Fiber Bragg Grating Spectrum Peak-Detection Algorithm Based on Difference of Gaussian

Yanzhang Lin; Yi Liu; Yuheng Pan; Guoyan Li

doi:10.3788/LOP202158.0706002

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 7 >Page 0706002 > Article

Laser & Optoelectronics Progress
Vol. 58, Issue 7, 0706002 (2021)

Fiber Bragg Grating Spectrum Peak-Detection Algorithm Based on Difference of Gaussian

Yanzhang Lin, Yi Liu, Yuheng Pan^*, and Guoyan Li

Author Affiliations

School of Computer and Information Engineering, Tianjin Chengjian University, Tianjin 300384, China

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DOI: 10.3788/LOP202158.0706002 Cite this Article Set citation alerts

Yanzhang Lin, Yi Liu, Yuheng Pan, Guoyan Li. Fiber Bragg Grating Spectrum Peak-Detection Algorithm Based on Difference of Gaussian[J]. Laser & Optoelectronics Progress, 2021, 58(7): 0706002 Copy Citation Text

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Abstract

To minimize demodulation error and system instability due to the Guassian white noise and power frequency noise, we presented a fiber Bragg grating (FBG) peak-detection algorithm based on difference of Gaussian (DoG). This algorithm enabled the detection of the peak wavelength of FBG reflection spectrum with strong noise. The mean error and standard deviation are 4 pm and 4.2 pm, respectively, which are much lower than those of other traditional algorithms. Experimental results show that the DoG algorithm can provide good stability and low demodulation error. In addition, it can substantially resist the noise in the FBG reflection spectrum, thereby improving the accuracy of the FBG demodulation system.

Keywords

DoG algorithm fiber Bragg grating fiber optics peak detection reflection spectrum

λ_{b} = 2 n_{e f f} Λ

，（1）

I (λ) = A e x p [- 4 l n 2 (\frac{λ - λ_{b}}{Δ λ})]

，（2）

F_{s, h} (x) = \{\begin{array}{l} h, |x| < \frac{s}{2} \\ 0, o t h e r w i s e \end{array}

。（3）

S_{h} (x) = \{\begin{array}{l} h, x > 0 \\ 0, o t h e r w i s e \end{array}

。（4）

G_{σ} (x) = \frac{1}{\sqrt[]{2 π} σ} e x p (\frac{- x^{2}}{2 σ^{2}})

，（5）

\frac{\partial G_{σ}}{\partial σ} = \frac{1}{\sqrt[]{2 π}} (\frac{- 1}{σ^{2}} + \frac{x^{2}}{σ^{4}}) e x p (\frac{- x^{2}}{2 σ^{2}})

，（6）

\frac{\partial^{2} G_{σ}}{\partial x^{2}} = \frac{1}{\sqrt[]{2 π} σ} (\frac{- 1}{σ^{2}} + \frac{x^{2}}{σ^{4}}) e x p (\frac{- x^{2}}{2 σ^{2}})

，（7）

\frac{\partial G_{σ}}{\partial σ} = σ \frac{\partial^{2} G_{σ}}{\partial x^{2}}

，（8）

\frac{G_{k σ} (x) - G_{σ} (x)}{k σ - σ} \approx \frac{\partial G}{\partial σ}

，（9）

G_{k σ} (x) - G_{σ} (x) \approx (k - 1) σ^{2} Δ^{2} G

。（10）

L (x, σ) = G_{σ} (x) * F_{s, h} (x)

，（11）

(k - 1) σ^{2} Δ^{2} G * F_{s, h} (x) \approx [G_{k σ} (x) - G_{σ} (x)] * F_{s, h} (x) = L (x, k σ) - L (x, σ)

，（12）

\int_{- \infty}^{+ \infty} S_{h} (u) \frac{\partial^{2} G_{σ} (x - u)}{\partial x^{2}} d u = h \int_{- \infty}^{0} \frac{\partial^{2} G_{σ} (x - u)}{\partial x^{2}} d u = h \frac{\partial G_{σ} (x)}{\partial σ}

，（13）

F_{s, h} (x) = S_{h} (x - \frac{s}{2}) + S_{h} (- x + \frac{s}{2}) - h

，（14）

F_{s, h} (x) * \frac{\partial^{2} G_{σ} (x)}{\partial x^{2}} = h \frac{\partial G_{σ} (x - \frac{s}{2})}{\partial x} - h \frac{\partial G_{σ} (x + \frac{s}{2})}{\partial x}

。（15）

s < 2 \sqrt[]{3} σ

。（16）

D_{σ_{1}, σ_{2}} (x) = G_{σ_{1}} (x) - G_{σ_{2}} (x) = \frac{1}{\sqrt[]{2 π} σ} e x p (- \frac{- x^{2}}{2 σ^{2}}) \times \{1 - \frac{σ_{1}}{σ_{2}} e x p \{\frac{- x^{2} [- x^{2} (σ_{1}^{2} - σ_{2}^{2})]}{2 σ_{1}^{2} σ_{2}^{2}}\}\}

。（17）

\underset{σ_{2} - σ_{1} \to 0^{+}}{l i m} e x p [\frac{- x^{2} (σ_{1}^{2} - σ_{2}^{2})}{2 σ_{1}^{2} σ_{2}^{2}}] = \frac{- x^{2} (σ_{1}^{2} - σ_{2}^{2})}{2 σ_{1}^{2} σ_{2}^{2}} + 1

。（18）

\underset{σ_{2} - σ_{1} \to 0^{+}}{l i m} D_{σ_{1}, σ_{2}} (x) = \frac{1}{\sqrt[]{2 π} σ_{1}} e x p (- \frac{- x^{2}}{2 {σ_{1}}^{2}}) \times [\frac{σ_{2} - σ_{1}}{σ_{2}} - \frac{x^{2} (σ_{1} + σ_{2}) (σ_{2} - σ_{1})}{2 σ_{1} σ_{2}^{3}}]

。（19）

\frac{1}{\sqrt[]{2 π}} (\frac{δ}{σ_{1}^{2}} - \frac{δ x^{2}}{σ_{1}^{4}}) e x p (- \frac{x^{2}}{2 σ_{1}^{2}}) = δ σ_{1} \frac{\partial^{2} G_{σ_{1}} (x)}{\partial x^{2}}

，（20）

W \approx \{\begin{array}{l} 2 \sqrt[]{3} σ_{1} + 2 (σ_{2} - σ_{1}), σ_{1} < σ_{2} \leq 1.2 σ_{1} \\ 2 \sqrt[]{3} σ_{1} + σ_{2} - σ_{1}, 1.2 σ_{1} < σ_{2} \leq 3 σ_{1} \\ 6 σ_{1}, σ_{2} > 3 σ_{1} \end{array}

。（21）

Yanzhang Lin, Yi Liu, Yuheng Pan, Guoyan Li. Fiber Bragg Grating Spectrum Peak-Detection Algorithm Based on Difference of Gaussian[J]. Laser & Optoelectronics Progress, 2021, 58(7): 0706002

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