A novel three-dimensional shape measurement method based on a look-up table

Fringe projection profilometry is widely used for three-dimensional shape measurement. In an oblique-angle projection, the fringe cycle is broadened on the reference plane. Phase errors are mainly caused by the nonlinear gamma of the projector and fringe cycle broadening. This study describes a phase error compensation method to eliminate these phase errors. A look-up table that stores phase errors is constructed for phase error compensation. Based on it, a new height equation is proposed. The experimental results show that the proposed method can compensate for the phase errors of the fringe projection profilometry, thereby improving the measurement accuracy significantly.     

数字条纹投射技术中改进的非线性校正方法

在数字条纹投射技术中,系统的非线性是影响投射条纹质量的主要因素,其直接导致变形条纹中出现高次谐波,从而影响系统的测量精度。提出了一种系统非线性校正的新方法,利用N阶多项式拟合代替传统的单一伽马参数表示系统的非线性关系,并依据条纹图像累积直方图匹配方法,通过迭代操作同时求得系统非线性关系和较高精度的物体位相分布。计算机模拟及实验结果表明,该方法能够有效地抑制系统非线性的影响,获得理想的物体位相分布,从而验证了该方法的可行性。     

A novel 3D measuring method for discontinuous object by non-integral twin-frequency grating

A new 3D shape measurement method based on non-integral twin-frequency grating projection is proposed. In this paper, the projected composite grating is composed of two sinusoidal gratings, and the quotient of whose frequencies is not an integer. By using appropriate phase-shifting algorithms, two wrapped phases can be obtained from sixteen frames of the distorted grating patterns. In aid of appropriate phase unwrapping method, the unwrapped phase of high frequency fringe is obtained only from the relation of the two wrapped phases by a pixel-to-pixel phase unwrapping technique. Therefore the unwrapped phase of high frequency fringe pattern is independent of the low frequency fringe pattern, different from traditional integral twin-frequency grating projection methods in which the phase unwrapping error of low frequency fringe pattern may be propagated onto the unwrapped phase of high frequency fringe pattern. The new theory proves that the proposed method is applicable to measure discontinuous object, and has considerable measurement accuracy.     

傅里叶变换轮廓术中相位失真的预矫正方法

介绍了一种基于傅里叶变换轮廓术的三维面形测量系统中相位失真的预矫正方法。由于投影系统和成像系统的空间三角位置关系、投影仪的发散照明和两套系统蕴含的光学畸变,投影一幅相位与空间坐标成理想线性关系的标准正弦光场,拍摄到的条纹相位和空间坐标不再呈线性分布,引起相位失真,甚至会影响系统测量精度。该方法借鉴反向条纹投影的思想,计算拍摄光场的非线性相位分布与理想的线性相位分布之间的关系,预先矫正,反算出一个新的待投影光场。实验结果表明这种方法能有效地减小该类相位失真所导致的测量误差,获得了更好的测量结果．     

Background and amplitude encoded fringe patterns for 3D surface-shape measurement

This paper presents a new fringe projection method for surface-shape measurement that uses background and amplitude encoded high-frequency fringe patterns. The background and amplitude, combined as a codeword, identify the wrapped phase fringe order to partially unwrap the phase to a low frequency. The low-frequency wrapped phase map is then directly used to reconstruct the surface based on geometry constraints without requiring additional images as in other temporal phase-unwrapping methods. Measurements performed on a double-hemisphere, mask, and manikin head, using projected fringe patterns with 48 periods, demonstrated the ability of the method to perform 3D shape measurement with only four projected patterns and captured images, using a single camera and projector.     

Simple calibration of a phase-based 3D imaging system based on uneven fringe projection

Phase-based fringe projection metrology systems have been widely used to obtain the shape of 3D objects. One vital step is calibration, which defines the relationship between the phase and depth data. Existing calibration methods are complicated because of the dependence of the relationship on the pixel position. In this Letter, a simple calibration procedure is introduced based on an uneven fringe projection technique, in which the relationship between phase and depth becomes independent of the pixel position and can be represented by a single polynomial function for all pixels. Therefore, given a set of discrete points with a known phase and depth in the measuring volume, the coefficient set of the polynomial function can be determined. A white plate having discrete markers with known separation is used to calibrate the 3D imaging system. Experimental results demonstrate that the proposed calibration method is simple to apply and can build up an accurate relationship between phase and depth data.     

