基于CORDIC算法的单频激光干涉信号处理系统半波长误差分析与消除

doi:10.3969/j.issn.1000-1158.2021.03.05

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摘要为了满足纳米级分辨率和高速处理,设计了基于CORDIC算法的激光干涉信号处理系统。研究发现信号处理系统存在半波长大小的粗大误差。对该半波长误差的特点与形成机理进行了研究,研究表明该半波长误差的根源为小数相位测量存在一定的误差区间,在干涉信号相位零点附近,该误差区间导致小数相位处于［2π^-,0⁺］,具有不确定性;与整数相位结合时,可能产生半波长误差。在对半波长误差深入研究的基础上,给出修正表,提出了基于CORDIC算法相位补偿技术,以消除半波长粗大误差对激光干涉测量系统的影响。实验结果表明:在信号处理系统中,该相位补偿技术能够有效地消除半波长粗大误差,由CORDIC算法引入的总量化误差小于±0.05nm。

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	樊宏伟
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	董欣媛
	铁咪咪

关键词 ：计量学, 激光干涉仪, CORDIC, 半波长误差, 近似误差

Abstract：In order to meet the nano-scale resolution and high-speed processing, a laser interference signal processing system based on CORDIC algorithm was designed. A gross error of half-wavelength in the signal processing system was founded during the research process. The characteristics and formation mechanism of the gross error were studied, and the research showed that the root cause of the half-wavelength error was the existence of a certain error interval in phase measurement, thus, near the zero-point of interferometric signal phase, the error interval caused the decimal phase to be in ［2π^-,0⁺］, which was uncertain. While the decimal phase combining with integer phase, the half-wavelength error might occur. On the basis of in-depth research of the gross error, a CORDIC algorithm phase compensation technique based on the correction table was proposed to eliminate the influence of the half-wavelength error on the laser interferometry system. The experimental results showed that the phase compensation technique could effectively eliminate the half-wavelength gross error in the signal processing system, and the total quantization error introduced by the CORDIC algorithm was less than ±0.05nm.

Key words： metrology laser interferometer CORDIC half-wavelength error approximation error

收稿日期: 2019-07-30 发布日期: 2021-03-23

PACS:

TB921

基金资助:国家重点研发计划资助(2016YFF0200601)

通讯作者: 刁晓飞(1984-),男,河北衡水人,中国计量科学研究院副研究员,从事几何量精密测量、激光干涉测量与直径形状计量技术研究。Email: diaoxf@nim.ac.cn E-mail: diaoxf@nim.ac.cn

作者简介: 樊宏伟(1994-),男,甘肃庆阳人,天津大学硕士研究生,研究方向为干涉信号处理。Email: 18293424595@163.com

引用本文:

樊宏伟,刁晓飞,张福民,薛梓,董欣媛,铁咪咪. 基于CORDIC算法的单频激光干涉信号处理系统半波长误差分析与消除[J]. 计量学报, 2021, 42(3): 287-293.
FAN Hong-wei,DIAO Xiao-fei,ZHANG Fu-min,XUE Zi,DONG Xin-yuan,TIE Mi-mi. Analysis and Elimination of Half-wavelength Error in Homodyne Laser Interference Signal Processing System Based on CORDIC Algorithm. Acta Metrologica Sinica, 2021, 42(3): 287-293.

