## Abstract

We proposed and demonstrated a low-cost optical system for surface profilometry with nanometer-resolution. The system is based on a composite interferometer consisting of a Michelson interferometer and a Mach-Zehnder interferometer. With the proposed phase compensating mechanism, the phase deviation due to the instability of the optical delay system and environmental perturbation can be compensated simultaneously. The system can perform a wide-field imaging in the millimeter range and a measurement with the axial resolution within ±5 nm without special shielding and protection of the system as well as any special preparation of the sample.

© 2007 Optical Society of America

Full Article |

PDF Article
### Equations (12)

Equations on this page are rendered with MathJax. Learn more.

(1)
$${E}_{S}={E}_{0S}{e}^{j(\mathrm{\omega t}+\varphi )},$$
(2)
$$\varphi =\frac{4\pi h}{\lambda},$$
(3)
$${E}_{R}={E}_{0R}{e}^{j\omega \left(t-\tau \right)},$$
(4)
$$\tau =\frac{2\left({\ell}_{R}-{\ell}_{S}\right)}{c},$$
(5)
$${I}_{1}\propto {\mid {E}_{S}+{E}_{R}\mid}^{2}$$
(6)
$$\phantom{\rule{12.2em}{0ex}}={\mid {E}_{0S}\mid}^{2}+{\mid {E}_{0R}\mid}^{2}+{2E}_{0S}{E}_{0R}\phantom{\rule{.2em}{0ex}}\mathrm{cos}\left(\omega \tau +\varphi \right).$$
(7)
$${\Gamma}_{1}={E}_{0S}{E}_{0R}\phantom{\rule{.2em}{0ex}}\mathrm{cos}\left(\omega \tau +\varphi \right).$$
(8)
$${E}_{R}={E}_{0R}{e}^{j[\omega \left(t-\tau \right)-\delta ]},$$
(9)
$$\delta =\frac{4\pi d}{\lambda},$$
(10)
$${\Gamma}_{1}={E}_{0S}{E}_{0R}\mathrm{cos}\left(\omega \tau +\delta +\varphi \right).$$
(11)
$${\Gamma}_{2}={E}_{0}^{\prime}{E}_{0R}^{\prime}\mathrm{cos}\left({\omega \tau}^{\prime}+\delta \right),$$
(12)
$${\tau}^{\prime}=\frac{2\left({\ell}_{R}^{\prime}-{\ell}^{\prime}\right)}{c},$$