An improved approximation for the spatial impulse response of a rectangular transducer

One common approximation for a field point located in the far field of the transducer is to trapezoidally-shaped function to approximate the true spatial impulse response. A quadrilaterally shaped function is proposed here. The quadrilaterally shaped function also includes the trapezoidally shaped function as a special case. This paper shows that the quadrilateral approximation applied in the specifically defined field location is superior to the trapezoidal approximation for the true spatial impulse response function when the transducer elements have the aspect ratio of approximately 10, typical of those found in 1.5 D arrays.