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Xiaoting Wang, Ruiqiang Chen, Shundi Hu, et al. Optical microcavity transmission spectrum fitting algorithm based on the implicit function model[J]. Opto-Electronic Engineering, 2017, 44(7): 701-709. doi: 10.3969/j.issn.1003-501X.2017.07.006
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Optical microcavity transmission spectrum fitting algorithm based on the implicit function model
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Abstract
The optical microcavity has high Q factors and high sensitivity, and has a good application prospect in high-precision biosensing. In order to deal with the problem that the Lorentz fitting algorithm cannot fit the asymmetric waveform and the splitting mode waveform of the optical microcavity, the implicit function model algorithm is proposed. Firstly, according to the method, the template waveform was established and operated by panning and zooming.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 coefficient of 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.-
Keywords:
- optical microcavity /
- implicit function model /
- LM algorithm /
- data fitting /
- transmission spectrum
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References
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Overview
Abstract: Due to its high quality factor and high sensitivity, the optical microcavity has well promising applications in optical sensing, biomedical, nonlinear optics, environmental monitoring and quantum physics. The principle is that when analyses enter the optical microcavity, the effective refractive index of the solution will change, and the resonant wavelength will be shifted. Therefore, it is very important to find out the variation of resonant wavelength to improve the sensing accuracy of the optical microcavity. A traditional method to do this is using the Lorentz algorithm to fit the transmission spectrum of the optical microcavity. However, the Lorentz fitting algorithm cannot well fit the spectrum when it is an asymmetric waveform or there is a splitting mode waveform within the optical microcavity. In order to deal with the problem, the implicit function model algorithm is proposed in this study. The process of our method can be described as follows. The template waveform was selected and established first, followed by the panning and zooming operations. Then, a traditional method was used to set the initial value of the parameter of objective function, and the parameter values were optimized by the Levenberg-Marquardt (LM) algorithm, which could achieve data fitting results of symmetrical waveform, asymmetric waveform and splitting mode waveform. Note that there was no definite mathematical expression according to the implicit function model algorithm, so different methods were used to obtain the partial derivative of the factor in the Jacobian matrix by means of the template data. In this study, experimental platform, including the optical microcavity, tunable laser source and controller, data acquisition and control system, was established. Different concentrations of solutions of dimethyl sulfoxide, glucose and glycerol were tested as the analyte, and the Gauss, the Lorentz and the implicit function model algorithm were used to fit the experimental data of different transmission spectrums. The results show that MSE of the implicit function model algorithm is one order of magnitude lower than other two algorithms, and the coefficient of determination (R2) is 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 and has a reliable basis on the follow-up to find the spectral resonance center to detect the biological components. The digital implicit function model algorithm will have a wide application prospect in any shape waveform data fitting.
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Xiaoting Wang, Ruiqiang Chen, Shundi Hu, et al. Optical microcavity transmission spectrum fitting algorithm based on the implicit function model[J]. Opto-Electronic Engineering, 2017, 44(7): 701-709. doi: 10.3969/j.issn.1003-501X.2017.07.006
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Figure 1.
The schematic diagram of implicit function model algorithm diagram.
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Figure 2.
The schematic diagram of actual sampling data waveforms.
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Figure 3.
The experimental device of optical microcavity. (a) Diagram of the experiment setup. (b) Photograph of the MBR coupling with a fused fiber, taken by microscope.
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Figure 4.
The distribution map of frequency detuning obtained by 100 sets of water solution data fitted by implicit function model algorithm.
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Figure 5.
Comparison of SSE values for Gaussian, Lorentz and implicit function model in three different solutions(IFM: Implicit function model). (a) DMSO RI=1.3526. (b) Glucose RI=1.3587. (c) Glycerol RI=1.3511.
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Figure 6.
Contrast map of three solutions fitted by Gaussian, Lorentz and implicit function model(ED: Experimental data; IFM: Implicit function model). (a) DMSO RI=1.3526. (b) Glucose RI=1.3587. (c) Glycerol RI=1.3511.
