An L × L square transducer, submersed in water, is centered at the origin and is pointed down the +z-axis. A large layer of homogeneous fat begins z = z0 and extends to the depth of penetration, so that the only possible returns are those from the interface between water and fat. The transducer is capable of rotating toward the x-axis by θ degrees. Assume that there is no attenuation in the water. Assume that the transmitted pulse is a gated sinusoid of duration T and height A0.
(a) Assume that z0 is in the far field and derive an expression for the strength of return as a function of angle. Make approximations where appropriate and do not forget the sidelobes.
(b) Assume that the transducer and preamplifier are able to detect signals 80 dB down from the transmitted pulse height. Assume also that a Bmode binary image is generated so that all signals above the detectable threshold are plotted in black and all signals below the threshold are plotted in white. Sketch the B-mode image that would result from this experiment.
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