Errors due to sensor and position mismatch in planar acoustic holography

Abstract

There are many sources of measurement errors when one attempts to construct a hologram of near-field acoustic holography. These errors are amplified when predicting pressure at a point which is located near an acoustic source. Errors due to a sensor mismatch and an inaccurate measurement location, or position mismatch, are the main interests of this study. We theoretically measure the errors in terms of their probabilities, bias, and random error. Analysis in a wave number domain shows that the bias error can be regarded as negligible, but the random error is significant in a backward prediction. The random error is suggested to be measured in terms of random error energy. Then, the amplification ratio of the random error energy is related to measurement spacing on a hologram plane, prediction spacing on a prediction plane, and the distance between the hologram and prediction plane.