三维光学体层析重建技术研究
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摘要
对复杂流场的流动显示和定量测量是现代航空、航天及能源工程中的基本而关键技术,例如对高超音速飞行器再入大气层时产生的高温流场、火箭发动机产生的高温燃气射流场、风洞中的高超音速流场等的诊断。光学层析技术由携带被测场信息的多方向投影数据来重建待测场,具有非接触、瞬态和三维全场测量的优点,是实现流场全场定量测量的重要技术之一。但是,传统的光学层析技术是基于二维Radon变换的“切片”式层析,即将三维流场划分成一组相互平行的二维切片,分别对各切片进行层析重建,再将二维重建结果“堆”成三维重建场,是一种二维“切片”式的准三维重建方法。本文针对三维流场的全三维重建问题,将体积层析理论与光学层析技术相结合,跨越二维“切片”过程,直接实现对流场的三维光学层析重建。主要工作如下：
1.针对三维干涉体层析重建问题,研究了进行精确重建所需的光学层析投影完全性条件；将体积层析理论引入到干涉体层析技术中,实现了干涉体层析重建算法；在此基础上,通过马赫-曾德干涉光路,对真实流场进行层析测量,并通过干涉体层析算法实现了重建。
2.针对体层析重建的特点与莫尔层析投影的剪切干涉特性,提出了双正交光栅莫尔体层析投影光路；通过标量衍射理论,分析了此光路莫尔条纹的成像过程,获得各级频谱对应的网格状莫尔条纹图的解析表达式,为莫尔体层析技术研究开拓了一条新的途径。
3.针对双正交光栅莫尔体层析的重建问题,根据所得网格状莫尔条纹图的解析表达式,采用傅立叶变换算法处理条纹图,实现了两个方向剪切投影相位的同时提取；提出了基于双正交光栅莫尔体层析光路的三维莫尔体层析重建算法；在此基础上,构建了双正交光栅莫尔体层析光路,以丙烷扩散火焰为对象,进行了三维温度场重建。
4.针对莫尔体层析投影数据的提取问题,通过对双正交光栅莫尔体层析光路中各级频谱对应的解析表达式的研究,发现不同频谱莫尔条纹图之间存在空间相移特性；针对此特性,提出了一种能够同时获得至少四幅空间相移图像的莫尔体层析空间相移投影光路；通过标量衍射理论分析其成像过程,推导出此空间相移光路各级频谱对应莫尔条纹图的解析表达式,并对莫尔条纹图之间的空间相移关系进行了研究。此研究结果将为基于空间相移方法的莫尔层析投影提取技术提供理论基础。
With the rapid development of aviation, aerospace and military techniques, methods for diagnosing complex flow fields such as exhaust plume and aerodynamic flow fields of supersonic wind tunnel and rocket engine are urgently needed. Optical Computerized Tomography (OCT) has been considered as a powerful diagnostic tool for flow fields because of its nonintrusive and instantaneous, which be applied to many fields, such as flow visualization and measurement of physical parameters. It is a combination of optical methods such as interferometry, moire tomography and CT. Traditional CT reconstruction methods, however, is based on2-D Radon transformation and split the object into several parallel slices. Each slice is independently reconstructed by2-D CT reconstruction methods. It is obviously that traditional optical tomography is a pseudo3-D reconstruction method. To obtain an accurate3-D reconstructed result, the Volume Optical Computerized Tomography (VOCT) based on3-D Radon transformation is adopted to get a real3-D whole-field reconstruction. Moreover, this method can maintain the relevance between slices of the reconstructed field. But up to now, the reconstruction methods of VOCT have not been studied systematically. Thus, emphasis of this dissertation is put on the3-D algorithms of VOCT for the complex flow fields. The main works are summarized as follows:
1. By combining volume CT method with interferometry, a real3-D reconstruction method via interferometric volume computerized tomography is discussed, which could reconstruct the measured flow field as a whole. This real three-dimensional method is verified by reconstructed the3-D temperature distribution of an actual hot flow field based on Mach-Zehnder interferometer.
2. In order to realize the volume moire tomography, double cross gratings are applied in the moire deflected system to gain the shearing phase distribution of the grid moire pattern in two mutually perpendicular directions simultaneously. Thus, the scalar diffraction theory is used for analyzing the imaging process of the volume moire tomography based on double cross gratings to achieve the explicit form of shearing phase.
3. According to the3-D Radon transformation and the shearing phase distribution of the grid moire pattern, the volume moire reconstruction algorithm is given and verified by the simulation experiment. Finally, the3-D temperature distribution of a propane flame has been reconstructed by moire reconstruction algorithms.
