Study on Generalized Analysis Model for Fringe Pattern Profilometry

This paper presents a generalized analysis model for fringe pattern profilometry. We mathematically derived a new analysis model that gives a more general expression of the relationship between projected and deformed fringe patterns. Meanwhile, based on the proposed generalized model, a new algorithm is presented to retrieve 3-D surfaces from nonlinearly distorted fringes. Without any prior knowledge about the projection system, we still can obtain very accurate measurement results by using a generalized analysis model and a proposed algorithm. Computer simulation and experimental results show that the generalized model and the proposed algorithm can significantly improve the 3-D reconstruction precision, especially when the projected fringe pattern is nonlinearly distorted.     

含孤立物体场景的高速、高密度三维面形采集

提出了一种用于采集含空间孤立物体场景的高速、高密度三维面形采集方法。该方法将三幅图案高速投影到被测物体上并同步采集图像,从而实现场景三维形貌及纹理的高速记录。其中两幅图案是互相具有π相移的正弦条纹,采用傅里叶变换法求解变形条纹相位。将拍摄到的两幅变形条纹图相加可得到物体表面纹理。另一幅图案用来确定条纹级次,实现绝对相位测量,解决高速形貌采集中孤立物体相位展开难题。它由一系列宽度与正弦条纹周期相同的竖条构成,采用三种灰度对竖条编码。每个竖条由单一灰度或两种在竖直方向上周期性分布的灰度构成,这样可编6个码。将竖条按由这些码构成的伪随机序列排列,得到编码图案。测量时,对拍摄的编码图案解码,通过子序列匹配来确定对应正弦条纹的级次。设计了采用DLP投影仪及高速摄像机的高速测量系统。采用提出的方法实现了640×480分辨率下每秒60帧和320×240分辨率下每秒120帧的三维形貌及纹理采集。     

Efficient fringe image enhancement based on dual-tree complex wavelet transform

In optical phase shift profilometry (PSP), parallel fringe patterns are projected onto an object and the deformed fringes are captured using a digital camera. It is of particular interest in real time three-dimensional (3D) modeling applications because it enables 3D reconstruction using just a few image captures. When using this approach in a real life environment, however, the noise in the captured images can greatly affect the quality of the reconstructed 3D model. In this paper, a new image enhancement algorithm based on the oriented two-dimenional dual-tree complex wavelet transform (DT-CWT) is proposed for denoising the captured fringe images. The proposed algorithm makes use of the special analytic property of DT-CWT to obtain a sparse representation of the fringe image. Based on the sparse representation, a new iterative regularization procedure is applied for enhancing the noisy fringe image. The new approach introduces an additional preprocessing step to improve the initial guess of the iterative algorithm. Compared with the traditional image enhancement techniques, the proposed algorithm achieves a further improvement of 7.2 dB on average in the signal-to-noise ratio (SNR). When applying the proposed algorithm to optical PSP, the new approach enables the reconstruction of 3D models with improved accuracy from 6 to 20 dB in the SNR over the traditional approaches if the fringe images are noisy.     

基于结构照明和BP神经网络的三维物体识别

提出一种具有旋转不变性的三维物体识别的新方法,该方法通过结构光照明的方法,使物体的高度分布以变形条纹的形式编码于二维强度图中,由于条纹图包含有物体的高度分布信息,因此对条纹的相关识别具有本征三维识别的特点.旋转不变性是通过BP神经网络实现的.计算机模拟结果表明,用二维强度像的基频分量做训练样本设计BP神经网络,选择训练样本和隐藏层神经元的数目,基于结构光编码的BP神经网络对三维物体具有良好的旋转不变识别效果.     

