光学学报, 2016, 36 (6): 0612003, 网络出版: 2016-06-06
一种一步π移相相位快速提取算法
A Fast Phase Extraction Algorithm with One-Step π Phase-Shifting
测量 时空条纹图 相位误差 傅里叶变换 干涉测量 measurement spatial-temporal fringes phase error Fourier transformation interferometry
摘要
提出可实现动态测量的一步π移相相位提取算法。该算法是将具有π移相的两幅干涉图进行重新排列组合,构造出一幅含有时域-空域信息的时空条纹图,通过提取时空条纹图中的信号谱来快速求解相位。在时空条纹图的频谱中,时间频率的引入使得信号频谱能够与背景干扰频谱有效分离,因此在不需要高载频的情况下依然能够对信号谱进行有效提取。将其应用在移相干涉测量中,与传统移相法进行对比发现,此算法不仅能够有效地消除移相误差,而且能够有效地消除高频噪声。另外,分析了此法在不同频率以及不同移相误差值下对测量精度的影响,在归一化空间频率大于0.03、移相误差值在±30°范围内,其面形恢复偏差均方根值能够控制在1.358×10-3λ以内。
Abstract
The one-step π phase-shifting phase extraction algorithm is presented to achieve dynamic measurement. Two interferograms with π phase-shifting are rearranged to form a spatial-temporal fringe containing time domain and space domain information. This algorithm can solve phase fast by extracting spatial-temporal pattern signal. In frequency spectrum of spatial-temporal fringe pattern, time frequency is introduced in this method, signal spectrum of spatial-temporal pattern is effectively separated from the background interference spectrum, and the signal spectrum can be extracted effectively without high carry frequency. The proposed algorithm is applied in phase-shifting interferometry. Comparing with the traditional phase shifting method, this method can eliminate phase-shifting error and high-frequency noise in test result effectively. In addition, the influence of different frequencies and phase-shifting errors on measurement accuracy is analyzed. The measurement error root mean square of the reconstruction surface can be controlled in 1.358×10-3λ when the normalized spatial frequency is more than 0.03 and phase-shifting error changes within ±30°.
朱荣刚, 朱日宏, 何勇. 一种一步π移相相位快速提取算法[J]. 光学学报, 2016, 36(6): 0612003. Zhu Ronggang, Zhu Rihong, He Yong. A Fast Phase Extraction Algorithm with One-Step π Phase-Shifting[J]. Acta Optica Sinica, 2016, 36(6): 0612003.