Generalized spin filtering and an improved derivative-sign binary image method for the extraction of fringe skeletons

Generalized spin filters, including several directional filters such as the directional median filter and the directional binary filter, are proposed for removal of the noise of fringe patterns and the extraction of fringe skeletons with the help of fringe-orientation maps (FOM's). The generalized spin filters can filter off noise on fringe patterns and binary fringe patterns efficiently, without distortion of fringe features. A quadrantal angle filter is developed to filter off the FOM. With these new filters, the derivative-sign binary image (DSBI) method for extraction of fringe skeletons is improved considerably. The improved DSBI method can extract high-density skeletons as well as common density skeletons.     

Phase extraction from a single fringe pattern based on guidance of an extreme map

A method for automatic phase extraction from a single fringe pattern based on the guidance of an extreme map is introduced. The method uses an adaptive weighted filter to reduce noise and enhance contrast and to locate the fringe extremes. Wrapped phase values are calculated by use of an arccosine function obtained from the extreme map. With this method, wrapped phase values can be efficiently demodulated from a single fringe pattern without the need for assigning fringe order or interpolating fractional fringe order. The validity of the method is demonstrated by use of closed-fringe patterns generated by digital speckle interferometry.     

High resolution speckle interferometry using virtual speckle pattern produced by information of deformation process

A high resolution new fringe analysis method for ESPI with only one camera is proposed by using features of speckle interferometry in a deformation process of a measured object. The profile of intensity of each speckle of the speckle patterns in the deformation process is analyzed by the Hilbert transform. A virtual speckle pattern for creating a carrier fringe image is produced artificially by using the information of profiles of intensities of speckles. The deformation map of the measured object can be detected by the virtual speckle pattern in an operation based on the spatial fringe analysis method. Experimental results show that the difference between the results by the new and the ordinary methods is 0.1 rad as standard deviation. From the results, it is confirmed that the high resolution measurement can be performed by this method the same as compared to the ordinary measurement method which needs to employ three speckle patterns.     

Spatial-fringe-modulation-based quality map for phase unwrapping

The quality-guided algorithm is a method widely used in phase unwrapping. The algorithm uses a quality map to guide its unwrapping process, and its validity depends on whether the quality map can truly reflect phase quality. In fringe projection surface profilometry, discontinuous surface structure, low surface reflectivity, and saturation of the image-recording system are sources of unreliable phase data. To facilitate the unwrapping process, we demonstrate an accurate quality map based on spatial fringe modulation, which is extracted from a single fringe pattern. Compared with temporal fringe modulation, the new criterion is more sensitive to spatial structure changes and less dependent on illumination conditions.     

Fringe-orientation estimation by use of a Gaussian gradient filter and neighboring-direction averaging

We analyze the effect of image noise on the estimation of fringe orientation in principle and interpret the application of a texture-analysis technique to the problem of estimating fringe orientation in interferograms. The gradient of a Gaussian filter and neighboring-direction averaging are shown to meet the requirements of fringe-orientation estimation by reduction of the effects of low-frequency background and contrast variances as well as high-frequency random image noise. The technique also improves inaccurate orientation estimation at low-modulation points, such as fringe centers and broken fringes. Experiments demonstrate that the scales of the Gaussian gradient filter and the direction averaging should be chosen according to the fringe spacings of the interferograms.     

Image encryption based on a grating generated by a reflection intensity map

A virtual optical technique for image encryption and decryption is presented in this paper. The technique is carried out using optical operation and computational algorithms. In this technique, a grey-level image is captured by a charge-coupled device camera and encrypted using a linear grating superposed on the reflected intensity map of the object. The grating is generated as a fringe pattern by a computer algorithm. The reflected intensity map is determined using the grey level of the image. This reflected intensity map is included in the fringe pattern as an optical phase. It generates a grating, which is represented as a fringe pattern deformed according to the reflected intensity map. The decryption method is performed by a phase recovery method. The technique used here is a spatial synchronous method. This encryption and decryption technique has been used to encrypt real face images. To describe the accuracy of results obtained by this technique, the rms of error is calculated using decrypted and original data images. This encrypting technique is a virtual optical method because all the optical operations are performed by computer processes, and optical components are not required, which are advantages over optical methods, where some physical optical components are used. Simulated images are used in order to assess the technique. Finally, results on real images are presented.     

Single-shot color fringe projection for three-dimensional shape measurement of objects with discontinuities

A simple but effective fringe projection profilometry is proposed to measure 3D shape by using one snapshot color sinusoidal fringe pattern. One color fringe pattern encoded with a sinusoidal fringe (as red component) and one uniform intensity pattern (as blue component) is projected by a digital video projector, and the deformed fringe pattern is recorded by a color CCD camera. The captured color fringe pattern is separated into its RGB components and division operation is applied to red and blue channels to reduce the variable reflection intensity. Shape information of the tested object is decoded by applying an arcsine algorithm on the normalized fringe pattern with subpixel resolution. In the case of fringe discontinuities caused by height steps, or spatially isolated surfaces, the separated blue component is binarized and used for correcting the phase demodulation. A simple and robust method is also introduced to compensate for nonlinear intensity response of the digital video projector. The experimental results demonstrate the validity of the proposed method.     

