Phase deviation analysis and phase retrieval for partial intensity saturation in phase-shifting projected fringe profilometry

Intensity saturation may take place as a sinusoidal fringe pattern is projected onto an object which has a relative high reflective index on some regions of the surface. If a phase-shifting method is used, the illuming light intensities at the same point of the object may have different values for each projected phase-shifting fringe pattern. Therefore, when the intensity at a point of the object exceeds the saturation level for a certain phase step of projected fringe pattern, other intensities obtained at the same point with different phase steps of projected fringe patterns do not exceed the saturation level. This kind of saturation is defined as partial intensity saturation. In the case of partial intensity saturation, a relative larger phase error is introduced when a conventional phase reconstruction algorithm is used in the phase-shifting projected fringe profilometry (PSPFP). To get rid of such disadvantage, an improved algorithm for phase reconstruction is proposed in this paper. By using the new algorithm, the effect of partial intensity saturation for the phase reconstruction can be decreased greatly and a good quality of reconstructed phase map can be obtained. Phase deviation of the reconstructed phase is also analyzed. Finally, an experimental result with PSPFP is presented to validate the feasibility of the proposed algorithm.     

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。     

A novel color fringe projection based Fourier transform 3D shape measurement method

A novel Fourier transform 3D shape measurement method based on color fringe projection is proposed in order to solve the spectrum overlapping and phase unwrapping problems existed in Fourier transform profilometry (FTP). The R and G components of the color fringe are set to two sinusoidal patterns with different frequencies and the B component is set to the average value of R or G component. Then this pattern is projected to the object and the deformed fringe image is captured. Three gray patterns are separated from the color fringe, the background and high frequency noise can be eliminated using our method and the accurate unwrapped phase can be got. Only one shot color pattern is projected to get the 3D information of the object. Experiment results show that the 3D information of an object can be obtained rapidly and accurately.     

Surface profile measurement of low-frequency vibrating objects using temporal analysis of fringe pattern

A simple and accurate algorithm (phase scanning method) is proposed for 3D surface contouring and dynamic response determination of a vibrating object. A sinusoidal fringe pattern is projected onto a low-frequency vibrating object by a programmable liquid crystal display projector. The fringe patterns are captured by a high-speed CCD camera with a telecentric gauging lens. Phase values are evaluated point by point using phase scanning method. From the phase values of each point on the object, the contour of the specimen at different instants of vibration can be retrieved. In this paper, a small vibrating coin is used to demonstrate the validity of the method and the experimental results are compared with test results on a stationary coin using four-step phase shifting and fast Fourier transform methods. The technique is especially useful in applications where the vibrating object has a complicated shape.     

A novel fringe adaptation method for digital projector

Aimed to obtain high-quality sinusoidal fringe projection, a new method to correct the output fringe of digital projector is presented. The method is based on the proposed fringe transform model, which describes the relationship of the input and output fringe pattern. Firstly, a series of fringe patterns are projected and from the fringe images, the transform function is calculated by the pattern shifting method. At last, by modifying the input fringe pattern, a standard sinusoidal output fringe can be achieved. Different from the previous methods, the waveform nonlinearity is estimated by varying the intensity of the projected fringe pixel by pixel; thus the waveform nonlinearity can be estimated precisely and the time cost is considerably reduced. Experimental results show that by modification of the input projection patterns the projector can project fringe with high-quality sinusoidal waveform leading to high performance of the projection system.     

一种用于在线三维测量的五步非等步相移算法

提出了一种五步非等步相移算法,并成功应用于在线三维测量中。仅投影一固定正弦光栅条纹到物体上,通过物体在线运动产生等效相移,在一个条纹周期范围内任意采集五帧变形条纹图,通过像素匹配使各帧条纹图中的物点一一对应并计算出相应的等效相移量。采用所提出的五步非等步相移算法,即可重构物体。计算机模拟与实验验证了该方法的可行性和有效...     

Three-dimensional profile measurement of the blade based on multi-value coding

As the blade must have precise size and accurate shape, three-dimensional (3D) profile measurement of the blade is very important. 3D profile measurement method based on multi-value coding is proposed. This method designs a multi-value coding stripe pattern combined with the four-step phase-shifting method. Two kinds of fringe patterns are projected onto the object respectively, one is sinusoidal intensity distribution used for wrapped phase, the other is multi-value coding fringe pattern for phase unwrapping. Because this encoding method is simple, and easy to implement, the absolute phase can be quickly implemented. Experimental results demonstrated that the proposed method can achieve a high precision, high speed and low cost 3D profile measurement of the blade.     

