Sound field calculations for an ultrasonic linear phased array with a spherical liquid lens

Lenses are often used to provide focusing in the elevation dimension of ultrasonic linear phased-array transducers. The use of a liquid lens in this application adds a variable geometric focusing capability, determined by the radius of curvature of the lens surface and speed of sound in the liquid, to the electronic focusing produced by the linear phased array. An efficient method to calculate the sound field radiated from the linear phased-array transducer through the liquid lens is presented. It treats the lens surface as a secondary source distribution according to Huygens's principle, and employs a modified form of the rectangular radiator method to calculate the field. The appropriate phases for the array elements to focus and steer the beam are calculated by considering the refraction on the lens surface. Comparisons of computer simulations and experimental measurements of the field intensity distribution of a prototype linear array transducer with a liquid lens demonstrate the accuracy of the proposed method.