Indirect calibration of a large microphone array for in-duct acoustic measurements

This paper addresses the problem of in situ calibration of a pin hole-mounted microphone array for in-duct acoustic measurements. One approach is to individually measure the frequency response of each microphone, by submitting the probe to be calibrated and a reference microphone to the same pressure field. Although simple, this task may be very time consuming for large microphone arrays and eventually suffer from lack of access to microphones once they are installed on the test bench. An alternative global calibration procedure is thus proposed in this paper. The approach is based on the fact that the acoustic pressure can be expanded onto an analytically known spatial basis. A projection operator is defined allowing the projection of measurements onto the duct modal basis. The main assumption of the method is that the residual resulting from the difference between actual and projected measurements is mainly dominated by calibration errors. An iterative procedure to estimate the calibration factors of each microphone is proposed and validated through an experimental set-up. In addition, it is shown that the proposed scheme allows an optimization of physical parameters such as the sound speed and parameters associated to the test bench itself, such as the duct radius or the termination reflection coefficient.