Method and apparatus for producing an acoustic field

A method comprising:

• i) producing an acoustic field from a transducer array having known relative positions and orientations;
• ii) defining a plurality of control points wherein each of the plurality of control points have a known spatial relationship relative to the transducer array;
• iii) assigning an amplitude to each of the plurality of control points;
• iv) computing a matrix containing elements which represent, for each of the plurality of control points, the effect that producing a modeled acoustic field having the assigned amplitude with a particular phase at that control point has on the consequential amplitude and phase of the modeled acoustic field at the other control points;
• v) calculating a plurality of eigenvectors of the matrix, each of the plurality of eigenvectors representing a set of relative phases and relative amplitudes of the modeled acoustic field at each of the plurality of control points;
• and
• vi) selecting one of the set of phases and relative amplitudes of the modeled acoustic field and operating the transducer array to cause at least one transducer from the transducer array to output an acoustic wave having an initial amplitude and phase such that the phases and amplitudes of the resultant acoustic field at the control points correspond to the phases and relative amplitudes of the selected set of phases and relative amplitudes of the modeled acoustic field.