Shifted Fringe Patterns Research Articles

Adequate phase unwrapping based on 2[formula omitted] cycle invariant between shifted phase maps

To obtain an adequate unwrapping solution for reliable phase measurement under noisy circumstances, a novel unwrapping algorithm is proposed. This algorithm extracts abundant valid pixels and rejects noise based upon revealing a property of 2π invariant, which is implied between wrapped phase maps with shifted fringe patterns. Distinct from conventional algorithms that use residues or minimum norm solution to attenuate the impacts of noise affected areas, this technique is free from the uncertainties arising from inadequate resources or over-smoothing effects during the unwrapping process. The performance of the proposed algorithm is demonstrated and confirmed through both computer simulations and practical experiments carried out using a fringe projection system. Superior capability in handling noise affected phase images is then achieved.

Single-shot detection of 8 unique monochrome fringe patterns representing 4 distinct directions via multispectral fringe projection profilometry

Spatial resolution in three-dimensional fringe projection profilometry is determined in large part by the number and spacing of fringes projected onto an object. Due to the intensity-based nature of fringe projection profilometry, fringe patterns must be generated in succession, which is time-consuming. As a result, the surface features of highly dynamic objects are difficult to measure. Here, we introduce multispectral fringe projection profilometry, a novel method that utilizes multispectral illumination to project a multispectral fringe pattern onto an object combined with a multispectral camera to detect the deformation of the fringe patterns due to the object. The multispectral camera enables the detection of 8 unique monochrome fringe patterns representing 4 distinct directions in a single snapshot. Furthermore, for each direction, the camera detects two π-phase shifted fringe patterns. Each pair of fringe patterns can be differenced to generate a differential fringe pattern that corrects for illumination offsets and mitigates the effects of glare from highly reflective surfaces. The new multispectral method solves many practical problems related to conventional fringe projection profilometry and doubles the effective spatial resolution. The method is suitable for high-quality fast 3D profilometry at video frame rates.

Estimation of the phase step between two fringe patterns based on the Gram–Schmidt algorithm

We present the evaluation of a closed form formula for the calculation of the original step between two randomly shifted fringe patterns. Our proposal extends the Gram--Schmidt orthonormalization algorithm for fringe pattern. Experimentally, the phase shift is introduced by a electro--mechanical devices (such as piezoelectric or moving mounts).The estimation of the actual phase step allows us to improve the phase shifting device calibration. The evaluation consists of three cases that represent different pre-normalization processes: First, we evaluate the accuracy of the method in the orthonormalization process by estimating the test step using synthetic normalized fringe patterns with no background, constant amplitude and different noise levels. Second, we evaluate the formula with a variable amplitude function on the fringe patterns but with no background. Third, we evaluate non-normalized noisy fringe patterns including the comparison of pre-filtering processes such as the Gabor filter banks and the isotropic normalization process, in order to emphasize how they affect in the calculation of the phase step.

Real-time 3-D shape measurement based on radial spatial carrier phase shifting from circular fringe pattern

In this paper, we propose a method to realize real-time three-dimensional (3-D) measurement with a radial spatial carrier phase shifting algorithm. The circular fringe patterns are continuously projected onto the moving object; the distorted fringe patterns are recorded by CCD. In the 3-D reconstruction process, three patterns consisting of one recorded image and two artificial phase shifting fringe patterns are used to implement phase shifting, where the two artificial patterns are formed by numerically shifting the recorded image along the radial direction. Compared with traditional carrier phase shifting method, the proposed method possesses lower phase error and higher accuracy. The simulations and two experiments are carried out to testify the proposed method. From the experimental results of the static object, we find that the standard deviation of the proposed method is better than that of the traditional one. The dynamic experiment of a moving lampshade shows that the time resolution of our method is the same as the CCD. As a real-time quantitative dynamic measurement method, it can be applied in various fields.

Instantaneous phase shifting deflectometry.

