Legendre-tapered drive levels give spherical-cap arrays constant beamwidth with low side lobes

Evidence

Keele (Keele, 2000, 2002, 2003a,b) extended the work of Van Buren et al. (Rogers and Van Buren, 1978; Van Buren et al., 1983) to develop the constant beamwidth theory (CBT) arrays. In his papers, the transducer is a spherical cap of arbitrary half-angle with Legendre function shading. It provides a constant beam pattern and directivity with extremely low side lobes for all frequencies above a certain cutoff frequency. … To maintain constant beamwidth behavior, CBT circular-arc loudspeaker line arrays require that the individual transducer drive levels be set according to a continuous Legendre shading function. This shading gradually tapers the drive levels from maximum at the center of the array to zero at the outside edges of the array. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2913

Keele (Keele, 2000, 2002, 2003a,b) extended the work of Van Buren et al. (Rogers and Van Buren, 1978; Van Buren et al., 1983) to develop the constant beamwidth theory (CBT) arrays. In his papers, the transducer is a spherical cap of arbitrary half-angle with Legendre function shading. It provides a constant beam pattern and directivity with extremely low side lobes for all frequencies above a certain cutoff frequency. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2913

Categorization

• DEFINE: Defines constant-beamwidth-theory (CBT) arrays and the Legendre shading function that shapes their behavior.
• XREF: Connects to the chapter’s earlier array theory: CBT is the payoff of combining shading functions with curved source geometry.
• corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2913