Performance evaluation of partial differential equation models in electronic speckle pattern interferometry and the delta-mollification phase map method

The ordinary differential equation (ODE) and partial differential equation (PDE) image- processing methods have been applied to reduce noise and enhance the contrast of electronic speckle pattern interferometry fringe patterns. We evaluate the performance of a few representative PDE denoising models quantitatively with two parameters called image fidelity and speckle index, and then we choose a good denoising model. Combining this denoising model with the ODE enhancement method, we make it possible to perform contrast enhancement and denoising simultaneously. Second, we introduce the delta-mollification method to smooth the unwrapped phase map. Finally, based on PDE image processing, delta mollification and some traditional techniques, an approach of phase extraction from a single fringe pattern is tested for computer-simulated and experimentally obtained fringe patterns. The method works well under a high noise level and limited visibility and can extract accurate phase values.     

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.     

Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting

The use of an optical fringe projection method with two-step phase shifting for three-dimensional (3-D) shape measurement of small objects is described. In this method, sinusoidal linear fringes are projected onto an object's surface by a programmable liquid-crystal display (LCD) projector and a long-working-distance microscope (LWDM). The image of the fringe pattern is captured by another LWDM and a CCD camera and processed by a phase-shifting technique. Usually a minimum of three phase-shifted fringe patterns is necessary for extraction of the object shape. In this method, a new algorithm based on a two-step phase-shifting technique produces the 3-D object shape. Unlike in the conventional method, phase unwrapping is performed directly by use of an arccosine function without the need for a wrapped phase map. Hence, shape measurement can be speeded up greatly with this approach. A small coin is evaluated to demonstrate the validity of the proposed measurement method, and the experimental results are compared with those of the four-step phase-shifting method and the conventional mechanical stylus method.     

Electronic speckle pattern interferometry based on spatial information using only two sheets of speckle patterns

Abstract

Speckle interferometry is an important deformation measurement method for an object with a rough surface. In this paper, a novel fringe analysis method is proposed that uses a new optical system, which uses a plane wave as the reference beam of the speckle interferometer. When the optical system is employed in fringe analysis, the deformation information and the bias components of the speckle patterns are clearly separated in the frequency domain. Therefore, the deformation information can be readily extracted using a Fourier transform, which gives a pair of real and imaginary components concerning the information. The specklegram is calculated using such a pair of components, and the phase map is obtained from the specklegram. Experimental results confirmed that the resolution power of this measurement method is higher than 1/261 of the wavelength of the light source of the optical system.     

Rotation-invariant optical recognition of three-dimensional objects

An automatic method for rotation-invariant three-dimensional (3-D) object recognition is proposed. The method is based on the use of 3-D information contained in the deformed fringe pattern obtained when a grating is projected onto an object's surface. The proposed method was optically implemented by means of a two-cycle joint transform correlator. The rotation invariance is achieved by means of encoding with the fringe pattern a single component of the circular-harmonic expansion derived from the target. Thus the method is invariant for rotations around the line of sight. The whole experimental setup can be constructed with simple equipment. Experimental results show the utility of the proposed method.     

Two-dimensional wavelet transform for reliability-guided phase unwrapping in optical fringe pattern analysis

This paper theoretically discusses modulus of two-dimensional (2D) wavelet transform (WT) coefficients, calculated by using two frequently used 2D daughter wavelet definitions, in an optical fringe pattern analysis. The discussion shows that neither is good enough to represent the reliability of the phase data. The differences between the two frequently used 2D daughter wavelet definitions in the performance of 2D WT also are discussed. We propose a new 2D daughter wavelet definition for reliability-guided phase unwrapping of optical fringe pattern. The modulus of the advanced 2D WT coefficients, obtained by using a daughter wavelet under this new daughter wavelet definition, includes not only modulation information but also local frequency information of the deformed fringe pattern. Therefore, it can be treated as a good parameter that represents the reliability of the retrieved phase data. Computer simulation and experimentation show the validity of the proposed method.     

Application of the radial basis function interpolation to phase extraction from a single electronic speckle pattern interferometric fringe

In this paper, we introduce the radial basis function (RBF) interpolation method to electronic speckle pattern interferometry (ESPI) and propose the RBF interpolation method to obtain unwrapped phase values based on a skeleton map. Because of the excellent approximation properties of the RBF interpolation, the proposed method can extract accurate phase values from a single fringe pattern effectively, even using a simple 3×3 mean filter as preprocessing. Using our method, both special filtering methods for ESPI fringes as preprocessing and postprocessing, including a dilatation and erosion algorithm for pruning and connecting and the smooth algorithm for improving the phase values are not needed. We test our method on a computer-simulated and two experimentally obtained poor-quality fringe patterns. The results have demonstrated that our RBF interpolation method works well even under a seriously disconnected skeleton map where it is impossible to apply the widely used, Matlab function grid data interpolation or the backpropagation neural networks method [Appl. Opt. 46, 7475 (2007)].     

