Mathematical characterization of the acoustic brightness and contrast control problem in complex vector space.

Abstract

The acoustic brightness and contrast control methods [J.-W. Choi and Y.-H. Kim, J. Acoust. Soc. Am. 111, 1695 (2002)] is one of the methods which can generate higher acoustic energy in desired space by controlling multiple control sources. Since the problem is represented with complex valued multidimensional vector, the relation between input control values (magnitude and phase information of control sources) and output value (acoustic energy level in desired zone) is somewhat hard to predict intuitively. In this paper, a visualized analysis method for the acoustic brightness and contrast control problems is proposed. A geometric structure is given to the problem and acoustic variables are corresponded with geometric quantities. To give a geometric structure to acoustic brightness and contrast problem, the problem is reformulated with inner product. From the geometric structure, the acoustic brightness and contrast control problems are interpreted as a simple geometry problem. From the proposed methods, various 2D simulation results with different conditions can be interpreted with simple geometry characteristic.