基于相位恢复的三维形貌复合通道测量技术研究及应用
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摘要
基于相位恢复的三维形貌复合通道测量技术集合了相位和复合通道的调制与解调,具有信息获取量大、测试精度高等优点,因而在航空航天、机器视觉、逆向工程、微结构器件制造等领域得到了应用。伴随着该技术的发展,一系列相关的科学技术问题仍亟待解决。本学位论文针对条纹投影和白光干涉中的复合通道测量关键技术,以及拓展的形貌测量单元关键技术展开了深入研究,包括：
针对单帧彩色相移条纹投影复合通道测量中的相位复原误差问题,基于多维希尔伯特变换和载频交叠重构法,提出了一种混合盲校正技术。在无需进行额外的系统预标定的情况下,有效地抑制和减小了由电子设备的伽马(Gamma)效应、颜色耦合所引入的相位解调误差,实现了对目标三维形貌的单帧、亚毫米精度的测量,算法精度优于λeq/38。
针对彩色白光干涉复合通道测量中感兴趣物理量的高精度解码问题,深入分析了各色彩通道中信号相位与零级条纹位置的内在关联,基于加窗傅里叶变换“脊”(Windowed Fourier transform ridge,WFTR)和相位交叉(Phase-crossing)技术提出了一种新颖的零位最小二乘估计策略。与现有技术相比,所提算法充分利用了干涉信号的色谱信息,对光强噪声和颜色耦合具有较强的免疫力,无需预知光源的中心波长和被测件的折射率分布,显著地提升了微结构器件三维形貌复原的精度,测量偏差小于3.5nm。
针对条纹投影形貌测量中存在的Gamma畸变,基于傅里叶谱分析(Fourier spectrum analysis,FSA)理论提出了一种准确、简便的系统Gamma系数预标定校正技术。与现有技术相比,所提策略仅需两幅空间载频条纹图像(其他算法≥32幅),即达到了相似的标定效果。该技术原理上可被直接应用于基于传统相移算法的轮廓形貌测量,具备快速/动态测试的潜力。
针对条纹投影形貌测量中存在的镜头成像畸变问题,在充分考虑了投影器——相机镜头畸变的基础上,基于普通红/蓝棋盘格标定板提出了一种柔性的非线性迭代形貌测量技术。与现有技术相比,所提方法的柔性体现在：对系统的结构设置无严格要求,方便了测试系统的调整；综合考虑了投影器——相机的镜头畸变,可根据需要便捷的将测量模型进行拓展；在迭代复原三维形貌的同时,优化校正了由镜头畸变引起的形貌误差。实验表明,所提算法的形貌复原均方根(Root mean square,RMS)误差小于0.040mm而定位误差不超过1‰,测量精度相比于现有的线性模型方法提升了8倍以上。
对于白光干涉形貌测量,深入分析了干涉信号的频率、相位信息,光源中心波长,微位移装置扫描间隔和零级条纹位置之间的内在关联,将抗噪性能优异、信号局部分析能力强的加窗傅里叶变换(Windowed Fourier transform,WFT)引入到了灰度白光干涉信号的解调,分别提出了一种单点相位补偿技术和一种多点最小二乘拟合估计技术。与以往的包络峰值点检测算法相比,所提两种算法具有更强的鲁棒性和抗噪性能,且无需预知光源的中心波长和被测件的折射率分布,即可实现偏差在6nm以内的高精度三维形貌测量。
将所研究的相关技术成功地应用到了瞬态目标三维形貌的多视角测量。基于条纹投影复合通道测量技术,提出和设计了一套正六边形结构的多视角测量系统,将高质量的结构光条纹瞬时投影到目标表面,有效地控制成像设备同步捕捉到了变形条纹图像,利用鲁棒性强、噪声免疫力高的连续小波变换解调出相位信息,进而较为精确地复原出了瞬态飞行目标的三维形貌,为相关的瞬态测试研究提供了有益的实验依据。
Technique based on phase retrieval with complex channels for three-dimensional profile measurement which combines the modulation/demodulation of phase and complex channels has the advantanges of huge information acquirement, high measurement precision, etc. Hence it has been applied in many fields, including aeronautics and astronautics, machine vision, reverse engineering, and micro-structure-device manufacturing. With the development of this technique, a series of related scientific and technical problems are still needed to be solved. This dissertation mainly focuses fringe projection and white light interference with the emphasis on the key techniques for complex-channel measurement and the unit key techniques for extended profile measurement, which includes the following aspects:
To correct phase retrieval errors occuring in complex-channel measurement with single-frame color phase-shifiting fringe projection, a hybrid blind correction technique based on multi-dimensional Hilbert transform and carrier squeezing interferometry (CSI) is proposed. The phase demodulation errors caused by the gamma effect and the color coupling phenomenon of the used electronic devices can be effectively suppressed without an extra system pre-calibration. A single-frame measurement with a sub-millimeter accuracy for the target has been achieved and the precision of the proposed technique is better than λeq/38.