基于自适应条纹投影的高反光物体三维面形测量

结构光投影方法在三维形貌测量中应用广泛,但是由于被测物体表面反射率变化范围较大,过度曝光会导致相位信息无法获取。而传统的高动态范围扫描技术步骤复杂,耗时较长。文中提出一种自适应条纹投影技术,向待测物体表面投射较高灰度级的条纹图,判断并标记过度曝光点。降低投射强度后通过非线性最小二乘法拟合来确定每个饱和像素点最适合的最大输入灰度,用重新生成的自适应条纹图来采集图像并进行相位计算和三维形貌恢复。通过实验验证,该方法可以对物体表面的高反光区域进行有效测量,避免过度饱和,仿真误差在0.02 mm范围内,实测误差约为0.14 mm,实际实验对过曝点的补偿率可达到99%。     

基于正弦和三角波条纹投影的三维测量方法

在现有的针对复杂物体表面形貌的三维测量方法中, 为了完成绝对相位的测量, 通常需要处理至少6幅条纹图像, 限制了测量速度。提出了采用2幅正弦条纹和2幅三角波条纹图来获得物体三维形貌的方法。利用两步相移正弦条纹和两步相移三角条纹得到截断相位, 再利用两步相移三角波条纹得到条纹级次, 减少了投影条纹幅数, 提高测量速度。在得到条纹级次时, 计算三角波条纹强度调制和强度对比度, 与计算相位相比, 可以减少数据处理的时间, 进一步提高测量速度, 同时能减小物体表面反射率的影响, 提高了测量精度。测量最大高度为39 mm的阶梯状标准块, 得到的最大绝对误差和最大的RMS误差分别为0.045 mm和0.041 mm。验证了该方法的有效性和实用性, 在高速实时的复杂形貌三维测量中有广泛的应用前景。     

基于彩色光栅投影的快速三维测量方法

 针对条纹投影术提取物体高度信息的问题,提出了一种新的基于彩色光栅投影的三维测量方法。对选取G分量为255,R,B分量各取0或255而组成的青、白、黄、绿四色遵循格雷码原理进行编码,然后将G分量作正弦调制形成投影光栅投向被测物体。提取采集到的光栅变形图中G分量,利用傅里叶变换方法得到其初始相位;同时对采集到图像中的R,B分量作阈值迭代分割而G分量自动赋值为255,综合三分量信息得到条纹颜色信息进而获取条纹的周期信息,从而展开相位。全过程仅需投影一幅彩色光栅图就能完成三维测量,实验结果表明该算法易于实现,在测量实时性和精确性上表现良好。     

两步相移实现投影栅相位测量轮廓术

提出一种新的投影栅相位测量方法--两步相移法。该方法只需两幅相移条纹图，因此计算量小，速度快。给出了实验及计算结果，并同四步相移法进行了比较，证明了该方法具有较高的精度。     

A study on carrier-removal techniques in fringe projection profilometry

This paper describes a comparison of several carrier-removal techniques normally used in fringe projection for surface shape measurement. The performance of various algorithms, including the necessity for manual intervention, the complexity in data recording, and the side effect on measurement accuracy, is evaluated. The applicability of nonlinear carrier removal and the restrictions on the direction of carrier fringe in various algorithms are also investigated in this paper. It is also shown that an advanced algorithm is able to achieve carrier removal with minimal manual intervention and significantly simplify the calibration process of a fringe projection system.     

单幅条纹图相位解调的小波分析方法

相位解调是条纹相位分析的关键问题.本文提出一种应用小波频率估计联合频率导数对变形条纹进行瞬时频率分析,从中提取参考基频,从而依靠单一变形条纹实现相位解调的方法.首先,理论上证明了当变形条纹瞬时频率空间导数等于零,该空间点的瞬时频率等于参考基频频率;其次,引入Gabor小波提取变形条纹的瞬时频率空间分布,利用变形条纹瞬时频率的空间导数分布识别提取参考基频,从而实现相位解调.利用该方法进行了三维形貌测量的实验,结果表明该方法在实现相位解调中效果良好.     

单幅条纹图相位解调的小波分析方法

相位解调是条纹相位分析的关键问题.本文提出一种应用小波频率估计联合频率导数对变形条纹进行瞬时频率分析,从中提取参考基频,从而依靠单一变形条纹实现相位解调的方法.首先,理论上证明了当变形条纹瞬时频率空间导数等于零,该空间点的瞬时频率等于参考基频频率;其次,引入Gabor小波提取变形条纹的瞬时频率空间分布,利用变形条纹瞬时频率的空间导数分布识别提取参考基频,从而实现相位解调.利用该方法进行了三维形貌测量的实验,结果表明该方法在实现相位解调中效果良好.     

