微悬臂振动干涉测量非正交信号的处理算法
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摘要
设计了干涉条纹形状对悬臂角度变化不敏感的干涉光路系统,针对实际干涉条纹光电转换信号的特点,提出了对难以保证正交化的两路信号进行实时椭圆拟合的方法。应用椭圆拟合及换算参数的结果,推导了干涉条纹相位变化的理论公式。最后,根据相位量与振动位移量的关系,以及振动位移连续性的特点,通过直接解包裹的衔接算法,得到了最终振动位移量。实验表明,该方法在保证足够采样频率的条件下,无需额外硬件计数电路,就能完成微悬臂振动位移的干涉量级精度的测量。
This paper designed interference measurement system which the stripe shape was less sensitive to cantilever's changing angles.Then analysing the characteristics of two-photoelectric receiving interference signals which were difficult to guarantee orthogonalization,a real-time ellipse fitting method was proposed.Using the ellipse fitting method and the conversion results,the theoretical formula of interference fringe phase change could be derived.Finally,according to the relationship between the phase and vibration displacement,and the property of vibration displacement's continuity,vibration displacement quantity could be obtained by using unwrapping algorithm.The results show that this method can achieve measurement level of interference precision order without additional hardware processing circuit wnder the conditions of the sufficient sampling frequency.
This paper designed interference measurement system which the stripe shape was less sensitive to cantilever's changing angles.Then analysing the characteristics of two-photoelectric receiving interference signals which were difficult to guarantee orthogonalization,a real-time ellipse fitting method was proposed.Using the ellipse fitting method and the conversion results,the theoretical formula of interference fringe phase change could be derived.Finally,according to the relationship between the phase and vibration displacement,and the property of vibration displacement's continuity,vibration displacement quantity could be obtained by using unwrapping algorithm.The results show that this method can achieve measurement level of interference precision order without additional hardware processing circuit wnder the conditions of the sufficient sampling frequency.
引文
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[16] 王选择.正交衍射光栅计量原理及在超精密工作台上的应用[D].武汉:华中科技大学,2004.
[17] 涂勇,钟金钢.一种应用于动态数字全息的快速相位解包裹算法[J].光电子激光,2012(1):148-153.Tu Yong,Zhong Jingang.A Method for Fast Phase Unwrapping in Dynamic Digital Holography[J].Journal of Optoelectronics·Laser,2012(1):148-153.
[18] 李国栋,韦春龙,于瀛洁,等.圆形域干涉图中的相位解包裹[J].光学精密工程,2000,8(5):473-477.Li Guodong,Wei Chunlong,Yu Yinjie,et al.Phase-unwrapping for Interferograms with Circle Field[J].Optics and Precision Engineering,2000,8(5):473-477.
[19] Wang Xin,Da Feipeng.Phase Unwrapping Algorithm Using Interlaced Fringe for 3DShape Measurement[J].Journal of Optoelectronics·Laser,2011,22(2):249-255.
[20] 朱勇建,李安虎,潘卫清,等.结构光测量中快速相位解包裹算法的讨论[J].光子学报,2009,38(1):184-188.Zhu Yongjian,Li Anhu,Pan Weiqing,et al.Fast Phase-unwrapping Algorithms Used for Structurallight Measurement[J].Acta Photonica Sinica,2009,38(1):184-188.
[21] 卓静一,孔令讲,周建华,等.一种液晶相控阵中基于迭代的相位恢复算法[J].光学学报,2014,34(5):0505001.Zhuo Jingyi,Kong Lingjiang,Zhou Jianhua,et al.An Iteration-based Phase Retrieval Algorithm in Liquid-crystal Phased Array[J].Acta Optica Sinica,2014,34(5):0505001.
[22] 王选择,翟中生,钟毓宁,等.应用动态调制与干涉条纹形状测量二维角度[J].光学精密工程,2014,22(2):274-279.Wang Xuanze,Zhai Zhongsheng,Zhong Yuning,et al.Measurement of Two-dimensional Angle Using Dynamic Modulation and Interference Fringe Shape[J].Optics and Precision Engineering,2014,22(2):274-279.
[2] Herfst R W,Klop W A,Eschen M,et al.Systematic Characterization of Optical Beam Deflection Measurement System for Micro and Nanomechanical Systems[J].Measurement,2014,56(10):104-116.
[3] 黄玉波,栗大超,胡小唐,等.测量微悬臂梁曲率的相移显微干涉法[J].光学精密工程,2007,15(9):1398-1402.Huang Yubo,Li Dachao,Hu Xiaotang et al.Curvature Measurement of Micro Cantilever Based on Phase-stepping Microscopic Interferometry[J].Optics and Precision Engineering,2007,15(9):1398-1402.
[4] 唐洁.压电微悬臂梁传感技术的研究[D].天津:天津大学,2005.
[5] 周雄图,张永爱,郭太良.SiO2微悬臂梁制备及其高阶谐振的传感器研究[J].光电子激光,2013(11):2055-2059.Zhou Xiongtu,Zhang Yongai,Guo Tailiang.Fabrication of SiO2 Micro-cantilever and its Sensor Application Based on Higher Resonance Modes[J].Journal of Optoelectronics·Laser,2013(11):2055-2059.
