Bessel and Conical Beams and Approximation With Annular Arrays

le those of a conical transducer with cone angle #. The equivalent angle can be shown to be: sin # = #/k (3) At a certain depth and with a finite aperture, the plane waves will no longer overlap. This results in a conical shadow zone which defines the depth of field [1]. The shadow zone starts at a depth: DOFBessel # R/ tan # = R p (k/#) 2 - 1 (4) where R is the transducer's radius. The contour plot of the acoustic field for an ideally excited transducer, i.e. one where the excitation follows the continuous curve in Fig. 1, is shown in Fig. 2. This transducer has only two peaks in the Bessel excitation, but still gives a good Bessel beam. A flat transducer of this size has a nearfield-farfield transition point at 128 mm. A step-wise approximation to the Bessel function corresponding to an equal-area annular tr