Concerning the null contours of vector sensors. Free

A common use of a vector sensor is to maximize the sensing of a plane wave coming from one direction while creating a null in regard to a plane wave coming from another direction. It is shown that when this is accomplished, there is a null not only in the desired direction but a whole contour of nulls. The shape of the contour is a function of a single parameter and is described by means of a contour plot in the azimuthal angle–elevation angle plane. Additional insight is found by mapping the contours onto a unit‐sphere in the spatial domain. One byproduct of the notion of null contours is a method for selecting the coefficients of the vector sensor for the case of two interfering sources. Finally, it is shown that once the null contour is understood for the vector sensor, it is a simple matter to extend the concept to directional acoustic sensors of higher order.