4. According to the analysis of grid Moire fringes of volume moire tomography, spatial phase-shifting relations exist between grid Moire patterns corresponding to different spectrum. On this basis, a new optical system of volume moire tomography is proposed, which could obtain four spatial phase-shifting moire patterns simultaneously. With analysis of this system via scalar diffraction theory, the spatial phase-shifting characteristics between grid moire patterns are carefully analyzed.
1.针对三维干涉体层析重建问题,研究了进行精确重建所需的光学层析投影完全性条件；将体积层析理论引入到干涉体层析技术中,实现了干涉体层析重建算法；在此基础上,通过马赫-曾德干涉光路,对真实流场进行层析测量,并通过干涉体层析算法实现了重建。
2.针对体层析重建的特点与莫尔层析投影的剪切干涉特性,提出了双正交光栅莫尔体层析投影光路；通过标量衍射理论,分析了此光路莫尔条纹的成像过程,获得各级频谱对应的网格状莫尔条纹图的解析表达式,为莫尔体层析技术研究开拓了一条新的途径。
3.针对双正交光栅莫尔体层析的重建问题,根据所得网格状莫尔条纹图的解析表达式,采用傅立叶变换算法处理条纹图,实现了两个方向剪切投影相位的同时提取；提出了基于双正交光栅莫尔体层析光路的三维莫尔体层析重建算法；在此基础上,构建了双正交光栅莫尔体层析光路,以丙烷扩散火焰为对象,进行了三维温度场重建。
4.针对莫尔体层析投影数据的提取问题,通过对双正交光栅莫尔体层析光路中各级频谱对应的解析表达式的研究,发现不同频谱莫尔条纹图之间存在空间相移特性；针对此特性,提出了一种能够同时获得至少四幅空间相移图像的莫尔体层析空间相移投影光路；通过标量衍射理论分析其成像过程,推导出此空间相移光路各级频谱对应莫尔条纹图的解析表达式,并对莫尔条纹图之间的空间相移关系进行了研究。此研究结果将为基于空间相移方法的莫尔层析投影提取技术提供理论基础。
With the rapid development of aviation, aerospace and military techniques, methods for diagnosing complex flow fields such as exhaust plume and aerodynamic flow fields of supersonic wind tunnel and rocket engine are urgently needed. Optical Computerized Tomography (OCT) has been considered as a powerful diagnostic tool for flow fields because of its nonintrusive and instantaneous, which be applied to many fields, such as flow visualization and measurement of physical parameters. It is a combination of optical methods such as interferometry, moire tomography and CT. Traditional CT reconstruction methods, however, is based on2-D Radon transformation and split the object into several parallel slices. Each slice is independently reconstructed by2-D CT reconstruction methods. It is obviously that traditional optical tomography is a pseudo3-D reconstruction method. To obtain an accurate3-D reconstructed result, the Volume Optical Computerized Tomography (VOCT) based on3-D Radon transformation is adopted to get a real3-D whole-field reconstruction. Moreover, this method can maintain the relevance between slices of the reconstructed field. But up to now, the reconstruction methods of VOCT have not been studied systematically. Thus, emphasis of this dissertation is put on the3-D algorithms of VOCT for the complex flow fields. The main works are summarized as follows:
1. By combining volume CT method with interferometry, a real3-D reconstruction method via interferometric volume computerized tomography is discussed, which could reconstruct the measured flow field as a whole. This real three-dimensional method is verified by reconstructed the3-D temperature distribution of an actual hot flow field based on Mach-Zehnder interferometer.
2. In order to realize the volume moire tomography, double cross gratings are applied in the moire deflected system to gain the shearing phase distribution of the grid moire pattern in two mutually perpendicular directions simultaneously. Thus, the scalar diffraction theory is used for analyzing the imaging process of the volume moire tomography based on double cross gratings to achieve the explicit form of shearing phase.
3. According to the3-D Radon transformation and the shearing phase distribution of the grid moire pattern, the volume moire reconstruction algorithm is given and verified by the simulation experiment. Finally, the3-D temperature distribution of a propane flame has been reconstructed by moire reconstruction algorithms.
4. According to the analysis of grid Moire fringes of volume moire tomography, spatial phase-shifting relations exist between grid Moire patterns corresponding to different spectrum. On this basis, a new optical system of volume moire tomography is proposed, which could obtain four spatial phase-shifting moire patterns simultaneously. With analysis of this system via scalar diffraction theory, the spatial phase-shifting characteristics between grid moire patterns are carefully analyzed.
引文
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