Fringe filtering technique based on local signal reconstruction using noise subspace inflation

A noise filtering technique is proposed to filter the fringe pattern recorded in the optical measurement set-up. A single fringe pattern carrying the information on the measurand is treated as a data matrix which can either be complex or real valued. In the first approach, the noise filtering is performed pixel-wise in a windowed data segment generated around each pixel. The singular value decomposition of an enhanced form of this data segment is performed to extract the signal component from a noisy background. This enhancement of matrix has an effect of noise subspace inflation which accommodates maximum amount of noise. In another computationally efficient approach, the data matrix is divided into number of small-sized blocks and filtering is performed block-wise based on the similar noise subspace inflation method. The proposed method has an important ability to identify the spatially varying fringe density and regions of phase discontinuities. The performance of the proposed method is validated with numerical and experimental results.     

Fourier fringe processing by use of an interpolated Fourier-transform technique

Recently a powerful Fourier transform technique was introduced that was able to extract the phase from only one image. However, because the method is based on the two-dimensional Fourier transform, it inherently suffers from leakage effects. A novel procedure is proposed that does not exhibit this distortion. The procedure uses localized information and estimates both the unknown frequencies and the phases of the fringe pattern (using an interpolated fast Fourier transform method). This allows us to demodulate the fringe pattern without any distortion. The proposed technique is validated on both computer simulations and the profile measurements of a tube.     

Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry

We extend and refine previous work [Appl. Opt. 46, 2907 (2007)]. Combining the coupled nonlinear partial differential equations (PDEs) denoising model with the ordinary differential equations enhancement method, we propose the new denoising and enhancing model for electronic speckle pattern interferometry (ESPI) fringe patterns. Meanwhile, we propose the backpropagation neural networks (BPNN) method to obtain unwrapped phase values based on a skeleton map instead of traditional interpolations. We test the introduced methods on the computer-simulated speckle ESPI fringe patterns and experimentally obtained fringe pattern, respectively. The experimental results show that the coupled nonlinear PDEs denoising model is capable of effectively removing noise, and the unwrapped phase values obtained by the BPNN method are much more accurate than those obtained by the well-known traditional interpolation. In addition, the accuracy of the BPNN method is adjustable by changing the parameters of networks such as the number of neurons.     

Estimation of dynamically varying displacement derivatives using fringe projection technique

This paper presents a pseudo Wigner-Ville-distribution-based method in fringe projection for analyzing temporal behavior of the displacement derivative for a continuously deformed object. In the proposed method, a computer generated fringe pattern is projected on an object undergoing dynamic deformation, and the reflected intensity is recorded in the form of video, i.e., a stack of images are captured sequentially by a CCD camera. Each image represents a recorded fringe pattern at a particular time instant whose phase contains information about the instantaneous out-of-plane displacement or deformation with respect to the undeformed object, and the corresponding spatial phase derivative relates to the displacement derivative. Subsequently, pseudo Wigner-Ville distribution is used for instantaneous phase derivative estimation from the stack of images. Simulation and experimental results are presented to demonstrate the method's potential.     

Denoising in digital speckle pattern interferometry using fast discrete curvelet transform

In digital speckle pattern interferometry, the denoising of speckle fringe patterns is of vital importance for quantitative extraction of phase distribution. A filtering method of fast discrete curvelet transform based on weighted average thresholding technique is proposed in this paper for noise removal in speckle fringe patterns. Both computer-simulated and experimental digital speckle pattern interferometry fringe patterns are adopted to evaluate the performance of the proposed filtering method. In addition, a widely used and representative filtering method, windowed Fourier filter, is introduced for making a comparison and validation in the image processing effect, and the parameter of peak signal noise ratio is also used for assessment of denoising effect. It is shown from the filtered results that the filtering method of fast discrete curvelet transform is effecitve to remove speckle noises and simultaneously preserve fringe structure information.     

电子错位散斑干涉系统中错位量的研究

电子错位散斑检测系统中,错位量对测量精度、灵敏度以及条纹对比度有很大影响。本文介绍了电子错位散斑干涉原理,研究了错位量与测量精度、灵敏度和条纹对比度之间的对应关系,并利用MATLAB模拟出不同错位量下干涉条纹图,将错位散斑模拟条纹图与理论分析有效结合,总结出选取错位量的方法,并将其应用于轮胎变形检测实验,取得了良好的实验效果。本文研究工作对无损检测中错位量定量选取具有实际指导意义。