The relationship between sound field reproduction and near-field holography

The problem of reproducing a desired sound field with an array of loudspeakers and the technique known as Near-Field Acoustical Holography share some fundamental theoretical aspects. It is shown that both problems can be formulated in terms of an integral equation which usually defines an ill-posed problem. The example of spherical geometry is discussed in detail. It is shown that for both the reproduction and the acoustical holography cases, the ill-conditioning of the problem is greatly affected by the distance between the source layer and the measurement/control surface.