Blind phase error suppression for color-encoded digital fringe projection profilometry

Color-encoded digital fringe projection profilometry (CDFPP) has the advantage of fast speed, non-contact and full-field testing. It is one of the most important dynamic three-dimensional (3D) profile measurement techniques. However, due to factors such as color cross-talk and gamma distortion of electro-optical devices, phase errors arise when conventional phase-shifting algorithms with fixed phase shift values are utilized to retrieve phases. In this paper, a simple and effective blind phase error suppression approach based on isotropic n-dimensional fringe pattern normalization (INFPN) and carrier squeezing interferometry (CSI) is proposed. It does not require pre-calibration for the gamma and color-coupling coefficients or the phase shift values. Simulation and experimental works show that our proposed approach is able to effectively suppress phase errors and achieve accurate measurement results in CDFPP.     

Multi-frequency inverse-phase fringe projection profilometry for nonlinear phase error compensation

A new multi-frequency inverse-phase method was proposed to compensate for nonlinear phase errors in fringe projection profilometry and to measure the three-dimensional shape of discontinuous objects. After introducing a phase offset of π/4 into the multi-frequency four-step phase-shifting method the corresponding nonlinear phase error reversed its sign, which allowed the addition of unwrapped phases before and after the phase-offset operation to compensate for the error. For the four-step phase-shifting method, simulation analysis showed that the nonlinear phase error had quadrupled the fringe frequency. Moreover, experimental results verified the feasibility and applicability of the proposed method.     

傅里叶变换轮廓术中频谱泄漏的讨论

讨论了频谱泄漏对傅里叶变换轮廓术测量精度的影响。由于用傅里叶变换轮廓术进行三维面形测量时 ,测得的变形光场是空间有限函数 ,故离散傅里叶变换时先要进行周期拓展 ,如果拓展周期选择不当 ,拓展后的条纹将不连续 ,对之进行傅里叶变换会产生频谱泄漏。文章从理论上推导了拓展周期与变形结构光场频谱泄漏之间的关系 ,给出了由泄漏引起的视场边缘误差的计算模型和定量分析。提出采用条纹外插以减小泄漏误差的方法 ,计算机模拟及初步实验证实了该方法的有效性。     

Least-squares calibration method for fringe projection profilometry with some practical considerations

Fringe projection profilometry (FPP) is a widely used three-dimensional profile measurement technique. One vital step in this technique is calibration, which determines the system accuracy. The least-squares method, because of its flexibility and simplicity, is commonly used in system calibration for FPP. However, calibration results are affected by the nonlinear gamma of the projector and projection fringe cycle broadening. This paper proposes a new look-up table (LUT) generation method by analyzing the differences between the real and ideal unwrapped phases. The aforementioned problems could then be solved after the phase error is compensated by the LUT. Finally, the validity of the proposed method is demonstrated through experiments, and the accuracy reaches 0.02 mm.     

The fluctuating phase error analysis in the digital grating phase-shifting profilometry

The nonlinear response of the experimental system and the saturation of fringe patterns can induce the fluctuating phase error in the projection grating phase-shifting profilometry. Two major factors of the fluctuating phase error are discussed by simulation. The fluctuating phase error caused by the nonlinear response of the system is four times the frequency of the fringe pattern when the conventional four-frame phase extracting algorithm is used. However, such error can be decreased by five-frame algorithm. On the other hand, the fluctuating phase error caused by the fringe saturation is five times the frequency of the fringe pattern by using conventional five-frame phase extracting algorithm. A novel phase recovering algorithm is used to decrease the phase error caused by the saturation. Furthermore, the applicability range of the proposed phase recovering algorithm is analyzed by simulation and experiments with different saturation degree of the fringe pattern and nonlinearity of the measurement system.     

关于提高傅里叶变换轮廓术测量精度的研究

针对傅里叶变换轮廓术在实际测量中容易受到光学成像系统和计算方法的影响而使得测量结果不精确的现象,提出基于最小二乘法的条纹图像预处理技术,并讨论了滤波器的设计、相位展开的方法及系统标定模型对测量结果的影响。实验表明,改进后的方法其测量误差在2%以内。     

改进的次条纹积分相位分析技术

条纹花样的单帧相位解调算法在实时、动态测量技术中具有广泛应用。次条纹积分算法具有较高抗噪能力,但其采用载频近似估算形变条纹周期时存在频率失配的固有缺陷,提出一种改进的次条纹积分算法,对条纹的局域频率进行探测,利用局域频率进行次条纹积分,然后再计算相位。模拟实验表明,改进算法的最大误差约为原算法的1/3,并通过条纹投影轮廓术实验进一步证明了改进算法的有效性,为单帧条纹相位分析技术提供了一种可供选择的新算法。     

Shifted-phase calibration for a 3-D shape measurement system based on orthogonal composite grating projection

This paper proposes a novel method for reducing measurement error caused by spectrum overlapping in orthogonal-composite-grating-based 3-D measurement method. For 3-D measurement systems based on orthogonal composite grating projection, spectrum overlapping causes phase of each deformed phase-shifting fringe changed differently, which violates the principle that the shifted phases between adjacent deformed fringes must be equivalent to 2π/3, and therefore results in phase measurement error. The proposed shifted-phase calibration method is based on that phase variation of each deformed fringe is independent of height and reflectivity of the measured object. Three composite gratings are projected on the reference plane, and each carrier channel includes three phase-shifting gratings needed in phase measuring profilometry (PMP). Because the adjacent phase-shifting fringes demodulated from the same carrier channel have the phase difference of 2π/3, we can respectively calculate the reference plane's phases of three carrier channels by the phase algorithm of PMP method, and the shifted phases between them are obtained. When an object is measured, the shifted phases between deformed phase-shifting fringes can be calibrated. A new 3-D measurement mathematical model is set to reconstruct object. Our experiments prove that the proposed method can effectively restrain the effect of spectrum overlapping and improve measurement accuracy almost one times.     