To high precisely demodulate the interested physical values in complex-channel measurement with color white light interference, a novel least-square strategy to estimate zero-order position based on Windowed Fourier transform ridge (WFTR) and phase-crossing techniques is proposed after an in-depth analysis of the inner relationship between the phase values of the signals in color channels and the position of zero-order white-light fringe. Compared with existing techniques, the proposed technique takes full advantages of the color information of the captured fringes and hence has a better immunity to the intensity noises and the color-coupling. Furthermore the center wavelength of the used light source and the refractive index of the test object are not required in advance. A higher precise result for the profile measurement of micro-structure-device with a deviation less than3.5nm can be finally attained.
For the gamma distortion problem in profile measurement with fringe projection, an accurate and simple correction technique which is based on the principle of Fourier spectrum analysis (FSA) for gamma coefficient pre-calibration is proposed. Compared with other existing methods, a similar result has been obtained by the proposed strategy which only needs two pre-encoded fringe patterns while others≥32frames. Therefore, in principle, the proposed technique can be applied in profile measurement using traditional phase-shifting algorithms and has a potential in rapid/dynamic profile measurement.
For the lens distortion problem in profile measurement using fringe projection, a flexible nonlinear-iterative profile measurement technique based on a simple red/blue checkerboard is proposed, which has fully considered the distortion of the projector-camera lens. Compared with existing techniques, the proposed method has no restrict requirement for the geometry of the measurement system which is convenience to the system adjustment. The distortion model can be easily extended as long as the profile measurement needs. The measurement errors caused by the lens distortion are able to be corrected during the iterative reconstruction for the desired three-dimensional morphology. Experimental works show that the reconstructed root mean square (RMS) error of the proposed algorithm is less than0.040mm, the location error is no more than1‰, and the measurement precision is improved over8times compared with existing linear-model-method.
For the profile measurement using white light interference, an in-depth analysis of the inner-relationships between the frequency and phase of the interference signals, the center wavelength of the used light source, the scanning interval of the micro-transducer device and the position of zero-order white-light fringe is given. Windowed Fourier transform (WFT) with a good anti-noise and partially analysis ability is introduced to process gray white light interferograms. Two different techniques, single-point-phase compensation and multi-point-phase least-square estimation, are hence proposed. Compared with previous envelope peak location methods, the proposed two strategies have a better robustness and immunity to noise. In addition, the center wavelength of the used light source and the refractive index of the test object are not needed. High-precision results with a deviation no more than6nm can be finally achieved.
The aforementioned related key techniques have been successfully applied into the multi-view profile measurement for transient moving targets. A multi-view measurement system with a hexagonal configuration for three-dimensional profile measurement based on complex-channel fringe projection profilometry is proposed and designed in this thesis. High quality fringes are instantaneously projected onto a test surface and the distorted fringe patterns are synchronously captured through imaging devices. The desired phase information is retrieved by continuous wavelet transform which has a good robustness and anti-noise ability. A precise three-dimensional profile of the transient moving target is then achieved which will provide helpful experimental foundations for the research of transient testing.
