Effect of the nonlinearity of CCD in Fourier transform profilometry on spectrum overlapping and measurement accuracy

In Fourier transform profilometry (FTP), we must restrain spectrum overlapping caused by the nonlinearity of charge coupled device (CCD) and increase the measurement accuracy of object shape. Firstly, the causes of producing higher-order spectrum components and inducing spectrum overlapping are analysed theoretically, and simple physical explanation and analytical deduction are given. Secondly, aiming to suppress spectrum overlapping and improve measurement accuracy, the influence of spatial carrier frequency of projection grating on them is analysed. A method of increasing the spatial carrier frequency of projection grating to restrain or reduce the spectrum overlapping significantly is proposed. We then analyze the mechanism of how the spectrum overlapping is reduced. Finally, the simulation results and experimental measurements verify the correction of the theory and method proposed.     

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.     

A composite-structured-light 3D measurement method based on fringe parameter calibration

This paper proposes a novel method for reducing measurement error caused by spectrum overlapping in composite-structured-light 3D measurement systems. For a composite-structured-light 3D measurement system, spectrum overlapping causes parameters of each deformed phase-shifting fringe to change, and therefore leads to phase measurement errors. The proposed fringe parameter calibration method is based on the fact that variations in each deformed fringe's parameters are independent of height and reflectivity of the measured object. Three frames of composite grating are projected on the reference plane, and each carrier channel includes the information of three phase-shifting sinusoidal gratings used in Phase Measuring Profilometry (PMP). With the parameter calculation formulas of PMP, the parameters of fringes demodulated from the same carrier channel can be calculated, and therefore parameter relation coefficients between fringes demodulated from different carrier channels may be obtained. When an object is measured, these relation coefficients can be used to calibrate the parameters of the deformed phase-shifting fringes. A new 3D measurement mathematical model is established to reconstruct the shape of the object. Experimental data proved that the proposed method can effectively restrain the effect of spectrum overlapping and improve measurement accuracy by more than three times.     

基于背景光调制的复合光傅里叶变换轮廓术

提出一种基于背景光调制的用于傅里叶变换轮廓术测量范围的复合光栅,该光栅通过调制一正弦条纹和不含任何相位信息的背景光来抑制零频,较基于相移技术的复合光栅有更大的优势:背景光只含直流分量,使得复合光栅的频谱更加简单,有利于滤出载波信息,提高测量精度;对从复合光栅中解调出来的背景光只涉及平均值校准,校准过程更为简单;解调出的背景光与物体表面的反射率成正比,具有潜在的应用价值。采用Matlab程序对该复合光栅进行了数值模拟,并对该光栅实用性进行了实验研究,结果证实了该光栅用于抑制零频、扩大傅里叶变换轮廓术测量范围的有效性,且提高了测量精度。     

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.     

Improved composite Fourier transform profilometry

An improved composite Fourier transform profilometry (ICFTP) is proposed through optimizing the composite grating. Compared with the composite Fourier transform profilometry (CFTP), the frequencies of the two sinusoidal images modulated along the orthogonal direction in the optimized composite grating are not equal. The overlapping degree of Fourier spectrum of the optimized grating is lowered. The measuring accuracy is improved because two frequencies are used to calculate phase more accurately. By using a more advantageous flat image extracted ingeniously from the optimized grating, the zero component of the lower frequency sinusoidal image in the Fourier spectrum can be eliminated. So the measuring range is extended the same as that by the π phase shifting technique. Both numerical simulation and experiment demonstrate the feasibility and validity of the proposed method.     

光学三维扫描仪光强传递函数的测量和校正

由于数字光栅投影仪的光强传递函数对于正弦投影条纹的质量以及相位测量精度起着至关重要的作用,本文提出了一种校正光学三维扫描仪光强传递函数的新方法。首先,分析了由于投影仪非线性响应引起的光栅谐波的相位测量误差;然后,通过投影一组不同灰度级的图像,并利用光功率计测出数字投影仪投出图像的亮度。接着,通过分析得到数字投影仪的非线性响应特性曲线,再经过数据处理,即可获得投影仪的光强传递函数;最后,对光强传递函数进行反函数逆变换,得到一个校正后的非正弦光栅,利用投影仪对该光栅的投影即可在被测物体表面上获得一个正弦光栅。数字投影仪对标准平板的测量结果表明,校正前平均误差为0.71 mm,校正后为0.55 mm;对于标准量块的测量,校正前的平均误差为0.62 mm,校正后为0.15 mm。上述结果表明,本文提出的方法可以减小由于系统非线性响应引起的测量误差并提高测量精度。     

