A technique for the in situ phase calibration of in-duct axial microphone arrays

In aeroengine noise experiments in-duct microphone arrays are often used to make detailed measurements of the sound field transmitted along the duct. The individual microphones in the array must be calibrated with respect to magnitude, and often more critically with respect to phase. Calibration is difficult to perform in situ due to the presence of the duct. This paper presents a technique to allow in situ phase calibration of axial microphone arrays. It relies on the observation that the measured cross-spectral pressure matrix at the array has a Hermitian Tِplitz form in the case where the propagating duct modes are mutually incoherent. Using this property a system of equations can be written which, when solved, allows the phase calibration factors to be obtained. The technique is verified experimentally using a no-flow laboratory rig by comparing the phase calibration factors obtained with those measured in free-field conditions. The accuracy of the phase calibration factors obtained by the technique is limited by the degree of deviation of the measured cross-spectral matrix from Tِplitz behaviour. In the experimental results shown this is less than 15° at duct frequencies below ka=25. The technique is a robust and rapid method for calibrating in-duct axial microphone arrays.