FIG. 5.

A comparison of measured computation times for beam patterns calculated with a constant number of Gauss abscissas using the expressions H₁, H₂, H₃, and H₄. As in Fig. 4, each beam pattern is computed on the same spatial grid as Fig. 3 for a piston with radius a = 5λ. A single sector that covers the entire computational grid in Fig. 1 is defined for these computations. A comparison of the raw computation times indicates that, for the same number of Gauss abscissas, the times required to compute the pressure field using the expressions in H₂, H₃, and H₄ are roughly the same, although H₃ (dot dash) is somewhat slower because of the additional complex term in the numerator of Eq. (7). Likewise, for the source geometry and computational grid evaluated here, the expressions H₂, H₃, and H₄ are all nearly three times faster than the impulse response solution H₁ (dotted line).