Combined Interrogation Algorithm of Amplitude Normalization and Minimum Mean Square Error for Fiber-optic Fabry-Perot Sensors

Jia-shuang FENG; Wei WANG; Xiong-xing ZHANG; Hai-bin CHEN; Zi-long GUO; Jia-xin SHEN; Jun-ying ZHANG

doi:10.3788/gzxb20204909.0906002

Journals >Acta Photonica Sinica >Volume 49 >Issue 9 >Page 0906002 > Article

Acta Photonica Sinica
Vol. 49, Issue 9, 0906002 (2020)

Combined Interrogation Algorithm of Amplitude Normalization and Minimum Mean Square Error for Fiber-optic Fabry-Perot Sensors

Jia-shuang FENG¹, Wei WANG^1,2, Xiong-xing ZHANG^1,2,*, Hai-bin CHEN^1,2..., Zi-long GUO¹, Jia-xin SHEN¹ and Jun-ying ZHANG¹|Show fewer author(s)

Author Affiliations

¹School of Optoelectronics Engineering, Xi'an Technological University, Xi'an 710021, China

²Shaanxi Province Key Lab of Photoelectric Measurement and Instrument Technology, Xi'an Technological University, Xi'an 710021, China

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DOI: 10.3788/gzxb20204909.0906002 Cite this Article

Jia-shuang FENG, Wei WANG, Xiong-xing ZHANG, Hai-bin CHEN, Zi-long GUO, Jia-xin SHEN, Jun-ying ZHANG. Combined Interrogation Algorithm of Amplitude Normalization and Minimum Mean Square Error for Fiber-optic Fabry-Perot Sensors[J]. Acta Photonica Sinica, 2020, 49(9): 0906002 Copy Citation Text

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Abstract

A combined algorithm of amplitude normalization and minimum mean square error for the cavity length interrogation of fiber-optic Fabry-Perot sensors is proposed. An amplitude normalization method is introduced to realize the equiamplitude of both the reflected and the simulated spectral signals, which helps improving the interrogating accuracy. Significant increasing of interrogating accuracy compared with conventional algorithms is verified through numerical simulations. And, a 0.72 nm resolution of cavity length interrogation is achieved in real experiment.

Keywords

Cavity length interrogation Fabry-Perot cavity Fiber-optic sensor Least square method Peak-to-peak method

$I_{\mathrm{r}}(\lambda)=I_{\mathrm{i}}(\lambda) R_{\mathrm{FP}}=I_{\mathrm{i}}(\lambda) \frac{r_{1}^{2}+\bar{r}_{2}^{2}+2 r_{1} \bar{r}_{2} \cos \left(\frac{4 \pi n L_{\mathrm{FP}}}{\lambda}\right)}{1+r_{1}^{2} \bar{r}_{2}^{2}+2 r_{1} \bar{r}_{2} \cos \left(\frac{4 \pi n L_{\mathrm{FP}}}{\lambda}\right)} $

(1)

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$\bar{r}_{2}=r_{2} \cdot l\left(L_{\mathrm{FP}}\right) $

(2)

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$\operatorname{MSE}\left(L_{\mathrm{s}k}\right)=\frac{1}{M} \cdot \sum\limits_{k=1}^{K}\left[I_{\mathrm{r}}-I_{\mathrm{s}}\left(L_{\mathrm{s}k}\right)\right]^{2} $

(3)

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$R_{\mathrm{a}}=\frac{I_{\mathrm{r}}}{I_{\mathrm{LS}}}=A(\lambda) \cdot R_{\mathrm{FP}}=A(\lambda) \cdot \frac{r_{1}^{2}+\bar{r}_{2}^{2}+2 r_{1} \bar{r}_{2} \cos \left(\frac{4 \pi n L_{\mathrm{FP}}}{\lambda}\right)}{1+r_{1}^{2} \bar{r}_{2}^{2}+2 r_{1} \bar{r}_{2} \cos \left(\frac{4 \pi n L_{\mathrm{FP}}}{\lambda}\right)} $

(4)

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