Stetson K A
Appl Opt. 1975 Sep 1;14(9):2256-9. doi: 10.1364/AO.14.002256.
When an object undergoes a combination of minute rigid-body motion and homogeneous deformation, its vectorial displacements can be described by a general, 3 x 3 matrix transformation. This same matrix can be used to transform the sensitivity vector of hologram interferometry into a fringe vector that defines the fringes as laminae that are intersected by the surface of the object. When fringes are observable on more than one surface of a three-dimensional object whose shape is known, it is possible to determine the fringe vector from the shape and spacing of the fringes on the object. If three holographic views are available, from which three fringe vectors can be determined for three known sensitivity vectors, it is possible to determine the transformation matrix, and this, in turn, can be decomposed into deformation and rotation matrices. More than three views allow the use of least-square-error theory to minimize errors in data taking.
当一个物体经历微小刚体运动和均匀变形的组合时，其矢量位移可以用一个通用的3×3矩阵变换来描述。同一个矩阵可用于将全息干涉测量的灵敏度矢量转换为条纹矢量，该条纹矢量将条纹定义为由物体表面相交的薄片。当在形状已知的三维物体的多个表面上都能观察到条纹时，就可以根据物体上条纹的形状和间距来确定条纹矢量。如果有三个全息视图，从这三个视图中可以为三个已知的灵敏度矢量确定三个条纹矢量，那么就有可能确定变换矩阵，进而可以将其分解为变形矩阵和旋转矩阵。超过三个视图则允许使用最小二乘法理论来最小化数据采集过程中的误差。
