粗糙目标激光散斑统计特性及微运动特征分析
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摘要
激光散斑测量技术具有结构简单、全场非接触测量、无损性、实时性等优点，在各光学测量中已逐渐成为理论和应用研究的热点。激光散斑携带的散射体的信息是进行目标探测、识别、特征分析、以及微运动检测的重要依据。本文从粗糙物体的激光波束散射理论出发，数值分析了粗糙物体的激光散射二阶统计特性及四阶统计特性，结合优化理论，提出了用粗糙物体的激光散斑时间-空间统计特性，分析旋转目标的微运动特征。论文的主要成果如下：
1.从粗糙面散射的标量近似理论出发，推导出了具有高斯分布随机粗糙面的任意形状凸目标的远区散射场的双频互相干函数的表达式，数值计算了粗糙球和柱的双频互相干函数，分析了目标的形状、尺寸及表面粗糙度参数对双频互相干函数及其相干带宽的影响。有助于进一步研究更为复杂粗糙目标的激光散射统计特性，为雷达系统设计、目标探测和识别、定位及特征提取提供理论依据。
2.基于Beckmann理论和高斯矩定理，研究了二维弱起伏粗糙面散射四阶统计特性，严格推导了二维弱起伏粗糙导体和介质面的散射强度起伏互相关函数的解析表达式，并重点分析了入射、观察条件及粗糙面特征参数对散射场强度起伏的双频互相关函数和角度互相关函数的影响。加深了对粗糙面散射特性的理解，为粗糙目标的散斑问题的研究提供理论基础。
3.基于标量Helmholtz积分关系，推导了出三维粗糙曲面的散射光经自由空间传输，在垂直于散射方向的远区观察面上所得到的散斑场的空间分布和散斑场强度起伏的空间互相关函数，得到了不同孔径粗糙面、球、柱及锥的散斑的横向尺寸与其形状和大小以及入射波长和传播距离之间关系的表达式。
4.研究了粗糙物体平动和转动所产生动态散斑的统计特性，推导出散斑强度起伏空间-时间互相关函数，得到了散斑时间相干长度和因目标平动或旋转而产生的多普勒展宽的表达式，讨论了散斑时间相干长度和多普勒展宽与目标的形状、运动状态及运动速度的关系。
5.推导了二维平动微粗糙和大粗糙平面平动所产生的多普勒频移公式，在此基础上，导出了轴对称粗糙体转动产生的多普勒频移的表达式。表明轴对称目标旋转产生的多普勒频移与转速和被照射面元的位置以及视线角正弦成正比，与波长成反比，与粗糙度无关。
6.搭建了动态激光散斑实验平台，获得了不同视线角和不同转速下旋转柱和锥动态散斑时序图像，对其进行了统计分析，并将之与理论模拟结果进行了比较，二者吻合得很好。利用实验所得到的散斑时间相干长度，采用粒子群算法，结合动态散斑的理论推导，反演了旋转柱体和锥体的视线角和转动角速度，实现了对倾斜旋转柱体和锥体微运动特征的检测。
Because of the advantage, such as simple-structure and noncontact and lossless andreal-time and so on, laser speckle measurement has been the research and applicationinterest. The message of the scatter in the speckle is important to detect and recognizeand analysis the micro-motion of the object. In the paper, with the theory of the laserscattering from rough objects, the second and the fourth order statistical properties ofthe scattered light have been studied, then the temporal and spatial statistical propertiesof the laser speckle which is applied to analyze the micro-motion of the object. Themain achievements are as followings:
1. From the scattering theory of rough surface, the expression of the two-frequencymutual coherence function from three-dimensional convex objects with rough surfaceobeying Gaussian distribution has been derived, and the influences of the shape and thesize as well as the surface roughness of the objects on the function and the coherencebandwidth have been discussed which will be for the recognization of the objects withmore complex shape.
2. Based on the Beckmann theory and Gaussian moment theorem, the expression ofthe fourth-order moment of the scattering from rough surfaces has been given which canbe expressed by two kinds of the second-order moment and the first-order moment ofthe scattered field. The influences of the incident and observation conditions and thecharacteristic parameters on the two-frequency correlation function and the angularcorrelation function of the fourth-order moment have been mainly discussed.
3. With scalar Helmholtz integral relation, the distribution on the observe plane inthe far field perpendicular to the scattering direction of the speckle filed formed in freespace from rough objects with three dimension and its intensity spatial correlationfunction have been derived, the expressions of the lateral sizes of the speckles fromrough surface with different apertures and balls and cylinders and cones have beenobtained, which is closely dependent on the shape and the size of the object and thelaser wavelength as well as the distance.
4. The temporal statistical properties of the dynamical laser speckle from in-planemoving rough surfaces and rotating rough objects have been investigated by thespatial-time correlation function of the speckle intensity fluctuation, and the expressionsfor the temporal correlation length of the speckle and the Doppler broadening due to therotating of the obeject have been obtained, and the relationships of them with themoving velocity and the shape as well as the size of the studied objects have been discussed respectively.
5.The expression of the Doppler frequency shift caused by the in-plane movingrough objects has been derived with which the Doppler frequency shift due to therotation of the objects with rotational symetry is obtained to show that the Doppler shiftis proportional to the rotating velocity and the situation of the surface elementilluminated and the sine of the sight-in-line angle, inversely proportional to the incidentwavelength, however, independent to the roughness of the objects.
