main advantage of this technique with reference to classical phase-shifting interferometry is its higher signal-to-noise rejection as well as a higher signal′s harmonics rejection. In the RPT technique the unwrapping process is implicit; so it is achieved simultaneously with the phase estimation process; then, no additional unwrapping process is required.

Phase unwrapping with a regularized phase-tracking system

We develop a regularized phase-tracking (RPT) technique tounwrap phase maps. The phase maps that can be unwrapped with thisnew method may be bounded by arbitrarily shaped boundaries. Moreover, the RPT unwrapper has a higher noise robustness than previously reported phase-unwrapping schemes.