## Abstract

A new method for noncontact, high-resolution measurement of gas
density is described. The method uses a two-frequency Zeeman-split
He–Ne laser and cumulative phase-measuring electronics. The
measurement is resolved in two dimensions and provides density that is
averaged only along the length of the laser beam that passes through
the test section. The technique is based on highly accurate
measurement of the optical path-length change of the laser beam as it
passes through a test cell (in principle, to within 0.001λ, where
λ is the wavelength of the laser). The technique also provides
a very large dynamic range (again, in principle, up to
10^{10}), which makes the method additionally
attractive. Although the optical path length through the test
section is directly related to the index of refraction, and hence to
the density of the gas, the method can also be used to measure
temperature (if the gas pressure is known) or pressure (if the
temperature is known).

© 2001 Optical Society of America

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### Equations (8)

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(1)
$$A={A}_{R}sin\left(2\mathrm{\pi}\mathit{\nu}t\right)+{A}_{T}sin\left[2\mathrm{\pi}\left(\mathit{\nu}+\mathrm{\Delta}\mathit{\nu}\right)t+\mathrm{\Theta}\right].$$
(2)
$$\u3008{A}^{2}\u3009=A_{R}{}^{2}\u3008{sin}^{2}\left(2\mathrm{\pi}\mathit{\nu}t\right)\u3009+A_{T}{}^{2}\u3008{sin}^{2}\left[2\mathrm{\pi}\left(\mathit{\nu}+\mathrm{\Delta}\mathit{\nu}\right)t+\mathrm{\Theta}\right]\u3009-{A}_{R}{A}_{T}\u3008cos\left[2\mathrm{\pi}\left(2\mathit{\nu}+\mathrm{\Delta}\mathit{\nu}\right)t+\mathrm{\Theta}\right]\u3009+{A}_{R}{A}_{T}\u3008cos\left(2\mathrm{\pi}\mathrm{\Delta}\mathit{\nu}t+\mathrm{\Theta}\right)\u3009,$$
(3)
$$S=C\left[\left(A_{R}{}^{2}+A_{T}{}^{2}\right)/2+{A}_{R}{A}_{T}cos\left(2\mathrm{\pi}\mathrm{\Delta}\mathit{\nu}t+\mathrm{\Theta}\right)\right],$$
(4)
$$\mathrm{\Delta}=L\left({n}_{0}-n\right).$$
(5)
$$\mathrm{\rho}=c\left(n-1\right),$$
(6)
$$\mathrm{\rho}=\left[1-\frac{\mathrm{\Delta}}{L\left({n}_{0}-1\right)}\right]{\mathrm{\rho}}_{0},$$
(7)
$$d\mathrm{\rho}=\frac{{\mathrm{\rho}}_{0}}{L\left({n}_{0}-1\right)}d\mathrm{\Delta},$$
(8)
$$d\mathrm{\rho}=\frac{4428}{L}d\mathrm{\Delta}.$$