## Abstract

To stabilize the phase-shifting Fizeau-type interferometer against environmental disturbances (namely, vibration and temperature variations), the feedback scheme that uses the current-induced frequency modulation of a laser diode (λ = 633 nm) and the two-frequency optical heterodyne method has been investigated, with particular attention to improvement of the achievable stabilization. It is demonstrated that introduction of the proportional-integral control into the feedback system improves stabilization against the proportional control case; e.g., stabilization is improved 5 times for 100-nm_{p-p} vibration at the frequency range at 30 Hz. The surface profile measurement for a sample mirror was conducted with a reproducibility of 6.8 nm in the root mean square under the subwavelength-amplitude vibration at 100 Hz.

© 2003 Optical Society of America

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### Equations (5)

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(1)
$$g={\left(\mathrm{\Delta}V/\mathrm{\Delta}\mathrm{OPD}\right)}_{\mathrm{PM}}{\left(\mathrm{\Delta}I/\mathrm{\Delta}V\right)}_{\mathrm{FB}}{\left(\mathrm{\Delta}f/\mathrm{\Delta}I\right)}_{\mathrm{LD}}\times {\left(\mathrm{\Delta}\mathrm{OPD}/\mathrm{\Delta}f\right)}_{\mathrm{OPD}},$$
(2)
$$G\left(s\right)=\left[B/\left(1+{\mathit{sT}}_{p}\right)\right]\left\{A\left[{G}_{p}+{G}_{i}/\left(1+{\mathit{sT}}_{i}\right)\right]\right\}\mathrm{\chi}4\mathrm{\pi}\mathit{ndf}/c,$$
(3)
$$S\left(s\right)={\mathrm{\delta}}_{\mathrm{off}}\left(s\right)/{\mathrm{\delta}}_{\mathrm{on}}\left(s\right),$$
(4)
$$S\left(s\right)=1+G\left(s\right).$$
(5)
$$S\left(s\right)=\frac{1+\mathrm{\alpha}\left({G}_{p}+{G}_{i}\right)+\left(\mathrm{\beta}+\mathrm{\alpha}{G}_{p}{T}_{i}\right)s+\mathrm{\gamma}{s}^{2}+{T}_{p}{T}_{i}{T}_{f}{s}^{3}}{1+\mathrm{\beta}s+\mathrm{\gamma}{s}^{2}+{T}_{p}{T}_{i}{T}_{f}{s}^{3}},$$