A sub-millimetre two-wavelength EDM that compensates the air refractive index: uncertainty and measurements up to 5 km

Abstract

Abstract Distance measurements over several kilometres with a sub-millimetre uncertainty are required for deformation monitoring in fields such as geodesy or civil engineering where well-controlled scale is critical. This paper presents a two-wavelength electro-optical distance meter (EDM) capable of such measurements and traceable to the SI (Système International d’unités). It is based on simultaneous measurements of optical path lengths, at two wavelengths, one at 780 nm and the other at 1560 nm, the dispersion between the two wavelengths allowing real-time compensation of the air refractive index along the optical paths. The uncertainty budget of this EDM has been established, taking into account both the telemetric and the mechanical contributions. One of the main sources of errors is crosstalk, which originates mainly from the optical splitters acting as circulators and becomes more pronounced for lower received powers over longer distances. For signal-to-crosstalk ratios (SCRs) higher than 60 dB, the instrumental uncertainty in the air-index compensated distance was assessed to be 320 µm (k = 1). In the field, two distance measurements, one over 2.6 km, the other over 5.4 km, were carried out over a period of up to 6 days, and for a temperature and pressure varying by as much as 10 °C and 17 hPa. For each distance, the standard deviation of the Gaussian fit of the experimental points was less than 250 µm. This level of refractivity compensation demonstrates that the developed instrument works properly. In addition, standard deviations lower than 140 µm were achieved for displacement measurements at distances around 2.6 km and 5.4 km. All these results were obtained for SCRs higher than 60 dB. Finally, solutions are proposed for mitigating the effect of high crosstalk values on instrumental uncertainty.