基于梯形与正弦相移算法的非线性误差校正北大核心CSCD

相移轮廓术是一种广泛使用的光学三维测量方法,其精度不仅受相位展开算法本身的影响,也受测量系统中投影仪和摄像机的非线性影响。理论上,投射更多的相移条纹可减弱非线性误差的影响,但是增加了测量时间。为了提高误差校正的效率,提出了一种基于梯形正弦相移的测量方法。该方法需要两组改进的梯形相移条纹和一幅正弦条纹。梯形条纹提供图像强度信息和条纹级次信息,图像强度信息用来求取系统的非线性响应曲线,进一步消除系统的非线性。正弦条纹经过希尔伯特变换可求得额外的条纹图像,用来计算截断相位信息。经过校正的截断相位信息,可进一步获取精度较高的三维信息。相较于先前的梯形与正弦误差校正方法,该方法的测量效率提高了28%。     

基于傅里叶频谱分析的相位测量轮廓术系统Gamma非线性校正方法

数字投影和成像系统的Gamma非线性效应是导致相位测量轮廓术（PMP）测量误差的重要原因。目前大多采用多帧条纹图进行Gamma校正,使测量的实时性受到限制。提出了一种Gamma校正方法,利用正交光栅像的傅里叶频谱分布计算Gamma值,再根据此Gamma值对投影相移条纹进行Gamma逆变换,实现投影条纹输入值的提前校正,以获取具有良好正弦性的结构条纹,从而降低PMP相位测量误差。校正过程中只需一帧条纹图,而且考虑了测量系统的离焦效应。实验证实了该方法的有效性和正确性。     

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%。     

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。     

Optical measurement on dynamic buckling behavior of stiffened composite panels under in-plane shear

The buckling behavior and failure mode of a composite panel stiffened by I-shaped stringers under in-plane shear is studied using digital fringe projection profilometry. The basic principles of the dynamic phase-shifting technique, multi-frequency phase-unwrapping technique and inverse-phase technique for nonlinear error compensation are introduced. Multi-frequency fringe projection profilometry was used to monitor and measure the change in the morphology of a discontinuous surface of the stiffened composite panel during in-plane shearing. Meanwhile, the strain history of multiple points on the skin was obtained using strain rosettes. The buckling mode and deflection of the panel at different moments were analyzed and compared with those obtained using the finite element method. The experimental results validated the FEM analysis.     

Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry

The phase error and its periodic behavior caused by the partial intensity saturation of fringe patterns in the digital projection grating phase-shifting profilometry are studied. A saturation coefficient K is defined to describe the saturation degree of the fringe patterns projected on a measured object. The distribution of the phase error is analyzed through a simulation method. Moreover, a novel phase-recovering algorithm is studied to resolve the phase error issue introduced by the partial saturated fringe patterns. The real phase can be recovered by the unsaturated intensity values. A series of results corresponding to different degrees of saturation defined by K are given to prove the validity of the proposed algorithm.     

用于三维测量的快速相位解包裹算法

减少条纹投影轮廓术的条纹图数量一直是本领域的研究热点。传统的时间相位解包裹算法,一般需要额外的条纹信息来确定条纹级次,导致条纹图数量过多。提出一种用于三维测量的快速相位解包裹算法,只需要N步标准相移正弦条纹图,就可以完成绝对相位的计算。首先,利用标准相移算法计算包裹相位和消除背景的掩膜;然后,直接利用包裹相位和掩膜,根据连通域标记算法计算条纹级次,进而求得绝对相位。该方法最少只需3幅条纹图,就可以完成三维测量,数据处理速度快。计算机仿真和实验结果验证了该方法的有效性和鲁棒性。     

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。     

平行光波阵面调制下的双频干涉条纹形貌测量

传统形貌测量多采用光栅投影,其投影条纹的非正弦性及条纹密度的限制将影响形貌测量的精度,为了实现高密度正弦条纹投影的可调性,采用平行光干涉投影形成明亮且对比度高的正弦条纹,避免条纹的正弦畸变。在平行光波阵面调制下,通过相控阵调节两光束交会角度得到所需的条纹频率,实现条纹投影的可调性,再将调制后双频应用到解包裹中提高解相精度。对比分析了单频和双频解包裹条件下,一个最大高度为35.80 mm物体形貌的恢复,其最高点恢复相对误差分别为2.7%、1.6%。实验结果表明该方法具有有效性与可行性,具有较高的精度。     

Gamma-distorted fringe image modeling and accurate gamma correction for fast phase measuring profilometry

In fast phase-measuring profilometry, phase error caused by gamma distortion is the dominant error source. Previous phase-error compensation or gamma correction methods require the projector to be focused for best performance. However, in practice, as digital projectors are built with large apertures, they cannot project ideal focused fringe images. In this Letter, a thorough theoretical model of the gamma-distorted fringe image is derived from an optical perspective, and a highly accurate and easy to implement gamma correction method is presented to reduce the obstinate phase error. With the proposed method, high measuring accuracy can be achieved with the conventional three-step phase-shifting algorithm. The validity of the technique is verified by experiments.     

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。     

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。