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.     

Photogrammetric endoscope for measurement of inner cylindrical surfaces using fringe projection

We present a photogrammetric endoscope to measure three dimensional (3D) shapes of inner cylindrical surfaces by fringe projection. The basic configuration includes two identical cameras aligned with the optical axis and facing each other, conical lenses, and a 360 degrees helical fringe projector. The helical fringe pattern is phase shifted and acquired by both cameras. The phase patterns are used to acquire data from the surface in a regular cylindrical mesh. A prototype was built, calibrated, and tested. We present the results and an application to inspect internal welding seams and misalignment of welded joints in 150 mm (6 in.) diameter pipelines.     

Multiperiod fringe projection interferometry using a backpropagation method for surface profile measurement

Interference fringes with different periods are projected on an object surface. There is a constant phase point where the phase of the fringe is kept at a constant value while the period is scanning. Multiple optical fields with different periods on the object surface are made from detected phases of the fringes. The multiple optical fields are backpropagated to the constant phase point of the phase where all of the phases of the multiple backpropagated fields become the same value and the amplitude of the sum of the multiple backpropagated fields becomes maximum. The distance of the backpropagation provides the position of the object surface. Some experiments show that this method can measure an object surface with discontinuities of several millimeters with high accuracy of several micrometers.     

基于三次插值坐标变换的反向条纹投影技术

反向条纹投影技术是一种应用于在线或批量检测的快速而稳定的光学三维面形检测技术。本文提出了一种利用分片二元三次多项式插值来确定摄像机和投影器坐标变换关系的方法,它通过在摄像机10个像素点区域内拟和两个二元三次多项式,来求得该区域内投影器像素点对应的摄像机坐标值。计算机模拟和实物的对比实验表明,该方法能有效地提高反向条纹投影的精度。     

光学三维测量中结构光栅投影系统的开发

为解决结构光三维测量系统中的光栅投影质量问题,提出并实现了以物理光栅为核心的结构光栅投影系统。该系统以现代光栅制造技术制造的精密光栅元件为核心,基于幻灯投影原理实现高质量的光栅条纹投影,利用步进电机带动高精密滚轴丝杆进行平移实现投影光栅的切换。实验结果表明,基于该系统实现的光学三维测量系统的可以达到1：100以上的对比度,具有较大的光强和良好的景深,同时能获得连续的强度分布及较好的正弦性,测量误差小于0．04mm,测量精度约为0．03mm,满足工业应用的要求。     

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.     

High-resolution two-dimensional angle measurement technique based on fringe analysis

A novel angle-measurement technique based on fringe analysis for phase-measuring profilometry is proposed. A two-dimensional (2-D) angle between two mirror surfaces is determined by least-squares fitting of a plane to the 2-D distribution of the phase difference introduced by the 2-D tilt angle. To evaluate the performance of the proposed technique, numerical simulations that use the Fourier-transform technique and the phase-shift technique for fringe analysis were performed, and the results are compared. A 2-D angle-measurement interferometer based on a Mirau interference microscope was developed that demonstrated the validity of the proposed principle. It is shown by simulation and experiment that the proposed 2-D angle-measurement technique can achieve both a wide measurement range and a high angular resolution simultaneously.     

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.     

Blind color isolation for color-channel-based fringe pattern profilometry using digital projection

We present an algorithm for estimating the color demixing matrix based on the color fringe patterns captured from the reference plane or the surface of the object. The advantage of this algorithm is that it is a blind approach to calculating the demixing matrix in the sense that no extra images are required for color calibration before performing profile measurement. Simulation and experimental results convince us that the proposed algorithm can significantly reduce the influence of the color cross talk and at the same time improve the measurement accuracy of the color-channel-based phase-shifting profilometry.     

Optimal intensity-modulation projection technique for three-dimensional shape measurement

A new pattern projection technique for measuring three-dimensional topography is presented, called the optimal intensity-modulation projection technique. The proposed technique dramatically shortens the measurement time and improves stripe detection accuracy compared with previous methods. Furthermore, the method deals reliably with discontinuous patterns and multiple objects.     

Optical roughness measurements with fringe projection

The characterization of roughness of engineering surfaces over an area is an important task for different applications as well as for manufacturing processes. The surface roughness is in particular an important factor in determining the performance of a workpiece. We demonstrate that the fringe projection technique allows very fast three-dimensional surface inspections. The inspection time for an entire measurement is reduced to less than 5 s with standard hardware. Based on a zoom stereo microscope setup, we demonstrate a modular measuring instrument. The magnification-dependent vertical resolution can be as high as 0.1 microm. The special properties for roughness measurements are demonstrated, especially the comparability with a tactile sensor and with other optical sensors, which is discussed in connection with amplitude parameters.     

