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.     

3-D Contouring of Diffuse Objects by Talbot-projected Fringes

Abstract

Talbot fringe projection, a moiré technique, is applied to three-dimensional contouring of diffuse targets for absolute shape measurement. The basic system relies on depth coding the test target surface by projecting the Talbot image of a linear grating. A second grating, similar to that used for the Talbot image, is employed to obtain the moiré fringes. These fringes represent surface contours of equal depth. Using a phase measurement technique and digital image processing algorithms, the surface shape information is obtained from the contour maps. Experimental results, merits and limitations of the system are discussed.     

Digital moiré fringe-scanning method for centering a circular fringe image

A digital moiré fringe-scanning method for centering a circular fringe image is proposed. The image of a nondiffracting beam, whose cross section is a circular fringe, is first downloaded onto a computer. The image is then superposed with a digital circular grating, whose center is close to the center of the image, to generate circular moiré fringes. Changing the phase of a digital grating can cause moiré fringe scanning. The global center of the image can be calculated by use of sets of the scanned picture. Because all the image data are used for the calculation, the effect of random noise on centering is greatly reduced and the center position resolution can reach the order of a subelement of a CCD. The measurement of spatial straightness is 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.     

相移条纹投影三维形貌测量技术综述

结构光三维形貌测量系统目前得到了越来越广泛的应用和研究,相移条纹投影三维形貌精密测量技术是其重要的发展方向。对结构光相移条纹投影三维形貌测量系统的应用发展、工作过程、不同系统构成方式、相移条纹的各种形式及特点、相位误差校正方法、不同相位解包裹算法及其优缺点和适用场合、测量系统数学模型的实现方法及其相应的优缺点、高动态范围测量技术等进行了详细的分析。对相移条纹投影系统的工作流程、实现方法、关键技术的发展及其存在问题等进行了比较全面的梳理,为三维形貌精密测量技术进一步满足先进制造中更高精度的要求指出了后续的研究方向。     

Three-dimensional shape measurement of large-aperture aspheric mirrors by off-axis null Ronchi test

An off-axis null Ronchi test is presented to measure the three-dimensional (3D) shape of a large-aperture aspheric mirror. The method designs curved fringe patterns as null sinusoidal gratings by means of phase information and ray tracing. In the process of measurement, the curved fringe patterns are displayed on a transmission-type liquid crystal display (T-LCD) screen, and a CCD camera records the fringe patterns containing the information of deviations of the mirror. The slopes of the deviations of the mirror are obtained by using the recorded fringe patterns. The deviations are restored by integrating, and then the 3D shape of the mirror can be reconstructed. Compared with the classical null Ronchi test, the method can provide enough measured data points and avoid the jagged edges of bands on the null gratings. Moreover, the method can conveniently change period and direction of the curved fringes and accurately control phase shifting. Computer simulations and a preliminary experiment are presented to show the performance of the method.     

大量程纳米级光栅干涉位移测量

针对传统光栅干涉仪中测量范围和分辨率难以同时提高的问题,提出利用单根大长度、低线数光栅实现大量程、高分辨率位移测量的方法.首先利用长度400mm,栅距10μm计量光栅的±5级衍射光生成条纹图,实现了条纹的10倍光学细分.然后提出一种基于傅里叶变换时移特性的条纹细分新方法,利用相邻两帧条纹图同一位置处相位的变化实现了高达1000倍的条纹电子细分.在此过程中,针对能量泄漏对傅里叶变换法相位提取精度的影响,提出条纹图整周期裁剪的方法,使条纹细分精度至少可达到1/1000条纹周期.仿真和实验结果表明,系统具有纳米级的分辨率和优于10nm的测量精度.     

相位扫描法制作变栅距光栅

提出了一种制作变栅距(VLS)光栅的相位扫描方法。该方法的主要装置包括一个用于控制刻划机运动的光栅干涉仪和一个相位扫描机构。如果调整光栅干涉仪,保证接收场中只有两条干涉条纹,然后改变用于对条纹进行计数的光电传感器的位置,就可以刻划出具有变栅距的刻槽。对光电式光栅刻划机的控制系统和结构都做了详细论述。按照上述方法成功刻划出了试验性的VLS光栅,它的最小栅距增量为0.33nm,并对在制作过程中产生的误差进行了讨论。采用测量衍射角的方法进行了栅距检测试验,由变栅距光栅和等栅距光栅作出的拟合曲线表明:相位扫描方法是加工具有亚纳米栅距增量的VLS光栅的有效方法,该方法对超精密定位也具有借鉴作用。     

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.     

