# Algorithm of FBG Spectrum Distortion Correction for Optical Spectra Analyzers with CCD Elements

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Explanation

## 3. Collecting of Initial Data

## 4. Mathematical Processing

_{0}) can be obtained:

_{0}is the initial TINT value, at which the calibration is performed; t is the arbitrary TINT value; k(A

_{0}) is the linear dependence slope; and A

_{0}is the amplitude, obtained at the initial TINT (t

_{0}).

_{0}is initial TINT, at which the amplitudes A

_{0}are measured.

_{0}to t

_{M}, namely t

_{j}= t

_{0}+ j(t

_{M}− t

_{0})/M.

_{i}

_{,j}(t

_{j},A

_{i}

_{,0}) for i-th sampling point can be written as dependence on TINT (t

_{j}) and on the initial amplitude value A

_{i,}

_{0}for each:

_{i}

_{,0}) in Equation (2) for each initial value of the amplitude in each i-th spectrum point by calculating the characteristic points {A

_{i}

_{,0}, k(A

_{i}

_{,0})}, i = 1,N using the least square method by formula:

_{i}

_{,0}, K

_{i}}, i = 1, N, which, in turn, allow determining the α and β values–the linear dependence coefficients of the slope on A

_{0}in Equation (3), by the linear equations system solving the following:

_{i}

_{,0}, K

_{i}}, i = 1, N, and the coefficients of the linear dependence of the slope in Equation (3)–α and β, in relation to Equation (6), the entire right-hand side becomes known. It allows to recalculate the initial amplitude of the arbitrary spectrum point, measured at initial TINT, depending on the amplitude, measured at arbitrary TINT (t):

_{i}

_{,0}) is the amplitude, measured at arbitrary TINT, α and β are the linear dependence coefficients of the slope in Equation (3), obtained as the solution of the linear equation system in Equation (8), and A

_{i}

_{,0}is the amplitude, measured at initial TINT.

## 5. Experimental Setup

## 6. Calibration Data

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The broadband radiation spectra, obtained at different TINT values (1–20 ms, 2–48 ms, 3–77 ms, 4–106 ms, 5–135 ms).

**Figure 5.**Experimental setup (

**a**); FBG interrogator (

**b**): 1–IBSEN I-MON 512 USB; 2–laser source SLD-761-HP1-DIL; 3–optic channel switch Sercalo MEMS switch rSC 1 × 8; 4–laser source and optical switch maintaining module; 5–computer Wafer ULT-3; 6–optical cross; 7–power supply.

**Figure 6.**Calibration curves–FBG central wavelength dependences on temperature. The measured data: (

**a**) without spectrum correction; (

**b**) with spectrum correction.

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**MDPI and ACS Style**

Anfinogentov, V.; Karimov, K.; Kuznetsov, A.; Morozov, O.G.; Nureev, I.; Sakhabutdinov, A.; Lipatnikov, K.; Hussein, S.M.R.H.; Ali, M.H.
Algorithm of FBG Spectrum Distortion Correction for Optical Spectra Analyzers with CCD Elements. *Sensors* **2021**, *21*, 2817.
https://doi.org/10.3390/s21082817

**AMA Style**

Anfinogentov V, Karimov K, Kuznetsov A, Morozov OG, Nureev I, Sakhabutdinov A, Lipatnikov K, Hussein SMRH, Ali MH.
Algorithm of FBG Spectrum Distortion Correction for Optical Spectra Analyzers with CCD Elements. *Sensors*. 2021; 21(8):2817.
https://doi.org/10.3390/s21082817

**Chicago/Turabian Style**

Anfinogentov, Vladimir, Kamil Karimov, Artem Kuznetsov, Oleg G. Morozov, Ilnur Nureev, Airat Sakhabutdinov, Konstantin Lipatnikov, Safaa M. R. H. Hussein, and Mustafa H. Ali.
2021. "Algorithm of FBG Spectrum Distortion Correction for Optical Spectra Analyzers with CCD Elements" *Sensors* 21, no. 8: 2817.
https://doi.org/10.3390/s21082817