A new algorithm for spatial impulse response of rectangular planar transducers

Previous solutions for spatial impulse responses of rectangular planar transducers require either approximations or complex geometrical considerations. This paper describes a new, simplified and exact solution using only trigonometric functions and simple set operations. This solution, which can be numerically implemented with a straightforward algorithm, is an exact implementation of the Rayleigh integral without any far field or paraxial approximation. Additionally, a nonlinear relationship was also established for spatial impulse responses from two field points which share the same projection point on the transducer surface plane. By incorporating this relationship in the algorithm, the computational efficiency of spatial impulse responses and continuous fields is improved about 20-folds and 14-folds, respectively. This algorithm has practical applications in designing l-D linear/phased arrays, 1.5-D arrays and 2-D arrays, as demonstrated through numerical simulations with array transducers. Experiments were also conducted to verify the new solution and results show that the algorithm is both accurate and efficient. The application of this method may include development of ultrasound imaging system for hard and soft tissue nondestructive assessment.