位相相关在大尺寸物体三维重构中的应用

提出了一种对大尺寸物体进行三维重构的方法.将一正弦光栅投影到物体表面,通过摄像机得到有变形条纹的二维子区域强度像.在频域中完成各二维子区域强度像之间的相关,根据输出的相关峰值位置即可得出平移量,通过图像拼接获得有变形条纹的整个物体的二维强度像.运用傅里叶变换轮廓术可得到大尺寸物体的三维型面,给出了实验结果.     

Fringe projection profilometry based on complementary color-encoded fringe patterns

3D measurement techniques based on color-encoded fringe pattern projection have been widely used in various fields of engineering recently. There is one problem that the surface color of measured object may interfere with the color of projected fringe pattern. To solve this problem, a novel method based on complementary color-encoded fringe projection is proposed. Two color-encoded fringe patterns whose fringe colors are complementary are designed. The first pattern is with the sinusoidal fringe embedding into the green color channel which is used to evaluate phases by Fourier transform method. The fringe color of the captured image is established with the help of the complementary color fringe pattern, which is based on the feature of color complementation. Thus, the influence brought by the color of object surface can be eliminated, and decoding errors can be further reduced. Experiment results indicate that the proposed method is valid and can be applied to the measured colorful objects.     

On-line phase measuring profilometry based on phase matching

On-line phase measuring profilometry based on phase matching is proposed. While just one fixed sinusoidal fringe is projected on a measured object moving with the pipeline, deformed patterns modulated by the object moving at the same distance moment are captured synchronously by the CCD camera. The phase information of the object in those captured deformed patterns can be predicted using FTP method to assist the pixel matching so as to realize the point-to-point correspondence of the object in the captured deformed patterns. Meanwhile, the equivalent phase-shifting deformed patterns can be extracted. So the three dimensional shape of the object can be reconstructed successfully with an equal phase-shifting algorithm. Numerical simulation and experiments show feasibility and validity of the proposed method.     

A three dimensional on-line measurement method based on five unequal steps phase shifting

A three-dimensional on-line measurement method based on five unequal steps phase-shifting with phase measuring profilometry is presented. While only one sinusoidal grating pattern is projected onto the measured object moving with the pipe-line, five arbitrary deformed patterns are captured by CCD as the measured object moves within a duty cycle of the grating pattern. The modulation distribution based on Fourier transform profilometry is introduced to realize pixel matching so as to calculate the corresponding equivalent shifted phase on the deformed patterns. A five unequal steps phase shifting algorithm is developed, which is suitable for non-uniform motion of the pipeline. The experiments verify its feasibility and validity.     

基于双色条纹投影的快速傅里叶变换轮廓术

在实际傅里叶变换轮廓术测量中，获取的条纹图扩展的零频分量对傅里叶变换轮廓术的测量精度和测量范围有很大影响，甚至妨碍正确三维面形的恢复。π相移技术常被用来消除零频分量对测量的影响，但需要在测量系统中安装精密相移装置，并需要采集两帧具有π相位差的条纹图。传统傅里叶变换轮廓术中，完成精密相移需要较长的时间，影响了傅里叶变换轮廓术测量方法的实时性。提出了采用双色正弦光栅投影来实现从一帧条纹图中消除零频对傅里叶变换轮廓术测量的影响。该方法同传统的π相移方法相比，不需要相移装置，测量系统简单，并且能真正实现高速测量。     

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.     

Surface profile inspection of a moving object by using dual-frequency Fourier transform profilometry

The 2π phase ambiguity caused by surface isolations and large height step can be solved by dual-frequency projection grating profilometry. However, in the Fourier transform profilometry (FTP) of a moving object, only one single deformed fringe pattern can be obtained. In order to introduce the dual-frequency technique into the FTP of moving object, a novel experimental system is designed to capture two fringe patterns with different frequency at the same time. A grating structure comprising two regions with different frequencies is projected upon the surface of the detected object. Two line-scan CCD cameras are used to capture the surface images encoded by the two kinds of patterns, respectively. By getting the corresponding image intensity at the same point of the object surface in the two acquired images, the dual-frequency technique is applied to extract the real phase without phase ambiguity. The surface profile of a specimen with a large height step is measured to prove the feasibility of the proposed method. The experimental results show that the proposed method can solve the 2π phase ambiguity problem successfully in the surface profile inspection of a moving object.     

