The frequency variable, u, has the dimensions of rad/mm, a is the acceptance angle of the DSF; that is, s(± a) = 0.5, s(0) = 1. Now since vsa(x) = vr1(x) vr2(x), p(x) = A 8(x), A = 1, P(u) = 1; hence, Vsa(u) = Vr1(u) * Vr2(u) and Vsa for the unit impulse input is Ssa(u), the Fourier transform of the synthetic aperture equivalent DSF. * denotes one-dimensional complex convolution. (Multiplication in the spatial (x) domain is equivalent to convolution in the spatial frequency (u) domain.) Thus, Ssa(u) can be written
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