﻿ 基于光纤迈克尔逊干涉仪的食用油折射率的快速测量

# 基于光纤迈克尔逊干涉仪的食用油折射率的快速测量Rapid Analysis of Edible-Oil Refractive Index Based on Fiber Optical Michelson Interferometer

Abstract: Refractive index is an important indicator of edible oil quality. In this paper, we proposed a rapid measurement method for the refractive index of edible oil based on a new fiber Michelson interferometry structure. It combined a glass capillary with the classical dual-arm fiber optical Michelson interferometer. The simulation results confirmed that this method could quickly measure the refractive index of edible oil, and has a high sensitivity. The resolution is lower than 0.000001. This method provides a convenient and effective way for testing edible oil quality.

1. 引言

2. 测量装置及原理

${I}_{1}=q\sqrt{{r}_{1}}I$ (1)

${I}_{2}=\left(1-q\right)\sqrt{{r}_{2}}I{\text{e}}^{-j2{\varphi }_{1}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\varphi }_{1}=\frac{2\text{π}{n}_{1}\left({l}_{2}-{l}_{1}\right)}{\lambda }$ (2)

${I}_{3}=\left(1-q\right)\left(1-{r}_{2}\right)\sqrt{{r}_{3}}{\alpha }^{2}I{\text{e}}^{-j2{\varphi }_{2}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\varphi }_{2}=\frac{2\text{π}\left({n}_{1}{l}_{2}+{n}_{2}{l}_{3}-{n}_{1}{l}_{1}\right)}{\lambda }$ (3)

${r}_{1}=\frac{{\left({n}_{1}-1\right)}^{2}}{{\left({n}_{1}+1\right)}^{2}}$ (4)

${r}_{2}=\frac{{\left({n}_{1}-{n}_{2}\right)}^{2}}{{\left({n}_{1}+{n}_{2}\right)}^{2}}$ (5)

$\begin{array}{c}{I}_{4}=|\frac{{I}_{1}+{I}_{2}+{I}_{3}}{I}|\\ ={q}^{2}{r}_{1}+{\left(1-q\right)}^{2}{r}_{2}^{2}+{\left(1-q\right)}^{2}{\left(1-{r}_{2}\right)}^{2}{r}_{3}^{2}+q\left(1-q\right)\sqrt{{r}_{1}}\sqrt{{r}_{2}}\mathrm{cos}\left(2{\varphi }_{1}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+q\left(1-q\right)\left(1-{r}_{2}\right)\sqrt{{r}_{1}}\sqrt{{r}_{3}}\mathrm{cos}\left(2{\varphi }_{2}\right)+{\left(1-q\right)}^{2}\left(1-{r}_{2}\right)\sqrt{{r}_{2}}\sqrt{{r}_{3}}\mathrm{cos}\left(2{\varphi }_{1}-2{\varphi }_{2}\right)\end{array}$ (6)

$a={n}_{1}{l}_{2}+{n}_{2}{l}_{3}-{n}_{1}{l}_{1}$ (7)

${\lambda }_{N}=\frac{{n}_{1}{l}_{2}+{n}_{2}{l}_{3}-{n}_{1}{l}_{1}}{2N+1},\text{\hspace{0.17em}}\text{\hspace{0.17em}}N=0,1,2,3,\cdots$ (8)

3. 模拟分析

(a) (b)

Figure 3. (a) Beam propagation in the glass capillary filled with oil; (b) optical power change with the length of the glass capillary

(a) (b)

Figure 4. (a) Beam propagation in the glass capillary filled with oil; (b) optical power change with the length of the glass capillary

4. 结论

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