The operating principle is quite simple conceptually.
The actual execution is rather more complex.
If a (flat) wave impinges the microphone support surface perpendicularly, it is observed with the same phase by all acoustic sensors, and so the sum of all signals reproduces the incident wave.
However, an angle of incidence of the wave on the support surface generates an attenuated sum, which results in a lesser output amplitude.
If a delay is added to each microphone and frequency, it is possible to 'pretend' that the wave is perpendicular to the support surface again.
Therefore, without having to move the microphone support surface, simply by using calculation algorithms, it is possible to move the sound source and so overlay the acoustic map on the image. As with thermography, the resulting map will show a range of colours corresponding to the width of the incident wave.