You are asked to select the best ultrasound imaging parameters for imaging a deep-lying small structure. Assume that this object is located at 20 cm depth and is embedded within a homogeneous tissue with sound speed c = 1, 500 m/s and absorption coefficient α = af, where a = 1.0 dB/(cm MHz). Also assume that the system is sensitive to at most a 100 dB signal loss.

You can choose one of three operating frequencies: f = 1 MHz, f = 2 MHz, or f = 5 MHz. Given any frequency, you can choose one of two transducer diameters: D = 1 cm or D = 2 cm. Assume that all transducers have flat faces and use the split-range field pattern approximation (i.e., geometric and far-field approximations in their appropriate ranges). Which combination of f and D will give the best image of this structure? Justify your answer.