基于隐函数模型的光学微腔传输光谱拟合算法

摘要

The optical microcavity has high Q factors and high sensitivity, and has a good application prospect inhigh-precision biosensing. In order to deal with the problem that the Lorentz fitting algorithm cannot fit the asymmetricwaveform and the splitting mode waveform of the optical microcavity, the implicit function model algorithm isproposed. Firstly, according to the method, the template waveform was established and operated by panning andzooming.Then the parameter values were optimized by the Levenberg-Marquardt (LM) algorithm. Finally, data fitting of symmetrical waveform, asymmetric waveform and splitting mode waveform could be achieved. Through constructing the data acquisition system of optical microcavity, the Gauss, the Lorentz and the implicit function model algorithm were used to fit the experimental data of different refractive index of solutions. The results show that MSE of the implicit function model algorithm is one order of magnitude lower than other two algorithms, and has a coefficientof determination (R2) of 0.99. The resonant frequency error of implicit function model algorithm is the smallest,the resonant frequency of implicit function model algorithm is the largest, and the sensitivity of implicit function model algorithm is the highest. Therefore, the fitting effect of the implicit function model algorithm is better and it can efficiently improve the sensitivity of the optical microcavity.%光学微腔品质因子高、灵敏度高,在精密生物传感方面有广阔的应用前景.针对洛伦兹拟合算法不能很好地拟合光学微腔输出端非对称波形和劈裂模式波形的问题,提出了隐函数模型算法.该算法首先建立模板波形,然后经平移、放缩理论实现模板波形操作,利用Levenberg-Marquardt(LM)算法优化参数值,能够实现对称波形、非对称波形和劈裂模式波形数据拟合.通过搭建光学微腔数据采集系统,采用高斯、洛伦兹和隐函数模型算法对不同折射率溶液的实验数据进行拟合.结果表明:隐函数模型算法比前两种算法的MSE低1个数量级,且拟合优度(R2)达到了0.99,拟合效果较好;隐函数模型算法谐振频率误差最小,谐振频率偏移量最大,对应的灵敏度最高,有利于提高光学微腔灵敏度.