神经网络获取三维面形研究

针对基于传统三角原理的结构光三维测量方法难以测量阶梯形物体的问题，应用神经网络对获取的变形条纹进行处理，获取物体的三维面形信息。该方法通过对神经网络的训练，直接建立条纹图分布与物体高度之间的对应关系，完成对物体的三维测量，即使在投影系统参数未知的情况下，也能取得较好的结果。论文中提出的神经网络三维面形测量方法测量时间短，测量过程中只需要一幅条纹图就能恢复阶梯物体的高度信息。计算机模拟及试验验证了方法的可行性。     

A fast 3D shape measurement method based on sinusoidal and triangular fringe projection

Existing methods to measure 3D shape of complex object involve processing more than six captured images to obtain the absolute phase, which limit the measurement speed. This paper presents two sinusoidal fringes and two triangular wave fringes which is used to measure 3D shape of complex object. The two-step phase-shifting sinusoidal fringes and two-step phase-shifting triangular wave fringes are calculated to obtain the wrapped phase, and then the two-step phase-shifting triangular wave fringes are used to determine the fringe order. Due to decrease the number of projection fringes, the speed of measurement increases. The triangular wave fringe carries more information of the object than linear increasing/decreasing ramp fringe in the actual measurement, more noise in the base phase to be overcome, thus improving the measurement accuracy. The benefits can be widely applied in high-speed, real-time 3D measurement of complex shape. Experimental results have demonstrated that the proposed method is simple, but effective.     

Phase error correction for fringe projection profilometry by using constrained cubic spline

In fringe projection profilometry, the nonlinear intensity response caused by the c effect of a digital projector results in periodic phase error and therefore measurement error. Previous error correction methods are largely based on the calibration of single c value. However, in practice, it is difficult to accurately model the full range of the intensity response with a one-parameter c function. In this paper, a compensated intensity response curve is generated and fitted with the constrained cubic spline. With the compensated curve, the full range of the nonlinear intensity response can be corrected and the periodic phase errors can be removed significantly. Experimental results on a flat board confirm the average root mean square (RMS) of the phase error which can be reduced to at least 0.0049 rad.     

虚拟光栅变频投影三维测量技术的研究

虚拟光栅变频投影三维测量技术采用多光束干涉条纹形成虚拟余弦光栅,将虚拟余弦光栅投影到被测物体上得到被物体形貌调制的变形虚拟光栅。通过调整多光束干涉的楔角改变虚拟光栅频率,将两幅不同频率的变形虚拟光栅经过光学接收系统成像在CCD像机上,对CCD像机记录的变频变形光栅图像进行综合处理从而获取被测物体的三位形貌。本文给出了这种测量技术的原理,实验结果表明,采用变频虚拟光栅投影三维形貌测量技术可以有效地解决三维测量中被测物体高度变化率过大引起相位展开困难的问题。     

Gamma correction for digital fringe projection profilometry

Digital fringe projection profilometry utilizes a digital video projector as a structured light source and thus gains great flexibility. However, the gamma nonlinearity of the video projector inevitably decreases the accuracy and resolution of the measurement. We propose a gamma-correction technique based on statistical analysis of the fringe images. The technique allows one to estimate the value of gamma from the normalized cumulative histogram of the fringe images. By iterating the two steps, gamma estimation and phase evaluation, the actual gamma value can be calculated. At the same time the phase distribution of the fringe pattern can be solved with higher accuracy. In so doing, neither photometric calibration nor knowledge of the device is required. Both computer simulation and experiment are carried out to demonstrate the validity of this technique.     

Microshape and rough-surface analysis by fringe projection

A fringe-projection system for microscopic applications, fringe-projecting microscopy, is developed and analyzed. Projection of the grating and imaging of the fringe system, modulated by the surface, are accomplished by the same high-aperture objective. The spectrum of the grating is spatially filtered and projected into the aperture with a lateral shift, which leads to a telecentric projection under oblique incidence and telecentric imaging. Topographies of specularly as well as diffusely reflecting surfaces can be obtained. The measurement of highly rough surfaces is described together with preprocessing steps. The resulting intensity distribution of the fringes is analyzed. Formulas for vertical and lateral resolution, measuring range, and dynamic range, based on noise considerations, are presented and verified by topographies of technical surfaces.     

Effective bias removal for fringe projection profilometry using the dual-tree complex wavelet transform

When reconstructing the three-dimensional (3D) object height profile using the fringe projection profilometry (FPP) technique, the light intensity reflected from the object surface can yield abruptly changing bias in the captured fringe image, which leads to severe reconstruction error. The traditional approach tries to remove the bias by suppressing the zero spectrum of the fringe image. It is based on the assumption that the aliasing between the frequency spectrum of the bias, which is around the zero frequency, and the frequency spectrum of the fringe is negligible. This, however, is not the case in practice. In this paper, we propose a novel (to our knowledge) technique to eliminate the bias in the fringe image using the dual-tree complex wavelet transform (DT-CWT). The new approach successfully identifies the features of bias, fringe, and noise in the DT-CWT domain, which allows the bias to be effectively extracted from a noisy fringe image. Experimental results show that the proposed algorithm is superior to the traditional methods and facilitates accurate reconstruction of objects' 3D models.