## Abstract

The theoretical results of the effects of a small inclination
misalignment, which is formed by rotation of the beam-splitter grating
around the axis on the grating plane when the axis has an arbitrary
angle with respect to the line direction of the grating, between the
two grating planes on the moiré fringes in the Talbot
interferometry are verified by experiment. The experimental results
coincide well with theoretical ones. Consequently, the effect of
the small arbitrary inclination on practical measurements based on the
Talbot interferometry is further explained by an example that examines
the beam collimation of a lens, and the advantages and limitations of
the effect are also discussed.

© 2001 Optical Society of America

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### Equations (3)

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(1)
$${\mathrm{\varphi}}_{\mathrm{LN}}=\left(90\xb0-\mathrm{\delta}\right)+{tan}^{-1}\times \left[\frac{sin\left(\mathrm{\theta}+\mathrm{\delta}\right){\left({sin}^{2}\mathrm{\delta}+{cos}^{2}\mathrm{\delta}{cos}^{2}\mathrm{\gamma}\right)}^{1/2}-sin\mathrm{\delta}}{cos\left(\mathrm{\theta}+\mathrm{\delta}\right){\left({sin}^{2}/\mathrm{\delta}+{cos}^{2}\mathrm{\delta}{cos}^{2}\mathrm{\gamma}\right)}^{1/2}cos\mathrm{\delta}}\right].$$
(2)
$${\mathrm{\varphi}}_{\mathrm{LN}}=\left(90\xb0-\mathrm{\delta}\right)+{tan}^{-1}\left[\frac{sin\left(\mathrm{\theta}+\mathrm{\delta}\right)-sin\mathrm{\delta}}{cos\left(\mathrm{\theta}+\mathrm{\delta}\right)-cos\mathrm{\delta}}\right]=\left(90\xb0-\mathrm{\delta}\right)+{\mathrm{\varphi}}_{x}=\frac{\mathrm{\theta}}{2},$$
(3)
$${\mathrm{\varphi}}_{x}={tan}^{-1}\times \left[\frac{sin\left(\mathrm{\theta}+\mathrm{\delta}\right){\left({sin}^{2}\mathrm{\delta}+{cos}^{2}\mathrm{\delta}{cos}^{2}\mathrm{\gamma}\right)}^{1/2}-sin\mathrm{\delta}}{cos\left(\mathrm{\theta}+\mathrm{\delta}\right){\left({sin}^{2}\mathrm{\delta}+{cos}^{2}\mathrm{\delta}{cos}^{2}\mathrm{\gamma}\right)}^{1/2}-cos\mathrm{\delta}}\right].$$