Stetson K A
Appl Opt. 1972 Aug 1;11(8):1725-31. doi: 10.1364/AO.11.001725.
In this paper, a mathematical technique called the method of stationary phase is presented for the purpose of obtaining approximate solutions for characteristic fringe functions in hologram interferometry. The cases of greatest concern are where holograms are formed of objects that vibrate simultaneously in different geometrical patterns according to sinusoidal time functions whose frequencies are related by rational numbers. The method assumes that the object motion is sufficiently large that contributions to the fringe function come only from the holographic recordings of the object at positions where its velocity is zero. At such position, the phase of the light scattered from an object point is stationary with respect to time, and the method permits the approximate calculation of the relative intensity of the partial recording at these positions. The fringe functions become expressions similar to those found in multiple-beam interferometry,and fringe patterns can be understood more easily. The case of two sinusoidal vibrations at a frequency ratio of 2: 1 is considered experimentally and theoretically according to the method presented.
本文提出了一种称为驻相法的数学技术，目的是获得全息干涉术中特征条纹函数的近似解。最受关注的情况是，全息图由根据频率呈有理数关系的正弦时间函数以不同几何模式同时振动的物体形成。该方法假设物体运动足够大，以至于条纹函数的贡献仅来自物体在其速度为零的位置的全息记录。在这样的位置，从物体点散射的光的相位相对于时间是静止的，并且该方法允许近似计算这些位置处部分记录的相对强度。条纹函数变得类似于多光束干涉术中发现的表达式，并且条纹图案可以更容易理解。根据所提出的方法，对频率比为2:1的两个正弦振动的情况进行了实验和理论研究。