An online triple-frequency color-encoded fringe projection profilometry for discontinuous object

Abstract

An online triple-frequency color-encoded fringe projection profilometry is proposed to measure the complex and discontinuous object at straight-line movement. N frames of color fringe patterns are specially designed. Three grayscale sinusoidal grating patterns with geometric progression frequency growth are encoded into red (R), green (G), and blue (B) channels separately to compose a color-encoded fringe pattern. If these three grayscale sinusoidal grating patterns are phase-shifted N steps with an equivalent shift phase of 2π/N, they can compose the corresponding N frames of color-encoded fringe patterns as above respectively. In order to avoid the movement’s interference to the phase shifting, position adjustment should be done to guarantee the phase-shifting direction to be perpendicular to the moving direction. While these N frames of specially designed color-encoded fringe patterns are projected onto the moving object one by one, the corresponding deformed color patterns are captured by a CCD camera in real time. By color separating, color crosstalk compensation, pixel matching, and phase calculation, three wrapped phase at different frequencies can be extracted. The unwrapped phase can be solved by a simplified algorithm based on temporal phase unwrapping method from the relationship of the three wrapped phase at the same pixel. Thus, it is very suitable to measure the online complex and discontinuous objects at straight-line movement. The experimental results show the feasibility and the validity of the proposed method.     

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.     

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.     

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.     

Technique for phase measurement and surface reconstruction by use of colored structured light

We present a new method for improving the measurement of three-dimensional (3-D) shapes by using color information of the measured scene as an additional parameter. The widest used algorithms for 3-D surface measurement by use of structured fringe patterns are phase stepping and Fourier fringe analysis. There are a number of problems and limitations inherent in these algorithms that include: that the phase maps produced are wrapped modulo 2pi, that in some cases the acquired fringe pattern does not fill the field of view, that there may be spatially isolated areas, and that there is often invalid and/or noisy data. The new method presented to our knowledge for the first time here uses multiple colored fringe patterns, which are projected at different angles onto the measured scene. These patterns are analyzed with a specially adapted multicolor version of the standard Fourier fringe analysis method. In this way a number of the standard difficulties outlined above are addressed.     

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.     

Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method

Electronic speckle pattern interferometry fringe patterns usually have poor contrast so it is important to enhance fringe contrast for the extraction of phase from a single fringe pattern. We present new enhancement methods based on differential equations (called DE enhancement methods) to electronic speckle pattern interferometry fringes. The DE enhancement methods transform the image processing to solve differential equations. With the proposed methods, the visibility of the correlation speckle fringe patterns can be improved significantly. We tested the proposed methods on computer-simulated speckle correlation fringes and experimentally obtained fringes, and we compared the new method with other contrast enhancement techniques. The experimental results illustrate the performance of this approach.     

Two improved algorithms with which to obtain contoured windows for fringe patterns generated by electronic speckle-pattern interferometry

Fringe patterns generated by electronic speckle-pattern interferometry are full of high-spatial-frequency and high-contrast speckle noise. Filtering with contoured windows has proved to be an efficient approach to filtering out speckle noise while retaining the fringe patterns. Furthermore, with contoured windows the contoured correlation fringe pattern method can be used to derive smooth, normalized, consistent fringes. Contoured windows previously were determined by fringe orientation only, and this process generated accumulated errors. We propose two new algorithms with which to obtain the contoured windows according to the fringe intensity slope and the distance ratio to neighboring skeletons. These new techniques can determine contoured windows more precisely.     

Effective reduction of the novel look-up table memory size based on a relationship between the pixel pitch and reconstruction distance of a computer-generated hologram

In this paper, we propose an approach, new to our knowledge, to effectively generate and reconstruct the resolution-enhanced computer-generated hologram (CGH) of three-dimensional (3-D) objects with a significantly reduced in memory size novel look-up table (N-LUT) by taking into account a relationship between the pixel pitch and reconstruction distance of the hologram pattern. In the proposed method, a CGH pattern composed of shifted versions of the principal fringe patterns (PFPs) with a short pixel pitch can be reconstructed just by using the CGH generated with a much longer pixel pitch by controlling the hologram reconstruction distance. Accordingly, the corresponding N-LUT memory size required for resolution-enhanced hologram patterns can be significantly reduced in the proposed method. To confirm the feasibility of the proposed method, experiments are carried out and the results are discussed.     

