## Abstract

The forward scattering of light by an optical fiber produces an interference fringe pattern, and the fringe period is inversely proportional to the fiber diameter. An electrooptic system has been developed to produce and detect this scattering pattern to provide an instrument which will measure fiber diameter during the drawing operation. The system measures the fiber diameter at a 1-kHz rate with a precision of 0.25 *μ*m and an accuracy of ±0.25 *μ*m over a range of 50–150-*μ*m diams. The instrument allows the fiber to move laterally in a 1-cm diam window maintaining the above accuracy. The system can be calibrated optically and does not need a standard fiber for this procedure. The instrument has been used for months without the need for recalibration. In addition to the digital diameter output, the system employs a microprocessor to compute mean and standard deviation values for various sample lengths and provides suitable signals for feedback control of fiber diameter.

© 1977 Optical Society of America

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### Equations (19)

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(1)
$${{d}_{f}}^{2}=({v}_{p}{{d}_{p}}^{2})/({v}_{f}),$$
(2)
$$\mathrm{\Delta}(\theta )=2b\hspace{0.17em}\left[\text{sin}\frac{\theta}{2}+{\left({{m}_{1}}^{2}+1-2{m}_{1}\hspace{0.17em}\text{cos}\frac{\theta}{2}\right)}^{1/2}\right]+\frac{\mathrm{\lambda}}{4},$$
(3)
$$A=1+\text{cos}k\mathrm{\Delta},$$
(4)
$$N=\{k[\mathrm{\Delta}({\theta}_{2})-\mathrm{\Delta}({\theta}_{1})]\}/(2\pi ),$$
(5)
$$N=\frac{2b}{\mathrm{\lambda}}\left\{\left[\text{sin}\frac{{\theta}_{2}}{2}+{\left({{m}_{1}}^{2}+1-2{m}_{1}\hspace{0.17em}\text{cos}\frac{{\theta}_{2}}{2}\right)}^{1/2}\right]-\left[\text{sin}\frac{{\theta}_{1}}{2}+{\left({{m}_{1}}^{2}+1-2{m}_{1}\hspace{0.17em}\text{cos}\frac{{\theta}_{1}}{2}\right)}^{1/2}\right]\right\}.$$
(6)
$$N=[(2b)/\mathrm{\lambda}]\xb71.28$$
(7)
$$\delta =2({m}_{2}-{m}_{1})a.$$
(8)
$$d=2{f}_{1}\hspace{0.17em}\text{tan}[({\theta}_{2}-{\theta}_{1})/2],$$
(10)
$${m}_{e}=\pm \frac{{f}_{1}M}{2{N}_{3}(M+1)},$$
(11)
$${m}_{e}=\pm \hspace{0.17em}\left[\frac{{f}_{1}M}{2(M+1){N}_{3}}\left(1-\frac{{N}_{3}{b}_{3}}{{f}_{3}}\right)\right],$$
(12)
$${m}_{z}=\pm \frac{{m}_{e}}{\text{tan}[({\theta}_{2}-{\theta}_{1})/2]}.$$
(13)
$$f(t)=\text{sin}(wt-\theta ),$$
(14)
$$g(t)=\pm (2/\pi )\hspace{0.17em}\text{cos}\theta ,$$
(15)
$$h(t)=(2/\pi )\hspace{0.17em}\text{cos}\theta \hspace{0.17em}\text{sin}wt.$$
(16)
$${E}_{d}=\pm [\pi /({n}_{d})].$$
(17)
$${E}_{p}=\pm [\pi /({n}_{p})].$$
(18)
$${E}_{p}=\pm [(3\pi )/(2{n}_{p})].$$
(19)
$${E}_{\text{max}}={E}_{p}+{E}_{d}=0.95\pi =0.24\hspace{0.17em}\mu \text{m}.$$