Abstract

A new system, consisting of a double-channel Fabry–Perot etalon and laser diodes emitting around 780 nm, is described and proposed for use for measuring air-refractive index. The principle of this refractometer is based on frequency measurements between optical laser sources. It permits quasi-instantaneous measurement with a resolution of better than 10-9 and uncertainty in the 10-8 range. Some preliminary results on the stability of this system and the measurements of the refractive index of air with this apparatus are presented. The first measurements of the index of air at 780 nm are, within an experimental uncertainty of the order of 2 × 10-8, in agreement with the predicted values by the so-called revised Edlén equations. This result is, to the best of our knowledge, the first to extend to the near IR the validity of the revised Edlén equation derived for the wavelength range of 350–650 nm.

© 1998 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]

1996

1994

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

O. Acef, F. Nez, G. D. Rovera, “Optical heterodyning with a frequency difference of 1 THz in the 850-nm range,” Opt. Lett. 19, 1275–1277 (1994).
[CrossRef] [PubMed]

1987

1966

D. W. Allan, “Statistics of atomic frequency standards,” Proc. IEEE 54, 221–230 (1966).
[CrossRef]

Acef, O.

Allan, D. W.

D. W. Allan, “Statistics of atomic frequency standards,” Proc. IEEE 54, 221–230 (1966).
[CrossRef]

Andersson, M.

Birch, K. P.

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Dandliker, R.

Downs, M. J.

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Eliasson, L.

Hall, J. L.

Jungner, P.

Nez, F.

Pendrill, L. R.

Quinn, T. J.

T. J. Quinn, “Mise en pratique of the definition of the Mètre (1992),” Metrologia 30, 523–541 (1993/94).

Rovera, G. D.

Salvadé, Y.

Swartz, S.

Ye, J.

Zimmermann, E.

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Figures (7)

Fig. 1
Fig. 1

Experimental setup of our refractometer.

Fig. 2
Fig. 2

Design (longitudinal and transverse sections) of the Fabry–Perot etalon.

Fig. 3
Fig. 3

Block diagram for stability measurements of the Fabry–Perot.

Fig. 4
Fig. 4

Relative standard deviation plot against integration time: ●, stability of the laser diode locked to the D 2 line of rubidum; ○, stability of the laser diode locked to a transmission peak of the Fabry–Perot etalon.

Fig. 5
Fig. 5

Change in the beat frequency between the reference frequency and the laser diode locked to the transmission peak of one cavity of the Fabry–Perot versus temperature.

Fig. 6
Fig. 6

Representation of the procedure used for measuring the refractive index of air.

Fig. 7
Fig. 7

Plot of measured values of the refractive index of air and those calculated by the revised Edlèn equation. The error bars are derived from the uncertainties quoted in the various optical measurements and instruments. The dotted line represents the bisecting line.

Equations (18)

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ν 1 = ν 2 = c n λ 1 a = c n λ 2 a .
λ 1 ν = 2 / k = λ 2 a .
ν 1 * = c / λ 1 ν ,
ν 1 = ν 1 * - Δ ν ,     ν 1 * = ν ref + Δ ν * .
n = ν 1 * ν 1 = ν ref + Δ ν * ν ref + Δ ν * - Δ ν .
σ = 1 ν k i = 1 N δ ν i - δ ν i - 1 2 2 N - 1 1 / 2 ,
ν 2 i = ν 2 + c 2 .
ν 1 * = ν r + δ ν 1 r .
ν 1 i = ν 1 + c 1 .
ν 2 i = ν 2 + c 2 .
ν 2 * = ν 2 i + p   c 2 n .
Δ ν FP air = c 2 n .
ν 2 * = ν r + δ ν 2 r ,
ν 1 i = ν 2 i - c 2 - c 12 + c 1 ,     ν 2 i = ν r + δ ν 2 r - p   c 2 n .
n = ν r + δ ν 1 r + p   c 2 ν r + δ ν 2 r + c 1 - c 2 - c 12 .
n - 1 tp = p / Pa n - 1 s 96095.43 × 1 + 10 - 8 0.601 - 0.00972 t / ° C p / Pa 1 + 0.0036610   t / ° C ,
n - 1 s × 10 8 = 8342.54 + 2406147 130 - λ - 1 / μ m - 1 2 - 1 + 15998 38.9 - λ - 1 / μ m - 1 2 - 1 ,
n tpf = n tp - f / Pa 3.7345 - 0.0401 λ - 1 / μ m - 1 2 × 10 - 10 .

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