基于时频波谱对易原理分析莫尔条纹谱
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摘要
数值解析信号波形时频域对易演变过程,研究任意信号波形与频率组分的内在联系,并将该对易原理应用于莫尔条纹相位分析,提取相位信息。采用矩形窗模拟冲激波形和直流波形的变换过程,通过控制矩形窗函数窗宽,获得各种宽度矩形脉冲,窗宽趋于零情况下获得冲激波形,趋于∞获得直流波形。自开发快速傅里叶变换(fast Fourier transform,FFT)系统,对矩形脉冲实施离散傅里叶变换,方便快捷获得相应频谱数值解析波形,分析波形与频谱对易关系。结果发现,矩形窗函数频谱是Sa函数,窗宽变化导致Sa函数波形变化。窗宽减小时,Sa函数波形展宽,振动舒缓,趋于零极限时,变成直流波形。窗宽增大时,Sa函数波形紧缩,振动加剧,趋于∞的极限时,演变成δ冲激波形,信号波形时频域是对易的。根据时频域波形与频谱对易关系,在分析莫尔条纹时,将莫尔条纹的一级谱滤出并归一,由波谱对易原理,时域信号将体现Sa函数,使条纹对比分明,便于提取相位信息。
The mutual evolving processes of signals' waveforms and their spectra were numerically analyzed in time and frequency domains.The purpose was to research the essential relation between the signals' waveforms and their spectra.Then,the mutual transform principle was applied to analyze moirépattern spectra,acquiring phase distribution information of the pattern.The rectangular window function was used to simulate the mutual transform between the impulse signal and direct-current waveform.Many rectangular window signals with deferent widths were obtained by changing the window width.The unit impulse signal was obtained by changing the width down to zero,and the direct-current waveform obtained by changing the width up to+∞.For smart,quick,and easy implementation of discrete Fourier transforms to rectangular pulses and obtain signals' spectra,a simple FFT system was worked out.With its calculating,the mutual evolving processes of signals' waveforms and their spectra were tracked deeply.All signals here were transformed with it.As the result,first,the spectra of rectangular window signals were in the form of sampling function[Sa(x)=sin(x)/x].Second,with the change in the window's width,the waveform of Sa(x)changed.Third,when the width decreased,the waveform of Sa(x)extended,and vibrated more slowly.It changed into direct-current waveform when the width decreased to zero.Last,when the width increased,the waveform of Sa(x)shranked,and vibrated faster.It changed into impulse waveform when the width increased to+∞.Signals' waveforms were in mutual transforms between the time and frequency domain.The transforming essence was considered as that the frequency component principle in Fourier series theory is reflected in the frequency domain.According to the principle of mutual transforms between signals' waveforms and their spectra,the first order spectrum of the moirépattern was extracted out and normalized to a constant one when the moirépatterns were analyzed for acquiring their phase information.By the normalization,the moirépattern should take on the sampling function model,which showed high contrast level.This new pattern was convenient for acquiring the phase information.
The mutual evolving processes of signals' waveforms and their spectra were numerically analyzed in time and frequency domains.The purpose was to research the essential relation between the signals' waveforms and their spectra.Then,the mutual transform principle was applied to analyze moirépattern spectra,acquiring phase distribution information of the pattern.The rectangular window function was used to simulate the mutual transform between the impulse signal and direct-current waveform.Many rectangular window signals with deferent widths were obtained by changing the window width.The unit impulse signal was obtained by changing the width down to zero,and the direct-current waveform obtained by changing the width up to+∞.For smart,quick,and easy implementation of discrete Fourier transforms to rectangular pulses and obtain signals' spectra,a simple FFT system was worked out.With its calculating,the mutual evolving processes of signals' waveforms and their spectra were tracked deeply.All signals here were transformed with it.As the result,first,the spectra of rectangular window signals were in the form of sampling function[Sa(x)=sin(x)/x].Second,with the change in the window's width,the waveform of Sa(x)changed.Third,when the width decreased,the waveform of Sa(x)extended,and vibrated more slowly.It changed into direct-current waveform when the width decreased to zero.Last,when the width increased,the waveform of Sa(x)shranked,and vibrated faster.It changed into impulse waveform when the width increased to+∞.Signals' waveforms were in mutual transforms between the time and frequency domain.The transforming essence was considered as that the frequency component principle in Fourier series theory is reflected in the frequency domain.According to the principle of mutual transforms between signals' waveforms and their spectra,the first order spectrum of the moirépattern was extracted out and normalized to a constant one when the moirépatterns were analyzed for acquiring their phase information.By the normalization,the moirépattern should take on the sampling function model,which showed high contrast level.This new pattern was convenient for acquiring the phase information.
引文
[1]ZHENG Jun-li,YING Qi-heng,YANG Wei-li(郑君里,应启珩,杨为理).Signals and Systems(信号与系统).Beijing:Higher Education Press(北京:高等教育出版社),2000.150.
[2]Oppenheim A V,Willsky A S,Hamid N S.Signals and Systems.Beijing:Publishing House of Electronics Industry,2002.
[3]Lee E A,Varaiya P.Structure Analyzing of Signals and Systems.Beijing:Publishing House of Electronics Industry,2006.
[4]Cheng H C,Shiu M S.Appl.Opt.,2012,51(36):8762.
[5]Xi P,Mei K,Brauler T,et al.Appl.Opt.,2011,50(3):366.
[6]PENG Guan-yun,JIANG Ze-hui,LIU Xing-e,et al(彭冠云,江泽慧,刘杏娥,等).Spectroscopy and Spectral Analysis(光谱学与光谱分析),2012,32(7):1935.
[7]Sebastien V,Daniel L,Kostadinka B,et al.Appl.Opt.,2012,51(11):1701.
[8]PENG Guan-yun,WANG Yu-rong,REN Hai-qing(彭冠云,王玉荣,任海青,等).Spectroscopy and Spectral Analysis(光谱学与光谱分析),2013,33(3):829.
[9]ZHANG Bin,SONG Yang,SONG Yi-zhong,et al(张斌,宋旸,宋一中,等).Chinese Journal of Laser(中国激光),2006,33(4):531.
[2]Oppenheim A V,Willsky A S,Hamid N S.Signals and Systems.Beijing:Publishing House of Electronics Industry,2002.
[3]Lee E A,Varaiya P.Structure Analyzing of Signals and Systems.Beijing:Publishing House of Electronics Industry,2006.
[4]Cheng H C,Shiu M S.Appl.Opt.,2012,51(36):8762.
[5]Xi P,Mei K,Brauler T,et al.Appl.Opt.,2011,50(3):366.
[6]PENG Guan-yun,JIANG Ze-hui,LIU Xing-e,et al(彭冠云,江泽慧,刘杏娥,等).Spectroscopy and Spectral Analysis(光谱学与光谱分析),2012,32(7):1935.
[7]Sebastien V,Daniel L,Kostadinka B,et al.Appl.Opt.,2012,51(11):1701.
[8]PENG Guan-yun,WANG Yu-rong,REN Hai-qing(彭冠云,王玉荣,任海青,等).Spectroscopy and Spectral Analysis(光谱学与光谱分析),2013,33(3):829.
[9]ZHANG Bin,SONG Yang,SONG Yi-zhong,et al(张斌,宋旸,宋一中,等).Chinese Journal of Laser(中国激光),2006,33(4):531.