双频光栅用于动态过程破裂表面的三维重建

针对在冲击炮轰等快变化过程的傅里叶变换轮廓术测量中,CCD的拍摄速度低于物体的运动速度导致对动态条纹的时间采样不足,提出了采用双频正弦光栅进行测量的三维轮廓术,以傅里叶轮廓术为基础,利用低频光栅条纹图的截断相位做标记条纹,跟踪锁定高频光栅条纹图的同一级次条纹,利用高频光栅的变形条纹进行动态破裂物体的三维面形重建,有效的解决了在快变化动态过程的三维测量中因时间采样不足和条纹断裂带来的问题,正确的获得了物体的面形分布.计算机模拟实验和对瓷砖破裂过程的实际测量验证了此种方法的正确性.     

Flexible three-dimensional measurement technique based on a digital light processing projector

A new method of 3D measurement based on a digital light processing (DLP) projector is presented. The projection model of the DLP projector is analyzed, and the relationship between the fringe patterns of the DLP and the fringe strips projected into the 3D space is proposed. Then the 3D shape of the object can be obtained by this relationship. Meanwhile a calibration method for this model is presented. Using this calibration method, parameters of the model can be obtained by a calibration plate, and there is no requirement for the plate to move precisely. This new 3D shape measurement method does not require any restrictions as that in the classical methods. The camera and projector can be put in an arbitrary position, and it is unnecessary to arrange the system layout in parallel, vertical, or other stringent geometry conditions. The experiments show that this method is flexible and is easy to carry out. The system calibration can be finished quickly, and the system is applicable to many shape measurement tasks.     

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.     

Discuss the structure condition and sampling condition of wavelet transform profilometry

The structure condition and sampling condition of a wavelet transform profilometry are deduced in this paper and an exhaustive discussion is accomplished. As we all know, by the wavelet transform profilometry, the shape of an object can be obtained by a correlation operation, which provides an approach to retrieve the phase when to some extent there is frequency overlapping between the fundamental spectrum and other spectra. However, it is impossible to obtain the correct phase if the wavelet coefficient at the ‘ridge’ position is not correct. Therefore, it is necessary to discuss the measurement range of the wavelet transform profilometry. Here, from the point of view of the frequency analysis, the discussions, including the structure condition of the measurement system and the sampling condition introduced by digitizing the deformed fringe, have to be done. The conclusion shows that as long as both of the two conditions are met, the correct phase included in the deformed fringe pattern can be retrieved by this method. The computer simulations and experiments verify our analysis.     

Virtually calibrated projection moire interferometry

Projection moire interferometry (PMI) is an out-of-plane displacement measurement technique that consists of differencing reference and deformed images of a grid pattern projected onto the test object. In conventional PMI, a tedious process of computing the fringe sensitivity coefficient (FSC), which requires moving the test object or the reference plane to known displacements, is used. We present a new technique for computing the FSC values that is called virtually calibrated projection moire interferometry (VCPMI). VCPMI is based on computer simulations of the conventional PMI process and does not require moving the actual test object or reference plane. We validate the VCPMI approach by comparing results for a flat plate and an airfoil with those made by use of other measurement methods.     

Control of phase of fringes in speckle interferometry for application of fringe scanning method

The speckle interferometry is an effective technique in the displacement measurement of a structure with a rough surface. However, when the fringe scanning technique is introduced to speckle interferometry for improving the measurement resolution, generally two speckle patterns before and after the deformation of the measurement object and another speckle pattern obtained under different conditions from these two speckle patterns are required at least. So, three speckle patterns are generally required for precise fringe analysis as a minimum condition. In this paper, a method for introducing the fringe scanning method is proposed by controlling the phase of the specklegram as a fringe image using filtering techniques. Then, the temporal fringe analysis method that uses only two speckle patterns are proposed for speckle interferometry. As the result of experiments, it is shown that high precise fringe analysis can be realized by the fringe scanning methods using only two speckle patterns for the displacement measurement with a large deformation.     

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.