Focused, phased-array plane piston and spherically-shaped concave piston transducers: comparison for the same...

It has sometimes been assumed that the phased-array plane piston transducer and the spherically-shaped concave piston transducer are equivalent structures when both have the same aperture and focal point. This assumption has not been previously examined, nor has an expression for the on-axis impulse response of the focused, phased-array plane piston transducer been derived. It is shown in this paper how such an expression can be obtained. Comparisons of the impulse response for both structures show similarities, as well as some differences that could be significant as the observation point approaches the focal point. Comparisons are also performed for wide-band pulses close to the focus as well as for sinusoidal excitation. A physical explanation for the cause of the impulse response discrepancy is shown to be due to the nature of the piston focusing delay and its effect on the Rayleigh integral.