## Abstract

The back-scattered pattern produced by a plane-polarized beam incident normally on a large uncladded optical fiber can be used to determine the refractive index and the radius of the fiber. The geometric-optics method is used to analyze the pattern. A new procedure to find the radius of the fiber is proposed. The procedure can make use of nearly the whole of the back-scattered pattern, without need to measure exactly the positions of all of the individual fringes. Special attention is given to the limits of accuracy.

© 1975 Optical Society of America

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### Equations (7)

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(1)
$${i}^{\prime}=2\hspace{0.17em}{\text{sin}}^{-1}(\text{sin}i/n)-i,$$
(2)
$${i}_{m}^{\prime}=2\hspace{0.17em}{\text{sin}}^{-1}\left(\frac{2}{n\surd 3}{(1-{\scriptstyle \frac{1}{4}}{n}^{2})}^{1/2}\right)-{\text{sin}}^{-1}\left(\frac{2}{\surd 3}{(1-{\scriptstyle \frac{1}{4}}{n}^{2})}^{1/2}\right).$$
(3)
$$S=4\hspace{0.17em}a\left[n{\left(1-\frac{{\text{sin}}^{2}i}{{n}^{2}}\right)}^{1/2}\left(1+\frac{{\text{sin}}^{2}i}{{n}^{2}}\right)-\frac{{\text{sin}}^{2}i\hspace{0.17em}\text{cos}i}{{n}^{2}}\right]$$
(4)
$$a=\frac{2\mathrm{\lambda}{h}^{2}}{L(\mathrm{\Delta}L)}(1-{\scriptstyle \frac{1}{2}}n),$$
(5)
$$\frac{d\mathrm{\Phi}}{dS}=-{a}^{-1}{(\text{sin}{i}_{2}+\text{sin}{i}^{\prime})}^{-1}.$$
(6)
$$K={n}^{-2}{(\text{sin}{i}_{2}+\text{sin}{i}^{\prime})}^{-1},$$
(7)
$$K={(\text{sin}{i}_{2}+\text{sin}{i}^{\prime})}^{-1}/{n}^{2},$$