基于蒙特卡洛方法的波导光栅响应谱测量的误差分析

Error Analysis of Waveguide Grating Response Spectrum Measurement Based on Monte Carlo Method

针对测量基于低相干干涉原理的波导光栅响应谱时存在的量化误差源和位置误差源,提出了一种基于蒙特卡洛原理的误差源分析方法。根据蒙特卡洛随机模拟原理,设定7400组标准的原始数据样本,在每一个采样点上叠加随机产生的误差数据,该误差数据由所设定的概率分布和误差源的误差范围所产生,再利用快速傅里叶变换计算得到含误差的幅值谱和相位谱,进而可得到标准谱与实际谱之间的误差,最后对误差进行统计。根据统计结果,分析了在叠加正态分布误差和均匀分布误差情况下,量化误差源和位置误差源分别同幅值误差和相位误差的关系,并且得到了同时叠加两种误差情况下幅值误差和相位误差的分布情况。分析结果表明:不管是叠加正态分布误差还是均匀分布误差,最后每个采样点的误差分布都是正态分布,并且幅值误差和相位误差都随所叠加误差值的增大而增大。该误差分布结果为波导光栅响应谱的精确测量提供了很有意义的参考价值,可根据误差分布结果确定实验所需要的A/D转换器的位数,以及电位移平台位置误差的控制范围,并且由于数据量很大,该方法也更加简单有效。

Aiming at the quantization error source and position error source that exist when measuring the response spectrum of the waveguide grating based on the principle of low coherence interference,an error source analysis method based on the Monte Carlo principle is proposed.According to the Monte Carlo stochastic simulation principle,7400 standard raw data samples are set,and randomly generated error data is superimposed on each sampling point.The error data is generated by the set probability distribution and the error range of the error source.Then the fast Fourier transform is used to calculate the amplitude spectrum and the phase spectrum with errors,and then the error between the standard spectrum and the actual spectrum can be obtained,and finally the error is counted.According to the statistical results,the relationship between the quantization error source and the position error source and the amplitude error and the phase error in the case of superimposing the normal distribution error and the uniform distribution error is analyzed,and the amplitude error in the case of superimposing the two errors at the same time is obtained.And the distribution of the phase error.The analysis results show that whether it is superimposed normal distribution error or uniform distribution error,the final error distribution of each sampling point is normal distribution,and the amplitude error and phase error increase with the increase of the superimposed error value.The error distribution result provides a meaningful reference value for the accurate measurement of the response spectrum of the waveguide grating.The number of bits of the A/D converter required for the experiment and the control range of the position error of the electric displacement platform can be determined according to the error distribution result.And because of the large amount of data,this method is simpler and more effective.