基于双频彩色条纹投影的相位测量去包裹方法

为了提高测量速度,提出一种基于双频彩色条纹投影的相位测量去包裹方法,只需采集一帧图像,就能实现高速测量以及动态物体轮廓测量中的相位去包裹。论述了双频相位测量和变精度去包裹原理,并详细分析影响测量精度的因素。该方法采用计算机生成一帧双频双色正弦条纹图,用液晶数字投影仪投影,并用傅里叶变换的方法对两个单色条纹图进行分析,获得高低两种精度的被测物体高度信息,从而进行变精度去包裹处理。结果表明,利用该方法提高了测量速度,可得到较高的去包裹精度,其测量最大绝对误差为 1．413～-1．582 mm,标准差为0．363 mm。     

A flexible 3D profilometry based on fringe contrast analysis

This paper proposed a flexible 3D profilometry based on fringe contrast analysis. A series of sinusoidal fringes are projected on the surface of the testing object that is laid in front of the imaging plane of the fringes, and captured through a beam splitter by a CCD camera in the same direction as the axis of the projection. After the fringe contrast obtained using phase-shifting technique, the height of the object can be restored through searching the look-up table of the contrast and the height. In the measurement process, we only need to capture fringe patterns in one position, without changing the imaging plane of the fringes, so it is faster and more convenient than the existing method based on fringe contrast analysis. Our system is simple and flexible by reason of no special devices used. In this paper, the principle of this method, the setup of the measurement system and primary experiment results are given. The experimental results prove this method can restore the height of the complex object accurately and effectively.     

An improved stair phase encoding method for absolute phase retrieval

An improved phase unwrapping method is proposed to reduce the projection fringes in three-dimensional (3D) surface measurement. Color fringe patterns are generated by encoding with sinusoidal fringe and stair phase fringe patterns in red and blue channels. These color fringe patterns are projected onto the tested objects and then captured by a color CCD camera. The recorded fringe patterns are separated into their RGB components. Two groups of four-step phase-shifting fringe patterns are obtained. One group of the stripes are four sinusoidal patterns, which are used to determine the wrapped phase. The other group of stripes are four sinusoidal patterns with the codeword embedded into stair phase, whose stair changes are perfectly aligned with the 2π discontinuities of sinusoidal fringe phase, which are used to determine the fringe order for the phase unwrapping. The experimental results are analyzed and compared with those of the method in Zheng and Da (2012. Opt Express 20(22):24139–24150). The results show that the proposed method needs only four fringe patterns while having less error. It can effectively reduce the number of projection fringes and improve the measuring speed.     

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。     

基于液晶显示投影技术的数字影栅云纹相移实现方法

影栅云纹是物体离面变形和表面形貌测量常用的一种比较简单的方法,用单纯的影栅云纹法即便在最好的光学系统配置情况下测量精度也只有1~100μm左右,在影栅云纹测试方法中引进相移技术是提高测量精度的主要手段。采用液晶投影仪和数字图像处理技术实现数字影栅云纹测量的准确数字相移,避免了在影栅云纹法中使用结构比较复杂或特制的相移机构。由计算机产生相移条纹图经液晶显示投影,应用实时图像灰度算术相减技术得到数字相移影栅云纹条纹图。该方法具有“基准栅”的栅距和相移步长实时可调,配置高速图像采集系统和图像后处理软件,可将相移技术引入动态测量中,从而提高动态测量的精度的优点。最后的悬臂梁实验结果证实了该方法的有效性。     

Surface profile measurement of moving objects by using an improved π phase-shifting Fourier transform profilometry

The π phase-shifting Fourier transform technique is introduced into the surface profile measurement of moving objects. A digital grating comprising two regions, which have a π phase shifting is projected onto the object. Two line-scan CCD cameras are used to capture two deformed fringe patterns with π phase shifting at the same time. As the object is moving, each point at the object surface can be captured twice. The digital correlation method is used to calibrate the experimental system. The zero-order component can be eliminated by subtracting intensities of the same surface point in two captured images. And then the phase can be extracted by Fourier transform without the disturbance of zero-order component. Experimental results demonstrate that this method is feasible for the moving surface profile detection and the measurable slope of height variation can be extended.