相移技术：五帧任意步距相移算法.doc

相移技术：五帧任意步距相移算法
G. Stoilov & T. Dragostinov
光信息存储和处理的科学院中心实验室，保加利亚，索菲亚，邮政信箱1113，
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摘要
The present paper offers a new formula for calculating the phase in interferometric measurements by the phase-stepping method. The proposed five-frame algorithm utilizes equal phase steps with an arbitrary value. Results are presented on computer simulation of the errors occurring at a phase-step different from 90and due to vibrations in the system‘interferometer-object’. © 1997 Elsevier Science Ltd.
本文提供了一种新的相移法计算在干涉测量中的相位计算公式。该算法所提出的五步运算法则利用相移量任意的等步长相移。用计算机模拟该算法得出的结果误差出现在相移步长不为90和系统中干涉对象的摆动。© 1997 Elsevier科学
1引言
It is known that the phase-stepping method (PSM), used to calculate the phase in interferometric measurements, is based on the basic interferometric equation. When two plane waves interfere, the interferometer can be adjusted to produce an interference pattern in the form of vertical fringes：
（1）
已知的相移法（PSM）是用于计算干涉测量中的相位，，干涉结果可以被校正产生垂直条纹的干涉图案：
where is the intensity of the nth picture, Z is the illuminating intensity, m is the modulation index, k is the spatial frequency, is the phase change, caused by the change in the measured quantity p, and is the angle of each phase step.
其中是第n个图像的强度，Z表示背景强度，k是空间频率，表示相位这个相位的变化，由被测量量p的变化而变化，是每个相位的变化角。
The phase is calculated by making at least three measurements of the intensity distribution at different phases. With the evolution of the phase-stepping method, several algorithms for phase calculation have become popular.
计算相位时至少要在不同相位下做三次强度分布的测量。随着相移法的发展，几种相移法的计算已经变得很普遍。
Three-frame method with a phase step 90：
90度相移的三帧法：
(2)
Three-frame method with a phase step 120:
120度相移的三帧法：

（3）
Four-frame method with a phase step 90:
90度相移的四帧法： C