针对单帧彩色相移条纹投影复合通道测量中的相位复原误差问题,基于多维希尔伯特变换和载频交叠重构法,提出了一种混合盲校正技术。在无需进行额外的系统预标定的情况下,有效地抑制和减小了由电子设备的伽马(Gamma)效应、颜色耦合所引入的相位解调误差,实现了对目标三维形貌的单帧、亚毫米精度的测量,算法精度优于λeq/38。
针对彩色白光干涉复合通道测量中感兴趣物理量的高精度解码问题,深入分析了各色彩通道中信号相位与零级条纹位置的内在关联,基于加窗傅里叶变换“脊”(Windowed Fourier transform ridge,WFTR)和相位交叉(Phase-crossing)技术提出了一种新颖的零位最小二乘估计策略。与现有技术相比,所提算法充分利用了干涉信号的色谱信息,对光强噪声和颜色耦合具有较强的免疫力,无需预知光源的中心波长和被测件的折射率分布,显著地提升了微结构器件三维形貌复原的精度,测量偏差小于3.5nm。
针对条纹投影形貌测量中存在的Gamma畸变,基于傅里叶谱分析(Fourier spectrum analysis,FSA)理论提出了一种准确、简便的系统Gamma系数预标定校正技术。与现有技术相比,所提策略仅需两幅空间载频条纹图像(其他算法≥32幅),即达到了相似的标定效果。该技术原理上可被直接应用于基于传统相移算法的轮廓形貌测量,具备快速/动态测试的潜力。
针对条纹投影形貌测量中存在的镜头成像畸变问题,在充分考虑了投影器——相机镜头畸变的基础上,基于普通红/蓝棋盘格标定板提出了一种柔性的非线性迭代形貌测量技术。与现有技术相比,所提方法的柔性体现在：对系统的结构设置无严格要求,方便了测试系统的调整；综合考虑了投影器——相机的镜头畸变,可根据需要便捷的将测量模型进行拓展；在迭代复原三维形貌的同时,优化校正了由镜头畸变引起的形貌误差。实验表明,所提算法的形貌复原均方根(Root mean square,RMS)误差小于0.040mm而定位误差不超过1‰,测量精度相比于现有的线性模型方法提升了8倍以上。
对于白光干涉形貌测量,深入分析了干涉信号的频率、相位信息,光源中心波长,微位移装置扫描间隔和零级条纹位置之间的内在关联,将抗噪性能优异、信号局部分析能力强的加窗傅里叶变换(Windowed Fourier transform,WFT)引入到了灰度白光干涉信号的解调,分别提出了一种单点相位补偿技术和一种多点最小二乘拟合估计技术。与以往的包络峰值点检测算法相比,所提两种算法具有更强的鲁棒性和抗噪性能,且无需预知光源的中心波长和被测件的折射率分布,即可实现偏差在6nm以内的高精度三维形貌测量。
将所研究的相关技术成功地应用到了瞬态目标三维形貌的多视角测量。基于条纹投影复合通道测量技术,提出和设计了一套正六边形结构的多视角测量系统,将高质量的结构光条纹瞬时投影到目标表面,有效地控制成像设备同步捕捉到了变形条纹图像,利用鲁棒性强、噪声免疫力高的连续小波变换解调出相位信息,进而较为精确地复原出了瞬态飞行目标的三维形貌,为相关的瞬态测试研究提供了有益的实验依据。
Technique based on phase retrieval with complex channels for three-dimensional profile measurement which combines the modulation/demodulation of phase and complex channels has the advantanges of huge information acquirement, high measurement precision, etc. Hence it has been applied in many fields, including aeronautics and astronautics, machine vision, reverse engineering, and micro-structure-device manufacturing. With the development of this technique, a series of related scientific and technical problems are still needed to be solved. This dissertation mainly focuses fringe projection and white light interference with the emphasis on the key techniques for complex-channel measurement and the unit key techniques for extended profile measurement, which includes the following aspects:
To correct phase retrieval errors occuring in complex-channel measurement with single-frame color phase-shifiting fringe projection, a hybrid blind correction technique based on multi-dimensional Hilbert transform and carrier squeezing interferometry (CSI) is proposed. The phase demodulation errors caused by the gamma effect and the color coupling phenomenon of the used electronic devices can be effectively suppressed without an extra system pre-calibration. A single-frame measurement with a sub-millimeter accuracy for the target has been achieved and the precision of the proposed technique is better than λeq/38.