6．The experiment plat form has been built to obtain the time-sequential dynamicalspeckle images of rotating rough cylinders and cones with different sight-in-line angleand different rotating velocity, which have been analyzed statistically. The results agreewell to the theoretical simulated results. With the particle group algorithm and thetheoretical derivation on the dynamic speckles, the experimental results for the timecorrelation length of the speckle have been applied to reverse the sight-in-line angle andthe rotating velocity to detect the micro-motion of the object.
1.从粗糙面散射的标量近似理论出发，推导出了具有高斯分布随机粗糙面的任意形状凸目标的远区散射场的双频互相干函数的表达式，数值计算了粗糙球和柱的双频互相干函数，分析了目标的形状、尺寸及表面粗糙度参数对双频互相干函数及其相干带宽的影响。有助于进一步研究更为复杂粗糙目标的激光散射统计特性，为雷达系统设计、目标探测和识别、定位及特征提取提供理论依据。
2.基于Beckmann理论和高斯矩定理，研究了二维弱起伏粗糙面散射四阶统计特性，严格推导了二维弱起伏粗糙导体和介质面的散射强度起伏互相关函数的解析表达式，并重点分析了入射、观察条件及粗糙面特征参数对散射场强度起伏的双频互相关函数和角度互相关函数的影响。加深了对粗糙面散射特性的理解，为粗糙目标的散斑问题的研究提供理论基础。
3.基于标量Helmholtz积分关系，推导了出三维粗糙曲面的散射光经自由空间传输，在垂直于散射方向的远区观察面上所得到的散斑场的空间分布和散斑场强度起伏的空间互相关函数，得到了不同孔径粗糙面、球、柱及锥的散斑的横向尺寸与其形状和大小以及入射波长和传播距离之间关系的表达式。
4.研究了粗糙物体平动和转动所产生动态散斑的统计特性，推导出散斑强度起伏空间-时间互相关函数，得到了散斑时间相干长度和因目标平动或旋转而产生的多普勒展宽的表达式，讨论了散斑时间相干长度和多普勒展宽与目标的形状、运动状态及运动速度的关系。
5.推导了二维平动微粗糙和大粗糙平面平动所产生的多普勒频移公式，在此基础上，导出了轴对称粗糙体转动产生的多普勒频移的表达式。表明轴对称目标旋转产生的多普勒频移与转速和被照射面元的位置以及视线角正弦成正比，与波长成反比，与粗糙度无关。
6.搭建了动态激光散斑实验平台，获得了不同视线角和不同转速下旋转柱和锥动态散斑时序图像，对其进行了统计分析，并将之与理论模拟结果进行了比较，二者吻合得很好。利用实验所得到的散斑时间相干长度，采用粒子群算法，结合动态散斑的理论推导，反演了旋转柱体和锥体的视线角和转动角速度，实现了对倾斜旋转柱体和锥体微运动特征的检测。
Because of the advantage, such as simple-structure and noncontact and lossless andreal-time and so on, laser speckle measurement has been the research and applicationinterest. The message of the scatter in the speckle is important to detect and recognizeand analysis the micro-motion of the object. In the paper, with the theory of the laserscattering from rough objects, the second and the fourth order statistical properties ofthe scattered light have been studied, then the temporal and spatial statistical propertiesof the laser speckle which is applied to analyze the micro-motion of the object. Themain achievements are as followings:
1. From the scattering theory of rough surface, the expression of the two-frequencymutual coherence function from three-dimensional convex objects with rough surfaceobeying Gaussian distribution has been derived, and the influences of the shape and thesize as well as the surface roughness of the objects on the function and the coherencebandwidth have been discussed which will be for the recognization of the objects withmore complex shape.
2. Based on the Beckmann theory and Gaussian moment theorem, the expression ofthe fourth-order moment of the scattering from rough surfaces has been given which canbe expressed by two kinds of the second-order moment and the first-order moment ofthe scattered field. The influences of the incident and observation conditions and thecharacteristic parameters on the two-frequency correlation function and the angularcorrelation function of the fourth-order moment have been mainly discussed.
3. With scalar Helmholtz integral relation, the distribution on the observe plane inthe far field perpendicular to the scattering direction of the speckle filed formed in freespace from rough objects with three dimension and its intensity spatial correlationfunction have been derived, the expressions of the lateral sizes of the speckles fromrough surface with different apertures and balls and cylinders and cones have beenobtained, which is closely dependent on the shape and the size of the object and thelaser wavelength as well as the distance.
4. The temporal statistical properties of the dynamical laser speckle from in-planemoving rough surfaces and rotating rough objects have been investigated by thespatial-time correlation function of the speckle intensity fluctuation, and the expressionsfor the temporal correlation length of the speckle and the Doppler broadening due to therotating of the obeject have been obtained, and the relationships of them with themoving velocity and the shape as well as the size of the studied objects have been discussed respectively.
5.The expression of the Doppler frequency shift caused by the in-plane movingrough objects has been derived with which the Doppler frequency shift due to therotation of the objects with rotational symetry is obtained to show that the Doppler shiftis proportional to the rotating velocity and the situation of the surface elementilluminated and the sine of the sight-in-line angle, inversely proportional to the incidentwavelength, however, independent to the roughness of the objects.
6．The experiment plat form has been built to obtain the time-sequential dynamicalspeckle images of rotating rough cylinders and cones with different sight-in-line angleand different rotating velocity, which have been analyzed statistically. The results agreewell to the theoretical simulated results. With the particle group algorithm and thetheoretical derivation on the dynamic speckles, the experimental results for the timecorrelation length of the speckle have been applied to reverse the sight-in-line angle andthe rotating velocity to detect the micro-motion of the object.
引文
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