An instantaneous phase shifting deflectometry measurement method is presented and implemented by measuring a time varying deformable mirror with an iPhone ® 6. The instantaneous method is based on multiplexing phase shifted fringe patterns with color, and decomposing them in x and y using Fourier techniques. Along with experimental data showing the capabilities of the instantaneous deflectometry system, a quantitative comparison with the Fourier transform profilometry method, which is a distinct phase measuring method from the phase shifting approach, is presented. Sources of error, nonlinear color-multiplexing induced error correction, and hardware limitations are discussed.

Two-dimensional discrete wavelets transform for optical phase extraction: application on speckle correlation fringes

A method for optical phase extraction based on two-dimensional discrete wavelets transform (2-DWT) decomposition is shown. From modulated fringe pattern, phase distribution is extracted by the ratio between detail and approximation. Modulation process is realized digitally by introducing high-frequency spatial carrier, and this process needs two π /2 -shifted fringe patterns. We propose to use only single fringe and generate its quadrature by spiral phase transform (SPT). After validation by computer simulation, we apply the 2-DWT algorithm on experimental speckle fringe correlation taken for hard disk surface. The extracted phase using SPT quadrature was compared with that given using this time experimental quadrature, and we show a good performance by multiscale structural similarity metric.

Measurement of transparence topography based on principal component analysis

An algorithm based on the principal component analysis (PCA) is proposed to measure transparent surface topography. First, many frames of random phase shifted fringe patterns are captured. Second, the first and second principal components are extracted from the phase shifted fringe patterns by PCA. Then, the phase is calculated from principal components. Finally, the correct global phase sign is determined by the clustering method considering local fringe phase monotonicity. The experimental results show that the proposed method can directly extract the three-dimensional (3D) shape, which does not need to determine the amount of phase shift, without precise phase shifter. It reduces the experimental hardware requirements and improves its adaptability in profilometry.

Squeezed Carrier Interferogram for Wavelet Phase Recovery

The purpose of the present work is the use of the Phase evaluation CWT algorith m to extract the phase from squeezing interferogram. The squeezing interfero metry technique generates a spatial carrier interferogram named squeezed interferogram by numerical co mbination of M shifted fringes patterns. The M shifted fringes patterns are digitally generated fro m co mb ination of t wo π/2 shifted fringe patterns. Fro m squeezed interferogram the phase is extracted in wavelet domain using CWT algorith m which leads directly to the phase distribution without the complex step of phase unwrapping. Simu lated fringe pattern are used to test our technique and real fringe pattern are used to improve the accuracy of this technique.

Squeezing Interferometry for Optical Phase Extraction in Digital Speckle Pattern Interferometry

The purpose of the present work is the use of squeezing interferometry Technique to provide an optical phase mapping from DSPI fringes. The main advantage of this technique is to demodulate by means of a quadrature Gabor filter, a single carrier-frequency fringe pattern formed from intermixing M shifted fringe patterns that are synthetised numerically by the combination of a primary interferogram and its quadrature, which leads directly to the phase without any speckle de- noising algorithm, and this after unwrapping the phase with a standard phase unwrapping algorithm and using a simple median filter to smooth the result. This approach was tested on simulated interferograms for different speckle sizes and fringes densities; it was found that the procedure was able to give the result with a good accuracy for all these cases. An application of the proposed procedure to retrieve the phase for experimental fringes recorded from the thermomechanical study of the MOS power transistor is also presented.

A novel two-dimensional method to measure surface shrinkage in cementitious materials

A novel experimental technique, Cure Reference Method (CRM), was developed for the measurement of surface shrinkage in cementitious materials. The technique combines the replication of diffraction grating on a specimen during the curing process and the use of high-sensitivity moiré interferometry. Once demolded, the specimen was stored in an environmental chamber in order to establish specific curing conditions. Measurements were conducted on a daily basis for the duration of 7 days by recording a set of the consecutive phase shifted fringe patterns using the Portable Engineering Moiré interferometer II (PEMI II). An automated fringe analysis system was developed and used to obtain displacement and strain information in two dimenzsions. Surface shrinkage behavior in both cement paste and mortar specimens was investigated by the use of the technique under controlled temperature and humidity conditions. Furthermore, an experimental control was developed in an effort to remove the effects of drying shrinkage on cementitious specimens at early ages. This was done in an effort to explore the relative contribution of autogenous shrinkage to the overall shrinkage in cementitious materials.

