Temperature and flow estimation in the atmosphere
Sound propagation in the atmosphere is strongly inﬂuenced by temperature and wind, and, therefore, it can be used to measure these physical phenomena. It is also important that the atmosphere is very transparent to low frequency sound, so that the acoustic signal can be transmitted over distances of several hundred meters with low attenuation. The advantage of tomography methods to provide a number of measurements proportional to the square of the number of sensors, can be well used to obtain high resolution reconstructions of temperature and wind ﬁelds. It then can be particularly useful for the study of small scale temperature variations and wind turbulences.
In the atmosphere, the transmitted signal has low frequency, that ranges from 100 Hz for the distances of few hundreds meters to 50 KHz for the distances up to ten meters. To be able to sample this signal without any aliasing, we need a sampling card that works at a frequency only twice higher that the maximal frequency of our signal. Hence, an accurate time-of-ﬂight estimation can be achieved without using expensive and fast audio acquisition cards (A/D convertors).
The setup consists of 12 emitters and 12 receivers placed on a 1 m radius ring. Piezoelectric transducers are used to send and receive the acoustic signal. The emitters are equipped with ampliﬁers, and the receivers with preampliﬁers, in order to guarantee the signal levels compatible with the audio card (Motu 24I/O card). This card is used to interface the transmitted and the acquired signals with a personal computer. To suppress the sound reﬂections the ring is covered with a foam.
Time of ﬂight estimation
The atmosphere has no strong inhomogeneities and the ﬁrst reﬂections in the ring setup can be approximatively determined from the geometry of the experimental setup. Our time-of-flight estimation technique has two steps: 1) coarse time-of-ﬂight estimation is obtained using the cross-correlation method, and 2) reﬁnement is gained by computing the phase of the sinusoidal part of the signal.