## Abstract

We describe an interferometric method that enables to measure the optical path delay between two consecutive femtosecond laser pulses by way of dispersive interferometry. This method allows a femtosecond laser to be utilized as a source of performing absolute distance measurements to unprecedented precision over extensive ranges. Our test result demonstrates a non-ambiguity range of ~1.46 mm with a resolution of 7 nm over a maximum distance reaching ~0.89 m.

© 2006 Optical Society of America

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### Equations (9)

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(1)
$$g\left(\nu \right)=a\left(\nu \right)+b\left(\nu \right)\mathrm{cos}\varphi \left(\nu \right).$$
(2)
$$a\left(\nu \right)=\frac{1}{2}s\left(\nu \right)\left[{{r}_{r}}^{2}\left(\nu \right)+{{r}_{m}}^{2}\left(\nu \right)\right]\phantom{\rule{.5em}{0ex}}\mathrm{and}\phantom{\rule{.5em}{0ex}}b\left(\nu \right)=s\left(\nu \right){r}_{r}\left(\nu \right){r}_{m}\left(\nu \right)$$
(3)
$$g\left(\nu \right)=s\left(\nu \right)\left[1+\mathrm{cos}\varphi \left(\nu \right)\right]$$
(4)
$$\varphi \left(\nu \right)=2\pi \nu \alpha $$
(5)
$$G\left(\tau \right)=\mathrm{FT}\left\{g\left(\nu \right)\right\}=S\left(\tau \right)\otimes \left[\frac{1}{2}\delta \left(\tau +\alpha \right)+\delta \left(\tau \right)+\frac{1}{2}\delta \left(\tau -\alpha \right)\right]$$
(6)
$$g\prime \left(\nu \right)={\mathrm{FT}}^{-1}\left\{S\left(\tau \right)\otimes \frac{1}{2}\delta \left(\tau -\Delta \tau \right)\right\}=\frac{1}{2}s\left(\nu \right)\mathrm{exp}\left(i\varphi \left(\nu \right)\right)$$
(7)
$$\varphi \left(\nu \right)={\mathrm{tan}}^{-1}\left(\frac{\mathrm{Im}\left\{g\prime \left(\nu \right)\right\}}{\mathrm{Re}\left\{g\prime \left(\nu \right)\right\}}\right)$$
(8)
$$\frac{d\varphi}{d\nu}=\frac{4\pi \mathrm{NL}}{c}$$
(9)
$$L=\left(\frac{c}{4\pi N}\right)\frac{d\varphi}{d\nu}.$$