一种制作投影灰度正弦光栅的新方法

针对传统方法难以制作结构光三维投影测量设备的灰度正弦光栅元件,并以Ronchi光栅代替从而影响测量准确度,提出了一种制作灰度按正弦分布的光栅模板的新方法.通过对银盐全息干板透过率特性曲线的理论分析,指出在对比度为一的正弦干涉条纹下曝光不能得到线性记录和变换的原因,并提出了采用均匀非相干光预曝光提供偏置点来实现线性记录的新方法.实验表明,采用空间滤波法能够获得对称双光束正弦干涉条纹记录,并准确控制正弦干涉条纹曝光在干板的线性区域,可以达到线性记录并获得尽可能高的反衬度.     

A modified phase diversity diffraction wavefront sensor with a grating

The phase diversity wavefront sensor is one of the tools used to estimate wavefront aberration, and it is often used as a wavefront sensor in adaptive optics systems. However, the performance of the traditional phase diversity wavefront sensor is limited by the accuracy and dynamic ranges of the intensity distribution at the focus and defocus positions of the CCD camera. In this paper, a modified phase diversity wavefront sensor based on a diffraction grating is proposed to improve the ability to measure the wavefront aberration with larger amplitude and higher spatial frequency. The basic principle and the optics construction of the proposed method are also described in detail. The noise propagation property of the proposed method is also analysed by using the numerical simulation method, and comparison between the diffraction grating phase diversity wavefront sensor and the traditional phase diversity wavefront sensor is also made. The simulation results show that the diffraction grating phase diversity wavefront sensor can obviously improve the ability to measure the wavefront aberration, especially the wavefront aberration with larger amplitude and higher spatial frequency.     

从变形光栅条纹提取基准光栅信息

基于傅里叶变换轮廓术,提出一种直接从变形光栅条纹中提取基准光栅条纹信息并重建基准光栅的测量方法.分析了基准光栅条纹和参考平面的功能,揭示变形光栅条纹和基准光栅条纹的关系;应用窗口傅里叶变换对变形光栅条纹中的各个微小区域进行频谱分析,从中识别并提取基准光栅的频率和相位信息;重构出一幅完整的基准光栅条纹,实现三维物体形貌测量.实验结果表明该方法是可行的,为三维形貌测量提供一种新手段.     

A modified phase diversity wavefront sensor with a diffraction grating

Phase diversity wavefront sensor is one of the useful tools to estimate the wavefront aberration, and it is often used as a wavefront sensor in adaptive optics system. However, the performance of the traditional phase diversity wavefront sensor is limited by the accuracy and dynamic ranges of the intensity distribution at focus and defocus positions of the CCD camera. In this paper, a modified phase diversity wavefront sensor based on a diffraction grating is proposed to improve the ability to measure the wavefront aberration with larger amplitude and higher spatial frequency. The basic principle and the optics construction of the proposed method are also described in detail. The noise propagation property of the proposed method is also analysed by using the numerical simulation method, and comparison between the diffraction grating phase diversity wavefront sensor and the traditional phase diversity wavefront sensor is also made. The simulation results show that the diffraction grating phase diversity wavefront sensor can obviously improve the ability to measure the wavefront aberration, especially the wavefront aberration with larger amplitude and higher spatial frequency.     

