## Abstract

We propose a new signal-processing method for eliminating measurement errors that occur in the wavelength-multiplexed phase-locked laser diode interferometer. The basic idea proposed here is a very simple but effective way to improve measurement accuracy. With our scheme, the phase in the interference signal is strictly shifted by 2π, which enables us to eliminate measurement errors. The equivalent wavelength Λ is 80 mm, and the measurement accuracy reaches ∼Λ/600. A step-height measurement was also carried out in the experiment.

© 1997 Optical Society of America

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### Equations (13)

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(1)
$${I}_{m}\left(t\right)=acos\left({\mathrm{\omega}}_{c}t+\mathrm{\theta}\right),$$
(2)
$$S\left(t,x\right)={S}_{1}+{S}_{0}cos\left[zcos\left({\mathrm{\omega}}_{c}t+\mathrm{\theta}\right)+\mathrm{\alpha}\left(x\right)\right],$$
(3)
$$z=4\mathrm{\pi}a\mathrm{\beta}{D}_{0}/\mathrm{\lambda}_{0}{}^{2}$$
(4)
$$\mathrm{\alpha}\left(x\right)=4\mathrm{\pi}{D}_{0}\left(x\right)/{\mathrm{\lambda}}_{0}$$
(5)
$${\mathrm{\alpha}}_{1}\left(x\right)=4\mathrm{\pi}{D}_{0}\left(x\right)/{\mathrm{\lambda}}_{1},$$
(6)
$${\mathrm{\alpha}}_{2}\left(x\right)=4\mathrm{\pi}{D}_{0}\left(x\right)/{\mathrm{\lambda}}_{2},$$
(7)
$$\mathrm{\Delta}\mathrm{\alpha}\left(x\right)=4\mathrm{\pi}{D}_{0}\left(x\right)/\mathrm{\Lambda},$$
(8)
$$\mathrm{\Lambda}={\mathrm{\lambda}}_{1}{\mathrm{\lambda}}_{2}/\left({\mathrm{\lambda}}_{1}-{\mathrm{\lambda}}_{2}\right)$$
(9)
$${D}_{0}\left(x\right)=\frac{\mathrm{\Lambda}}{4\mathrm{\pi}}\mathrm{\Delta}\mathrm{\alpha}\left(x\right).$$
(10)
$${D}_{0}\left(x\right)=C\frac{\mathrm{\Delta}\mathrm{\alpha}\left(x\right)}{\mathrm{\Delta}V},$$
(11)
$${p}_{i}\left(x\right)={\int}_{\left(T/4\right)\left(i-1\right)}^{\left(T/4\right)i}S\left(t,x\right)\mathrm{d}t\left(i=1\sim 4\right),$$
(12)
$${F}_{s}\left[\mathrm{\alpha}\left(x\right)\right]={p}_{1}+{p}_{2}-{p}_{3}-{p}_{4}={A}_{s}sin\mathrm{\alpha}\left(x\right),$$
(13)
$${F}_{c}\left[\mathrm{\alpha}\left(x\right)\right]={p}_{1}-{p}_{2}+{p}_{3}-{p}_{4}={A}_{c}sin\mathrm{\alpha}\left(x\right),$$