To high precisely demodulate the interested physical values in complex-channel measurement with color white light interference, a novel least-square strategy to estimate zero-order position based on Windowed Fourier transform ridge (WFTR) and phase-crossing techniques is proposed after an in-depth analysis of the inner relationship between the phase values of the signals in color channels and the position of zero-order white-light fringe. Compared with existing techniques, the proposed technique takes full advantages of the color information of the captured fringes and hence has a better immunity to the intensity noises and the color-coupling. Furthermore the center wavelength of the used light source and the refractive index of the test object are not required in advance. A higher precise result for the profile measurement of micro-structure-device with a deviation less than3.5nm can be finally attained.
For the gamma distortion problem in profile measurement with fringe projection, an accurate and simple correction technique which is based on the principle of Fourier spectrum analysis (FSA) for gamma coefficient pre-calibration is proposed. Compared with other existing methods, a similar result has been obtained by the proposed strategy which only needs two pre-encoded fringe patterns while others≥32frames. Therefore, in principle, the proposed technique can be applied in profile measurement using traditional phase-shifting algorithms and has a potential in rapid/dynamic profile measurement.
For the lens distortion problem in profile measurement using fringe projection, a flexible nonlinear-iterative profile measurement technique based on a simple red/blue checkerboard is proposed, which has fully considered the distortion of the projector-camera lens. Compared with existing techniques, the proposed method has no restrict requirement for the geometry of the measurement system which is convenience to the system adjustment. The distortion model can be easily extended as long as the profile measurement needs. The measurement errors caused by the lens distortion are able to be corrected during the iterative reconstruction for the desired three-dimensional morphology. Experimental works show that the reconstructed root mean square (RMS) error of the proposed algorithm is less than0.040mm, the location error is no more than1‰, and the measurement precision is improved over8times compared with existing linear-model-method.
For the profile measurement using white light interference, an in-depth analysis of the inner-relationships between the frequency and phase of the interference signals, the center wavelength of the used light source, the scanning interval of the micro-transducer device and the position of zero-order white-light fringe is given. Windowed Fourier transform (WFT) with a good anti-noise and partially analysis ability is introduced to process gray white light interferograms. Two different techniques, single-point-phase compensation and multi-point-phase least-square estimation, are hence proposed. Compared with previous envelope peak location methods, the proposed two strategies have a better robustness and immunity to noise. In addition, the center wavelength of the used light source and the refractive index of the test object are not needed. High-precision results with a deviation no more than6nm can be finally achieved.
The aforementioned related key techniques have been successfully applied into the multi-view profile measurement for transient moving targets. A multi-view measurement system with a hexagonal configuration for three-dimensional profile measurement based on complex-channel fringe projection profilometry is proposed and designed in this thesis. High quality fringes are instantaneously projected onto a test surface and the distorted fringe patterns are synchronously captured through imaging devices. The desired phase information is retrieved by continuous wavelet transform which has a good robustness and anti-noise ability. A precise three-dimensional profile of the transient moving target is then achieved which will provide helpful experimental foundations for the research of transient testing.
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