基于时频波谱对易原理分析莫尔条纹谱

Analyzing MoiréPattern Spectra Based on the Mutual Transform between Signals' Waveform in Time Domain and Their Spectra in Frequency Space

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 frequen cy domains. The purpose was to research the essential relation between the signals＇waveforms and their spectra. Then, the mu tual transform principle was applied to analyze moir6 pattern 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 wave form. 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 -]-oo. 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 wave form 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 q-oo. Signals＇ waveforms were in mutual transforms between the time and frequency domain. The transforming essence was considered as that the frequency com ponent principle in Fourier series theory is reflected in the frequency domain. According to the principle of mutual transforms be tween signals＇ waveforms and their spectra, the first order spectrum of the moire pattern was extracted out and normalized to a constant one when the moire patterns were analyzed for acquiring their phase information. By the normalization, the moire pat tern should take on the sampling function model, which showed high contrast level. This new pattern was convenient for acqui ring the phase information.