Measurement of air-refractive-index fluctuation from laser frequency shift with uncertainty of order 10⁻⁹

Abstract

In the previous work (Ishige et al 2009 Meas. Sci. Technol. 20 084019), we presented a method of measuring the relative air-refractive-index fluctuation (Δnair) from the laser frequency shift with the measurement uncertainty of order 10−8 using a phase modulation homodyne interferometer (Basile et al 1991 Metrologia 28 455), which was supported by an ultralow thermal expansion material (ULTEM) and an external cavity laser diode (ECLD). In this paper, an improvement in the uncertainty of the Δnair measurement is presented. The improvement method is based on a Fabry–Perot cavity constructed on the ULTEM, which has a thermal expansion coefficient of 2 × 10−8 K−1 and an ECLD. The Pound–Drever–Hall method (Drever et al 1983 Appl. Phys. B 31 97) is also used to control the ECLD frequency to track the resonance of the cavity. Δnair can be derived from the ECLD frequency shift. The estimated measurement uncertainty of Δnair for a short time (∼150 s) in the experiment is of order 2.5 × 10−9 or less.

Investigation of Short-term Amplitude and Frequency Fluctuations of Lasers for Interferometry

“…The relative frequency stability of DPSSL (diode pumped solid state laser) monolithic Nd:YAG lasers stabilized by this technique was measured in range of 4x10 -9 for an integration time of 100 s and measurements were performed on air conditions (frequency modulation of the laser was done through slow thermal tuning only) [20][21][22]. This frequency stability is fully sufficient for measurements that are done on air conditions -the influence of the refractive index of air fluctuations is in the order of 10 -7 or can be compensated up to this level [23][24][25][26][27][28][29][30][31]. Next, the relative frequency stability of frequency doubled Nd:YAGs stabilized by some more sophisticated technique like saturated subdoppler spectroscopy in iodine vapor can be in the range close to the 10 -14 level for 100 s integration times [32][33][34][35][36][37][38].…”

Multiaxis interferometric displacement measurement for local probe microscopy

“…Changes of the refractive index influence the whole beam length. Still with the evaluation of the refractive index through indirect measurement of the fundamental parameters of air [24,25] the theoretical precision of interferometric measurements may be below 10 −8 in good laboratory conditions [26]; air flow and air thermal gradients being the main limiting factors. An enclosed laser beam, thermal stabilization of the air around the setup and preferably horizontal beam paths should be part of the design.…”

Precision displacement interferometry with stabilization of wavelength on air

“…The laser beam of the refractometer can be again placed only close to the measuring path. While the evaluation of the refractive index of air through direct refractometery under laboratory conditions can be done with an uncertainty close to the 10 -9 [12,13]. The most precise laboratory techniques seem to be those exploiting optical frequency comb synthesis [14,15,16,17,18].…”