Consider a stable optical ring cavity with the round-trip path between the mirrors entirely in air. If we frequency-lock a tunable laser to a particular resonance, we have a wavelength in the air of the cavity of roughly λ = L/m, where L is the cavity round-trip path-length and m is the integral number of optical wavelengths in the round-trip. This simple relation neglects phase-shifts upon reflection at the cavity mirrors, φ_M, and also the subtle phase difference of a Gaussian wave in relation to plane-wave propagation, φ_Gouy.

Sinceφ_M and φ_Gouy are relatively constant, the wavelength stability is largely a function of how stable the cavity length L is. By using ultra-low thermal expansion glass (ΔL/L~ 20 x 10 ^-9cm/cm/ °C) and correcting for residual temperature and pressure effects, our goal is to demonstrate length metrology in air at the Δλ/λ~10^-8 level.

The resonance wavelengths are calibrated by measuring the frequency of a laser locked to a mode while the cavity is in a chamber under vacuum. The wavelength (in vacuum) may then be calculated from λν=c. As the air is subsequently returned to the chamber, the laser frequency decreases as the electronic feedback works to keep the laser locked to the resonance. The wavelength remains as constant as the cavity length, and independent of the air's index of refraction.

However, the cavity length actually does contract slightly with isotropic pressure, as all materials do. A small correction (about 1 part-per-million) to the measured wavelength based on the material properties must be applied to account for the contraction.