基于单目结构光的大物体三维测量关键方法的研究

在单目结构光的三维测量系统中,由于投影仪倾斜投影, 参考平面上的条纹周期展宽, 给测量带来误差,降低了测量精度。同时受大物体自身几何和形貌等因素的影响,以及相交轴测量系统的限制,其单幅面测量范围受限,很难一次测量大物体完整的三维形貌,而且在测量大物体时,摄像机镜头非线性畸变也影响测量精度。根据参考平面上光栅条纹的周期变化规律,提出了一种适用性好、方便快捷的条纹周期校正的理论模型, 在此基础上, 提出了基于条纹周期校正的四步相移法的理论模型,进而提出了基于条纹周期校正的时间相位展开法的理论模型。采用摄像机镜头非线性畸变校正模型,提高测量精度。在被测物表面粘贴标志点,获取其三维坐标,利用SVD分解和L-M优化算法求取转换矩阵,并在设定的全局坐标系下实现三维图像拼接,采用线性加权算法,对重叠区域进行图像融合。实验结果表明,X轴的拼接误差为0.14 mm,Y轴的拼接误差为0.16 mm,Z轴的拼接误差为0.19 mm,其拼接误差均在测量误差允许范围之内。     

加窗傅里叶变换在三维形貌测量中的应用

采用加窗傅里叶变换技术(GTGM)对变形光栅图像进行分析在窗口区域内提取基频,并随着窗口的移动进行叠加,有效地重构出全部的基频信息,改善了不同频谱的叠加现象,提高测量的精度.     

光栅式成像光谱仪空间均匀性测试研究

空间均匀性是成像光谱仪辐射定标的核心参数之一。通过对国内外均匀性测试方法研究，提出采用空间分布法对光栅式成像光谱仪的空间均匀性进行测试研究。该方法能准确给出各个位置点信号响应的详细分布，对于提高并改善光栅式成像光谱仪的图谱质量具有重要的意义。空间分布法建立在高稳定性、高均匀性标准光源的基础上，由计算机软件对测试结果进行图谱分离，提取同波长下空间响应信号获得光栅式成像光谱仪的空间均匀性。最后分析了空间均匀性测量不确定度的影响因素，并分析了空间均匀性对绝对辐射定标和光谱精度的影响。     

基于光栅投影的轮廓测量改进方法

传统傅里叶变换轮廓方法(FTP)在测量表面突变的物体时,受物体高度变化所引起的非截断相位变化的影响,相位难以正确展开。利用双频光栅投影可以解决这一问题。在总结了传统测量方法与双频光栅测量方法的基础上,提出采用彩色复合光栅投影的测量方法。该方法只需一次采集,就能消除图像背景分量与高次分量对测量的影响,在扩大测量范围的同时可达到双频技术测量突变效果。最后,对3种方法的实际测量结果作了对比分析,证明彩色复合光栅投影方法得到的测量精度最高。     

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。     

光谱分析方法测试GMLM微间距的实验和方法推广

基于MEMS的光栅平动式光调制器(GMLM)依靠结构中可动光栅和下反射镜之间的微间距的变化来实现光的调制作用,被应用于显示领域。可动光栅和下反射镜之间的微间距是一个关键的参数,传统的测试方法如台阶仪等要破坏结构,WYKO白光干涉仪测量成本高,所以要寻求一种测试成本较低、测量精度较高的测试方法。文章采用非接触的波长扫描式光谱分析方法进行了GMLM可动光栅和下反射镜之间的微间距测试实验研究。实验表明：实验结果和理论分析吻合,验证了理论模型的正确性;对比WYKO白光干涉仪测试,该方法的相对测试误差小于1%;具有很好的重复性。对该光谱分析方法进行了推广,从理论上推导了该方法可以实现准动态测量GMLM器件吸合电压、共振频率以及其他基于衍射/干涉的MEMS器件的微小间距测试等。     

均值量化与中值量化光栅性能的理论研究

对相移技术的投影栅相位法的传统中值量化方法提出改进,设计和制作出小误差、低高阶谐波的均值量化光栅.理论讨论了相位值、离散等级和量化等级等因素对两种量化光栅性能的影响;在标准偏差和频谱分布两方面比较后,得出均值量化光栅性能优于中值量化光栅且更接近正弦光栅的结论.     

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。     

非线性小数重合法及其在轮廓测量中的应用

叠相还原的困难是光栅投影式轮廓测量技术中影响可靠性和阻碍自动化测量的最大问题。本文提出了一种新型的时域叠相还原算法－－非线性小数重合法,这种新方法可以将可靠测量扩大数部,而不失测量精度。文中详细论述了非线性小数重合法的原理,并给出了轮廓的可靠测量的实验结果。