[6] Li Liyan,Wang Jian,Han Chunyang,et al.Integration Single-frequency Laser Interferometer Used to Nanometer Measurement[J].Chinese Journal of Lasers,2011,38(4):0408001-1-5.
[7] Xiong Liangcai,Zhou Quansheng,You Wu,et al.New Laser Excitation Method for Modal Analysis of Microstructure[J].Mechanical Systems and Signal Processing,2015,50:227-234.
[8] 袁群,高志山,李建欣,等.基于π/4相移平均的多光束干涉相位提取算法[J].光学学报,2011,31(11):140-145.Yuan Qun,Gao Zhishan,Li Jianxin,et al.Phase Extraction Algorithms of Multi-beam Interference Based on Phase-shifting Averaging[J].Acta Optica Sinica,2011,31(11):140-145.
[9] 黄强辉,曹益平,张可雄,等.基于四象限探测器检测干涉条纹正交信号[J].强激光和粒子束,2008,20(8):1253-1256.Huang Qianghui,Cao Yiping,Zhang Kexiong,et al.Detecting Orthogonal Signals of Interference Fringes Based on Four Quadrant Detector[J].High Power Laser and Particle Beams,2008,20(8):1253-1256.
[10] 周浩,王选择,翟中生,等.基于圆形四象限光电探测器的条纹形状识别方法研究[J].中国激光,2012,39(7):0708002-1-7.Zhou Hao,Wang Xuanze,Zhai Zhongsheng,et al.Research on Fringe Shape Recognition Methods Based on Circular Four-quadrant Photoelectric Detect[J].Chinese Journal of Lasers,2012,39(7):0708002-1-7.
[11] 黄强辉,曹益平.采用四象限探测器检测干涉条纹正交信号的新方法[J].中国激光,2009,36(5):1166-1170.Huang Qianghui,Cao Yiping.New Method for Detecting Orthogonal Signals of Laser Interference Fringes Using Four-quadrant Detector[J].Chinese Journal of Lasers,2009,36(5):1166-1170.
[12] Kakuma S,Hoshii J,Takahashi N,et al.Precision Length Change Followed by Dynamic Detection of the Laser Frequency Locked to Interference Fringe[C]//18th Congress of the International Commission for Optics.San Francisco,1999:643.
[13] Ge Z T,Takeda M.High-resolution Two-dimensional Angle Measurement Technique Based on Fringe Analysis[J].Applied Optics,2003,42(34):6859-6868.
[14] 彭东林,付敏,朱革,等.一种光强正交调制的新型线性位移传感器研究[J].光学学报,2014,34(12):1212007.Peng Donglin,Fu Min,Zhu Ge,et al.Study on a Novel Linear Displacement Sensor Based on the Orthogonal Modulating Light Intensity[J].Acta Optica Sinica,2014,34(12):1212007.
[15] 陈家凤,陈海清.基于小波变换的加权最小二乘相位解缠算法[J].光电子激光,2008(4):514-517Chen Jiafeng,Chen Haiqing.Weighted Least Squares Phase Unwrapping Algorithm Based on Multiresolution Wavelet Transform[J].Journal of Optoelectronics·Laser,2008(4):514-517.
[16] 王选择.正交衍射光栅计量原理及在超精密工作台上的应用[D].武汉:华中科技大学,2004.
[17] 涂勇,钟金钢.一种应用于动态数字全息的快速相位解包裹算法[J].光电子激光,2012(1):148-153.Tu Yong,Zhong Jingang.A Method for Fast Phase Unwrapping in Dynamic Digital Holography[J].Journal of Optoelectronics·Laser,2012(1):148-153.
[18] 李国栋,韦春龙,于瀛洁,等.圆形域干涉图中的相位解包裹[J].光学精密工程,2000,8(5):473-477.Li Guodong,Wei Chunlong,Yu Yinjie,et al.Phase-unwrapping for Interferograms with Circle Field[J].Optics and Precision Engineering,2000,8(5):473-477.
[19] Wang Xin,Da Feipeng.Phase Unwrapping Algorithm Using Interlaced Fringe for 3DShape Measurement[J].Journal of Optoelectronics·Laser,2011,22(2):249-255.
[20] 朱勇建,李安虎,潘卫清,等.结构光测量中快速相位解包裹算法的讨论[J].光子学报,2009,38(1):184-188.Zhu Yongjian,Li Anhu,Pan Weiqing,et al.Fast Phase-unwrapping Algorithms Used for Structurallight Measurement[J].Acta Photonica Sinica,2009,38(1):184-188.
[21] 卓静一,孔令讲,周建华,等.一种液晶相控阵中基于迭代的相位恢复算法[J].光学学报,2014,34(5):0505001.Zhuo Jingyi,Kong Lingjiang,Zhou Jianhua,et al.An Iteration-based Phase Retrieval Algorithm in Liquid-crystal Phased Array[J].Acta Optica Sinica,2014,34(5):0505001.
[22] 王选择,翟中生,钟毓宁,等.应用动态调制与干涉条纹形状测量二维角度[J].光学精密工程,2014,22(2):274-279.Wang Xuanze,Zhai Zhongsheng,Zhong Yuning,et al.Measurement of Two-dimensional Angle Using Dynamic Modulation and Interference Fringe Shape[J].Optics and Precision Engineering,2014,22(2):274-279.