## Abstract

We demonstrate a novel interferometric technique for highly accurate characterization of phase masks used in optical fiber grating fabrication. The principle of the measurement scheme is based on the analysis of the interference pattern formed between the first- and zero-order beams transmitted through or reflected from the grating under test. For spatial resolution of a few millimeters, our methods allow the determination of local variations of the order of 1-µm grating period with an accuracy of a few picometers. These methods are applicable to a broad class of diffractive grating structures.

© 2003 Optical Society of America

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### Equations (6)

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(1)
$$sin\left[{\mathrm{\theta}}_{21}\left(x\right)\right]=sin\left({\mathrm{\theta}}_{10}\right)-\frac{\mathrm{\lambda}}{d\left(x\right)}+\mathrm{const},$$
(2)
$$\frac{2\mathrm{\pi}}{P\left(x\right)}=\frac{2\mathrm{\pi}}{\mathrm{\lambda}}|sin\left[{\mathrm{\theta}}_{21}\left(x\right)\right]-sin\left({\mathrm{\theta}}_{10}\right)|=\left|\frac{2\mathrm{\pi}}{d\left(x\right)}-\frac{2\mathrm{\pi}}{\mathrm{\lambda}}\mathrm{const}\right|,$$
(3)
$$\mathrm{\Delta}d\left(x\right)=\pm \frac{d_{0}{}^{2}}{P\left(x\right)}+{\mathrm{const}}_{1},$$
(4)
$$h_{\mathrm{Litt}}{}^{\mathrm{meas}}\left(x\prime \right)=\frac{1}{cos{\mathrm{\theta}}_{\mathrm{Litt}}}{h}_{\mathrm{norm}}\left(\frac{x\prime}{cos{\mathrm{\theta}}_{\mathrm{Litt}}}\right)+\frac{1}{2}\stackrel{x\prime}{\int}\mathrm{\Delta}\mathrm{\theta}\left(\frac{x\prime}{cos{\mathrm{\varphi}}_{\mathrm{Litt}}}\right)\mathrm{d}x\prime ,$$
(5)
$$\mathrm{\Delta}\mathrm{\theta}\left(x\right)=\frac{2\mathrm{\Delta}d\left(x\right)}{{d}_{0}}\mathrm{tan}{\mathrm{\theta}}_{\mathrm{Litt}}.$$
(6)
$$\mathrm{\Delta}d\left(x\right)=\frac{2{d}_{0}}{sin\left(2{\mathrm{\theta}}_{\mathrm{Litt}}\right)}\left[\frac{\mathrm{d}{h}_{\mathrm{Litt}}\left(x\right)}{\mathrm{d}x}cos\left({\mathrm{\theta}}_{\mathrm{Litt}}\right)-\frac{\mathrm{d}{h}_{\mathrm{norm}}\left(x\right)}{\mathrm{d}x}\right]+\mathrm{const},$$