Application of the Golden Numerical Rings for Configure Acoustic Systems of Fine Resolution

The paper presents a new mathematical principle for improving the quality indices of acoustic systems with non-uniform structure (e.g. overlapping masks utilizing the entire ultra-acoustic aperture) with respect to the wavelength scale, where each pair of holes serves as an interferometer selecting the signal component at a spatial frequency, using novel design based on the combinatorial sequencing theory, namely the concept of golden numerical rings. The concept can be used for finding optimal placement of structural elements in spatially distributed systems, for example, positioning of holes elements in sonar antenna array. Golden numerical rings are cyclic sequences of positive integers which form perfect partitions of a finite interval [1, S] of integers. The sums of connected sub-sequences of a GRB enumerate the set of integer [1, S] exactly R-times. These design techniques make it possible to configure non-redundant masks in order to avoid interference of signal components of the same spatial frequency because phases of the components are unknown.