## Abstract

A wavelength meter based on a heterodyne interferometer is presented. A single-wavelength test laser beam is modulated to two orthogonal linearly polarized components with different frequencies by a pair of acousto-optic modulators. Then the modulated laser beam and a two-wavelength laser beam are sent to a heterodyne interferometer in a common path. The ratio of two laser interference phase shifts in the heterodyne interferometer is equal to the ratio of their wavelengths. The heterodyne technique measures the heterodyne interference phase but not the interference intensity, which means that it could measure a light source whose intensity is not stable.
The heterodyne interference signal is an alternating signal that can easily magnify and process the circuit that makes up the heterodyne wavelength meter and could be used to measure the low-intensity light source even when there are environmental disturbances. A tunable diode laser wavelength range of
$630\u2013637\text{\hspace{0.17em} nm}$ has been measured to an accuracy of 5 parts in
${10}^{7}$.

© 2007 Optical Society of America

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### Equations (9)

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(1)
$${I}_{A}=\text{cos}\left(\text{2}\pi {f}_{d}t+\alpha \right)\text{,}$$
(2)
$${I}_{B}=\text{cos}\left(\text{2}\pi {f}_{d}t+\beta \right).$$
(3)
$$\varphi =\beta -\alpha =\frac{2\pi \left({f}_{1}{L}_{1}-{f}_{2}{L}_{2}\right)}{c}\text{,}$$
(4)
$$\Delta \varphi =\frac{2\pi \left[{f}_{1}\Delta L-{f}_{2}\left(-\Delta L\right)\right]}{c}=2\pi \text{\hspace{0.17em}}\frac{\Delta L\left({f}_{1}+{f}_{2}\right)}{c}.$$
(5)
$$\Delta \varphi =2\pi \text{\hspace{0.17em}}\frac{\Delta L\left({f}_{1}+{f}_{2}\right)}{c}\text{,}\Delta \phi =2\pi \text{\hspace{0.17em}}\frac{\Delta L\left({f}_{3}+{f}_{4}\right)}{c}.$$
(6)
$${f}_{1}+{f}_{2}=\frac{\Delta \varphi}{\Delta \phi}\left({f}_{3}+{f}_{4}\right)\text{,}$$
(7)
$$\Delta \varphi =\left[\beta \left({t}_{2}\right)-\alpha \left({t}_{2}\right)\right]-\left[\beta \left({t}_{1}\right)-\alpha \left({t}_{1}\right)\right]=2\pi \text{\hspace{0.17em}}\frac{[{f}_{1}\left({t}_{2}\right)\left({L}_{1}+\Delta L\right)-{f}_{2}\left({t}_{2}\right)\left({L}_{2}-\Delta L\right)]-\left[{f}_{1}\left({t}_{1}\right){L}_{1}-{f}_{2}\left({t}_{1}\right){L}_{2}\right]}{c}=2\pi \text{\hspace{0.17em}}\frac{\Delta L\left[{f}_{1}\left({t}_{2}\right)+{f}_{2}\left({t}_{2}\right)\right]+{L}_{1}\left[{f}_{1}\left({t}_{2}\right)-{f}_{1}\left({t}_{1}\right)\right]-{L}_{2}\left[{f}_{2}\left({t}_{2}\right)-{f}_{2}\left({t}_{1}\right)\right]}{c}=2\pi \text{\hspace{0.17em}}\frac{\Delta L\left[{f}_{1}\left({t}_{2}\right)+{f}_{2}\left({t}_{2}\right)\right]}{c}+2\pi \text{\hspace{0.17em}}\frac{\left({L}_{1}-{L}_{2}\right)\Delta {f}_{1}+{L}_{2}\Delta \left({f}_{1}-{f}_{2}\right)}{c}\text{,}$$
(8)
$$\frac{\left({L}_{1}-{L}_{2}\right)\Delta {f}_{1}+{L}_{2}\Delta \left({f}_{1}-{f}_{2}\right)}{c}$$
(9)
$$\theta =2\text{\hspace{0.17em} arcsin}\left(\frac{\lambda}{\text{2}\Lambda}\right)\approx \frac{\lambda}{\Lambda}=\frac{\lambda}{V}\text{\hspace{0.17em}}f\text{,}$$