Dense and sparse 2-D array radiation patterns in lossy media

Two-dimensional (2-D) transducer arrays are potentially able to generate real-time volumetric images of internal organs of the human body, and much work has been done on the subject in recent years. A 2-D array with high resolution and low grating lobe level requires a prohibitively large number of elements for existing technology. A successful solution to reduce the number of elements, without sacrificing the above mentioned characteristics, is to select a limited number of elements in a random way or combining transmitting and receiving apertures with element spacing greater than one-half of a wavelength. In this work, the effect of the human body attenuation on the performances of these so-called sparse arrays is investigated. We analytically demonstrate that, for continuous wave excitation and under paraxial approximation, the medium losses can be modeled as a Gaussian weighting function, acting off-axis in the observation plane. The variance of this weighting function decreases with the covered distance. Radiation patterns computed with both this simple model and with a more exact expression, are presented for sparse and dense 2-D arrays under continuous and pulsed wave operation. Comparisons between the results obtained with and without attenuation also are shown.