## Abstract

What we believe to be a new instrument for measuring the end-face geometrical parameters of fiber connectors is described. In this apparatus, a
Mirau-type interferometric objective is employed to measure a small area of the connector end face and generate
an interferogram corresponding to the surface profile. Various new technologies are used to ensure excellent performance
and high measurement repeatability. A multipoint method is proposed to adjust the inclination of the physical contact sample
stage. The physical contact angle of the sample stage is adjusted directly on the instrument by use of a special tool whose angle is
calibrated with the reversal method. Measurement results of important parameters of the fiber connector end face are
compared with those inspected by a commercial profiler or with a standard sample. Optical insertion losses of connectors
inspected by the developed system are also evaluated.

© 2006 Optical Society of America

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### Equations (15)

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(1)
$${g}_{j}\left(x,y\right)=a\left(x,y\right)+b\left(x,y\right)\text{cos}\left[\phi \left(x,y\right)+{\delta}_{j}\right](j=0,1\text{,}\dots ,4),$$
(2)
$${\delta}_{j}=j\text{\hspace{0.17em}}\frac{\pi}{2}\left(j=0,1\text{,}\dots ,4\right).$$
(3)
$$\phi \left(x,y\right)={\text{tan}}^{-1}\left[\frac{2\left({g}_{1}-{g}_{3}\right)}{2{g}_{2}-\left({g}_{0}+{g}_{4}\right)}\right].$$
(4)
$$\{\begin{array}{c}x=\frac{\left[2\left({y}_{1}-{y}_{3}\right){c}_{1}-2\left({y}_{1}-{y}_{2}\right){c}_{2}\right]}{M}\\ y=\frac{\left[2\left({x}_{1}-{x}_{2}\right){c}_{2}-2\left({x}_{1}-{x}_{3}\right){c}_{1}\right]}{M}\end{array},$$
(5)
$$M=4\left[\left({x}_{1}-{x}_{2}\right)\left({y}_{1}-{y}_{3}\right)-\left({y}_{1}-{y}_{2}\right)\left({x}_{1}-{x}_{3}\right)\right],$$
(6)
$${c}_{1}={{x}_{1}}^{2}-{{x}_{2}}^{2}+{{y}_{1}}^{2}-{{y}_{2}}^{2},$$
(7)
$${c}_{2}={{x}_{1}}^{2}-{{x}_{3}}^{2}+{{y}_{1}}^{2}-{{y}_{3}}^{2}.$$
(8)
$$L=\sqrt{{\left({x}_{1}-x\right)}^{2}+{\left({y}_{1}-y\right)}^{2}}.$$
(9)
$$\phi \left(x,y\right)=px+qy+c,$$
(10)
$$\{\begin{array}{c}{\theta}_{x}=\mathrm{arctan}\left(p\right)\\ {\theta}_{y}=\mathrm{arctan}\left(q\right)\end{array}.$$
(11)
$$\{\begin{array}{c}{\theta}_{x}=p\\ {\theta}_{y}=q\end{array}.$$
(12)
$$\{\begin{array}{c}{\alpha}_{x}={\gamma}_{x}+{\theta}_{x}\\ {\alpha}_{y}={\gamma}_{y}+{\theta}_{y}\end{array},$$
(13)
$$\{\begin{array}{c}{\beta}_{x}=180-{\gamma}_{x}+{\theta}_{x}\\ {\beta}_{y}=180-{\gamma}_{y}+{\theta}_{y}\end{array},$$
(14)
$$\{\begin{array}{c}{\theta}_{x}=\frac{{\alpha}_{x}+{\beta}_{x}-180}{2}\\ {\theta}_{y}=\frac{{\alpha}_{y}+{\beta}_{y}-180}{2}\end{array},$$
(15)
$$\{\begin{array}{c}{\gamma}_{x}=\frac{180+{\alpha}_{x}-{\beta}_{x}}{2}\\ {\gamma}_{y}=\frac{180+{\alpha}_{y}-{\beta}_{y}}{2}\end{array}.$$