Multi-channel calibration of microphone arrays based on the array related transfer function

For microphone arrays, conventional calibration procedures typically characterize microphones individually. However, this component-level approach often neglects the influence of the array structure itself, leading to systematic errors when the microphones are operated as a complete array system. This study evaluates two free-field substitution calibration strategies for a digital MEMS array. The first is the standard substitution method, based on IEC 61094-8, in which each microphone is calibrated individually at a fixed position using the reference microphone. The second is a proposed multi-channel calibration strategy using an array related transfer function (ARTF). By utilizing numerical models to correct for non-planar wave incidence and geometric mismatches, the multi-channel method enables the concurrent characterization of all array elements. For the on-axis free-field calibration case, the method agrees with the sequential benchmark within 0.3 dB, while phase calibration is evaluated as relative inter-channel calibration with respect to a designated reference channel. Model-based directional-response analysis further estimates that, at high frequencies, the diffuse-field sensitivity can differ from the on-axis free-field sensitivity by about 0.5 dB, while directional scattering can exceed 2 dB for rear-incident sound. These results support ARTF-based calibration as a practical on-axis system-level approach for digital MEMS arrays and show the importance of matching the sensitivity definition to the application environment of microphone arrays.