To measure a distance of 10 m with an accuracy of 10 μm, we need to know n to within 1 part in 10 6 (1 ppm). The measurement of distances in air by optical means, notably laser telemetry, requires an accurate knowledge of the refractive index n of the medium. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Mimoune et al., Published by EDP Sciences, 2023 To solve this problem, appropriate values for the Cramer coefficients a 0 and a 1 for an acoustic frequency of about 40 kHz have been determined, which contributes to improved knowledge of this equation as a function of acoustic frequency. In practice, an experimental comparison with Pt100 probes (uncertainty of 0.1 K) has shown that the estimated uncertainty levels are relatively compatible, although the linearity of the system does not appear to be very good. The uncertainty of the instrument itself, independent of that of the Cramer equation has been estimated at between 0.13 K to 0.09 K for distances ranging from 3 m to 11 m respectively. Several methods for the detection of arrival times were investigated, notably cross-correlation and cross-spectrum. It is based on time-of-flight measurement of ultrasound pulses at frequencies close to 40 kHz. * Corresponding author: present article describes an acoustic thermometer to measure the average air temperature integrated along a path ranging from 1 m to 11 m. Karim Mimoune, Joffray Guillory * and Mark Plimmer
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