Vibration-compensated interferometry system using phase-modulating interference fringe subdivision technology

An innovative vibration-compensation method, with phase-modulating interference fringe subdivision technology, is described. It simulates fringe movement by the phase difference of signals and can detect the fringe movement with an accuracy of 1/400 fringe spacing using this subdivision technology. A closed-loop vibration-compensation system is built, and the measurement of an interference fringe movement and a vibration-compensation test are successfully demonstrated. Because of this new method and a new feedback algorithm that was introduced, interference fringes can be stabilized at any preset phase position in real time. Compared with known methods, this method is simple and inexpensive, as well as effective.     

Intensity-modulated moiré topography

Moiré topography has the advantage of requiring only a single image to obtain a three-dimensional measurement, but it cannot discern the fringe order. Because there is an ambiguity problem when calculating the depth range by use of fringe intensity or phase unwrapping, it is impossible to obtain an absolute phase and an absolute depth range. It is therefore difficult to discern the relation between fringes in the cases in which the fringes are discontinuous or the objects are isolated. An intensity-modulated moiré topography method is presented. By modulation of the transmission factors of the projection and the observation gratings by exponential functions a new moiré pattern whose fringe intensity changes with its order can be produced. The fringe order can be extracted easily from the fringe intensity, and the absolute range of the skeleton line can be obtained solely from its intensity. At the same time, we can segment the moiré pattern by its fringe order. For every segment the absolute phase and the absolute depth range of every point of the moiré pattern can be obtained solely from its intensity with no need for interaction with the user.     

一种改进的基于条纹对比度的三维测量方法

基于条纹对比度的三维测量方法由于具有垂直测量的特点,可用于测量表面有突变的复杂物体的三维信息.本文在现有方法的基础上,提出了一种改进的基于条纹对比度的三维测量方法.该方法利用投影仪将一组相移的正弦条纹依次投射在被测物体上,并使被测物体位于投影仪成像面的前方,CCD相机通过一个半透半反镜从投影方向获取物体表面的条纹图像,...     

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.     

Dependence of fringe spacing on the grating separation in a long-period fiber grating pair

The spectral spacing of the interference fringes formed by a pair of long-period fiber gratings was investigated. The variation of the fringe spacing was measured while the separation between the gratings was changed from 22 to 500 mm. When the grating separation was much longer than the length of the individual grating, the inverse of the fringe spacing became linearly proportional to the grating separation and to the differential effective group index of the fiber. In the third stop band of the grating pair, made along a dispersion-shifted fiber centered at 1.55 mum, the differential effective group index was calculated to be ~6.4 x 10(-3), which is approximately twice the differential effective index of the fiber. The discrepancy between the two indices was observed to decrease with the band order, a phenomenon that is explained by the first-order dispersion of the fiber. The measured interference fringes were not regularly spaced in the frequency domain, but regular spacing is required in wavelength-division multiplexing communication systems. Analysis of the second-order dispersion of the fiber and the grating-induced nonlinear phase shift within grating regions as the factors that induce chirping on the fringe spacing is presented.     

Uneven fringe projection for efficient calibration in high-resolution 3D shape metrology

A novel uneven fringe projection technique is presented whereby nonuniformly spaced fringes are generated at a digital video projector to give evenly spaced fringes in the measurement volume. The proposed technique simplifies the relation between the measured phase and the object's depth independent of pixel position. This method needs just one coefficient set for calibration and depth calculation. With uneven fringe projection the shape data are referenced to a virtual plane instead of a physical reference plane, so an improved measurement with lower uncertainty is achieved. Further, the method can be combined with a radial lens distortion model. The theoretical foundation of the method is presented and experimentally validated to demonstrate the advantages of the uneven fringe projection approach compared with existing methods. Measurement results on a National Physical Laboratory (UK) "step standard" confirm the measurement uncertainty using the proposed method.     

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.     

两种莫尔条纹信号对光栅系统测量精度的影响

对两种莫尔条纹（光闸条纹和横向条纹）信号的谐波含量以及它们对光栅系统测量精度的影响进行了分析，并用实测数据加以比较，指出在光栅系统中，取横向莫尔条纹信号的谐波量小，正弦性好，细分误差小，在其它参数相同的情况下，可提高系统的测量精度2倍左右。     

Measurement of focal length with phase-shifting Talbot interferometry

Phase-shifting interferometry with a Fourier fringe analysis technique is implemented to analyze Talbot interferometric fringes and to evaluate the focal length of a lens. A four-step algorithm is used to obtain the phase map of the lens. The slope of the phase map is related to the focal length, and it is from this relationship that we evaluate the focal length. Experimental results are presented. Our experimental study suggests that phase-shifting Talbot interferometry combined with a Fourier fringe analysis technique can be advantageously used to improve the accuracy of measurement.