基于二进制条纹加相位编码条纹离焦投影的三维测量方法

复杂表面的精密三维测量在工业无损检测中非常重要。二进制条纹离焦投影方法在快速三维测量中有重要的应用前景,但该方法难以实现复杂表面高精度三维测量。为此,提出了基于二进制条纹加相位编码条纹离焦投影的三维测量方法。由于离焦投影滤除了高次谐波和高频噪声,可以克服投影仪的非线性伽马效应,与传统投影正弦条纹方法相比,提高了其测量精度。针对离焦投影时,随着相位编码条纹频率增大,条纹级次判决困难,出现周期错位,导致相位解包裹出错,提出了相移编码方法来解决以上问题。采用相移编码方法校正周期错位,使条纹级次判决准确,进一步提高其测量精度。实验结果表明,其测量精度可以达到0.044 mm,验证了本方法的有效性和实用性。     

一种针对彩色物体的光栅投影三维测量方法

针对传统彩色编码光栅三维轮廓术中光栅易受到物体表面彩色纹理的干扰,从而造成编码条纹颜色误判和相位误差增大这一问题,提出一种基于互补彩色光栅的三维测量方法,给出了理论分析、光栅设计原理、补偿算法与实验分析。对图像进行初步的解耦校正后,通过预先设计的光栅互补特性,依据彩色响应模型求取物体表面逐点的反射率,并对红绿蓝(RGB)三通道反射率的不平衡进行补偿,消除物体表面彩色纹理的干扰,改善光栅的正弦性。以补偿后的图像来指导彩色编码条纹的分割解码并用傅里叶变换法提取出包裹相位,依据解码结果指导相位展开,继而完成整个三维测量过程。实验证明该方法对彩色纹理的补偿准确有效,降低了彩色纹理对测量的影响。     

单幅彩色条纹投影的不连续物体表面三维形貌测量

提出了基于单幅彩色条纹投影的不连续物体及动态三维形貌的测量方法。该方法利用计算机产生一幅正弦条纹图和两幅单一强度图分别通过红蓝绿三个通道合成为一幅彩色条纹图,由液晶投影仪投影到被测物体表面,彩色CCD采集变形条纹图并保存在计算机中。通过三色分离,同时获得正弦条纹图和反映表面反射率分布及背景信息图,通过图像除法运算及亚像素精度归一化处理实现物体三维形貌的恢复。对于表面形貌不连续的物体,利用蓝色分量的灰度图像进行二值化处理定位阴影或暗背景,从而引导正确的相位求解。实验验证了该方法对不连续物体动态测量方面的可行性。     

Deformation and profile measurement using the digital projection grating method

This paper presents a digital projection grating method for full field measurement of out-of-plane deformation and shape of an object. Two grating patterns on an object before and after deformation are captured by a CCD camera and stored in a computer. With the aid of Fast Fourier Transform (FFT) and signal demodulating techniques, a wrapped phase map is generated. The phases are expanded in the range of 0–2π and compared with the resulting moiré pattern. An unwrapping procedure is used to obtain a continuous phase. In addition, a digital method for fractional fringe multiplication is also developed. Results on deformation and object profile measurements are presented.     

3D shape measurement of larger complex objects based on fringe cycle correction

The grating fringe on the reference plane is broadened in the intersecting axis system because of oblique-angle projection. In order to solve this problem, we study the theoretical model of the temporal phase unwrapping method based on the fringe cycle correction. We also study the 3D shape measurement theoretical model of the larger complex objects after considering the coordinate deviation and lens distortion. Experimental results demonstrate that the fringe cycle on the reference plane can be corrected to a constant value, the lens distortion can be corrected, and 3D shape of larger complex objects can be accurately measured.     

Period correction method for binary fringe defocused projection

Binary fringe defocused projection can resolve the problem caused by the nonlinear gamma of the projector. Owing to the intersecting axis measurement system, the broadening of the fringe period on the reference plane can cause measurement errors. Non-uniform periodical binary fringe defocused projection is utilized to overcome this problem. After appropriate defocused projection of non-uniform periodical binary fringe, uniform periodical sinusoidal fringe can be obtained on the reference plane. This method can prevent the nonlinear gamma effect and broadening of the fringe period, and filter high harmonics and high-frequency noise. Three-dimensional (3-D) shape measurement experiments of standard flat are performed with four-step phase-shift method. Experimental results demonstrate that the proposed method exhibits high measurement precision. Highly accurate 3-D measurements of large objects can also be performed with the proposed method.     

影响条纹图形拼接法测量精度的主要误差因素

通过对计算机模拟和实验结果的分析表明，影响条纹图形拼接法测量精度的主要因素是子孔径面形测量精度，重叠区的大小，面形拟合阶次和拼接模式等。