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［1］周奇, 刘炳锋, 连笑怡, 等. 大范围二维纳米位移台的控制及非线性校准的实验研究［J］. 计量学报, 2018, 39(6): 771-776.
Zhou Q, Liu B F, Lian X Y, et al. Experimental research on the control and non-linear calibration of large-scale two-dimensional nanometer displacement stage［J］. Acta Metrologica Sinica, 2018, 39(6): 771-776.
［2］施玉书,张树,连笑怡,等. 毫米级纳米几何特征尺寸计量标准装置多自由度激光干涉计量系统［J］. 计量学报, 2020, 41(7): 769-774.
Shi Y S,Zhang S,Lian X Y, et al. Multi-DOF Laser Interferometry System for Metrological Standard Device for Nano-geometrical Characteristic Size in Millimeter Range［J］. Acta Metrologica Sinica, 2020, 41(7): 769-774.
［3］贾平平. 激光干涉仪在PCB数控机床精度检测中的应用研究［J］. 机床与液压, 2018, 46(8): 129-131.
Jia P P. Application research of laser interferometer in accuracy detection of PCB NC machine［J］. Machine Tool & Hydraulics, 2018, 46(8): 129-131.
［4］Diao X F, Xue Z, Kang Y H. High resolution aspheric surface measurement technology based on laser interferometer［C］// Eighth International Symposium on Advanced Optical Manufacturing & Testing Technology (AOMATT). Suzhou, 2016.
［5］蔡海蛟. 皮米分辨力双频激光干涉仪相位细分技术研究［D］. 哈尔滨:哈尔滨工业大学, 2015.
［6］Lei Y, Hu P C, Diao X F, et al. Fast and ultra-precision laser heterodyne interferometry signal processing method based on digital delay line loop［C］// Fifth International Symposium on Instrumentation Science and Technology. Shenyang, 2009.
［7］张朝柱, 韩吉南, 燕慧智. 高速高精度固定角度旋转CORDIC算法的设计与实现［J］. 电子学报, 2016, 44(2): 485-490.
Zhang C Z, Han J N, Yan H Z. Design and Implementation of CORDIC Algorithm for High Speed and Precision Fixed Angle of Rotation［J］. Acta Electronica Sinica, 2016, 44(2): 485-490.
［8］宋定昆, 刘桂雄, 唐文明. 基于CORDIC算法的动态FIR数字滤波器FPGA实现与应用［J］. 中国测试, 2017, 43(7): 97-102.
Song D K, Liu G X, Tang W M. FPGA implementation and application of dynamic FIR digital filter based on CORDIC algorithm［J］. China Measurement & Test, 2017, 43(7): 97-102.
［9］郭玄标. 单频激光干涉测振关键技术研究［D］. 哈尔滨:哈尔滨工业大学, 2015.
［10］夏豪杰, 胡梦雯, 张欣. 单频激光干涉仪正交信号的高精度处理［J］. 光学精密工程, 2017, 25(9): 2309-2316.
Xia H J, Hu M W, Zhang X. High precision processing of quadrature signals for homodyne interferometer［J］. Optics and Precision Engineering, 2017, 25(9): 2309-2316.
［11］王晓娜, 钟玉龙, 朱维斌, 等. 光栅数字细分CORDIC算法总量化误差分析［J］. 计量学报, 2016, 37(01): 10-14.
Wang X N, Zhong Y, L Zhu W B, et al. Analysis of the overall quantization error for CORDIC algorithm in grating digital subdivision［J］. Acta Metrologica Sinica, 2016, 37(01): 10-14.
［12］Tan J B, Yang H X, Hu P C, et al. Identification and elimination of half-synthetic wavelength error for multi-wavelength long absolute distance measurement［J］. Measurement Science and Technology, 2011, 22(11): 115-301.
［13］Abouzeid A, Pollinger F, Meinershagen K, et al. Diode-laser-based high-precision absolute distance interferometer of 20 m range［J］. Applied Optics, 2009, 48(32): 88-94.
［14］赵素文. 单频干涉精密距离测量关键技术研究［D］. 西安:中国科学院研究生院(西安光学精密机械研究所), 2012.
［15］Volder J E. The CORDIC trigonometric computing technique［J］. IRE Transactions on Electronic Computers, 1959, 8(3): 330-334.
［16］HuY H. The quantization effects of the CORDIC algorithm ［J］. IEEE Transactions on Signal Processing, 1992, 40(4): 837-839.