## Abstract

We report the influence of the nonlinearities in the wavelength-sweeping speed on the resulting interferometric signals in an absolute distance interferometer. The sweeping signal is launched in the reference and target interferometers from an external cavity laser source. The experimental results demonstrate a good resolution in spite of the presence of nonlinearities in the wavelength sweep. These nonlinearities can be modeled by a sum of sinusoids. A simulation is then implemented to analyze the influence of their parameters. It shows that a sinusoidal nonlinearity is robust enough to give a good final measurement uncertainty through a Fourier transform technique. It can be concluded that an optimal value of frequency and amplitude exists in the case of a sinusoidal nonlinearity.

© 2007 Optical Society of America

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### Equations (8)

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(1)
$${I}_{i}\left(r,t\right)=\left({I}_{1i}\left(r,t\right)+{I}_{2i}\left(r,t\right)\right)\left(1+{V}_{i}\left(t\right)\text{cos}\left(2\pi {L}_{i}/\lambda \left(t\right)+{\Phi}_{0i}\right)\right)\text{.}$$
(2)
$${f}_{{b}_{i}}=\frac{{\alpha}_{0}\times {L}_{i}}{{\lambda}_{0}^{2}}\text{.}$$
(3)
$$\lambda \left(t\right)={\lambda}_{0}+{\alpha}_{0}t+{\alpha}_{\text{nl}\lambda}\left(t\right)\text{.}$$
(4)
$$\Delta \Phi =2\pi \text{\hspace{0.17em}}\frac{{L}_{i}}{\lambda}-2\pi \text{\hspace{0.17em}}\frac{{L}_{i}}{\lambda +\Delta \lambda}\text{.}$$
(5)
$${f}_{{b}_{i}}\left(t\right)=\frac{\Delta \Phi}{2\pi \Delta t}=\frac{1}{\Delta t}\left(\frac{{L}_{i}\Delta \lambda}{\lambda \left(\lambda +\Delta \lambda \right)}\right)\text{.}$$
(6)
$${f}_{{b}_{i}}\left(t\right)=\frac{{L}_{i}{\alpha}_{0}}{{\lambda}^{2}}+\frac{{L}_{i}}{{\lambda}^{2}}\text{\hspace{0.17em}}{\alpha}_{\text{nl}\lambda}\left(t\right)\text{.}$$
(7)
$$\lambda \left(t\right)={\lambda}_{0}+{\alpha}_{0}t+{\displaystyle \sum {A}_{k}\text{\hspace{0.17em} sin}\left(\text{2}\pi f{m}_{k}t+{\phi}_{k}\right)}\text{.}$$
(8)
$${f}_{{b}_{i}}\left(t\right)=\frac{{L}_{i}{\alpha}_{0}}{{\lambda}^{2}}+\frac{{L}_{i}}{{\lambda}^{2}}{\displaystyle \sum _{k=1}{A}_{k}\text{\hspace{0.17em} sin}\left(\text{2}\pi f{m}_{k}t+{\phi}_{k}\right)}\text{.}$$