Spatial carrier interferometry from M temporal phase shifted interferograms: Squeezing Interferometry

It is well known that having 3 temporal phase shifting (PS) interferograms we do not have many possibilities of using an algorithm with a desired frequency spectrum, detuning, and harmonic robustness. This imposes severe restrictions on the possibilities to demodulate such set of temporal interferograms. It would be nice to apply for example a 7 step PS algorithm to these 3 images in order to have more possibilities to phase demodulate them; even further, it would be even better to apply a quadrature filter having a spatial spread given by a real number to these 3 interferograms. In this paper we propose to do just that; namely we show how to demodulate a set of M-steps phase shifting images with a quadrature filter having a real-number as spatial spread. The interesting thing in this paper is to use a higher than M spread quadrature filter to demodulate our interferograms; in traditional PS interferometry one is stuck to the use of M step phase shifting formula to obtain the searched phase. Using a less than M PS formula is not interesting at all given that we would not use all the available information. The main idea behind the "squeezing" phase shifting method is to re-arrange the information of the M phase shifted fringe patterns in such a way to obtain a single carrier frequency interferogram (a spatio-temporal fringe image) and use any two dimensional quadrature filter to demodulate it. In particular we propose the use of Gabor quadrature filters with a spread given by real-numbers along the spatial coordinates. The Gabor filter may be designed in such way that we may squeeze the frequency response of the filter along any desired spatio-temporal dimension, and obtain better signal to noise demodulation ratio, and better harmonic rejection on the estimated phase.

A digital spatial carrier for wavelet phase extraction

In this paper, we present a new method to digitally add a high-frequency spatial carrier in order to use the wavelet phase extraction algorithm, which leads directly to the phase without the unwrapping process. The method needs a fringe pattern and its π/2 shifted version. The application is performed with two shifted fringe patterns obtained from the phase shifting images of the thermomechanical study of an MOS power transistor. A comparison with the phase shifting results is made.

Automatic analysis of three-dimensional displacement field using ESPI

Electronic speckle pattern interferometry (ESPI) has been used to study the in-plane and out-of-plane displacements of the object. In order to improve the accuracy, a Fourier filtration algorithm has been used to remove the speckle noise and get the holographic-quality ESPI fringe pattern. The processing steps of this method are described in detail in this paper. In addition, a phase shifter, which is easily used with simplified structure and high stability, is also presented. It can be applied to various coherent arrangements in experiments to obtain phase shifted fringe patterns. Experiments of determining the 3D displacement field of a circular fixed plate with a uniform load have been carried out using these methods. The results presented in this paper indicate that the accuracy of this method is satisfactory.

A comparison of phase shifting and fourier methods in the analysis of discontinuous fringe patterns

Phase Shifting Interferometry is a highly accurate data acquisition technique that efficiently utilizes several frames of information for each measurement. In this work, the advantages of phase shifting have been applied to a conventional moiré interferometer, yielding a system capable of recording phase shifted fringe patterns for both in-plane displacement components. Using this method, the phase of a wavefront of interest can be determined at each detector location, so that the resolution of the phase measurements is limited primarily by the detector discrimination and geometry. Unlike traditional Fourier fringe analysis, the noise rejection of phase shift processing algorithms does not degrade image fidelity in the presence of edges and discontinuities. A general discussion of both the phase shifting technique and the Fourier fringe analysis method is included to provide insight into the problems of processing discontinuous fringe patterns.