1. A piezoelectric probe for use in conjunction with an ultrasonic imaging system, comprising: a) a two-dimensional thinned array of piezoelectric elements of varying size, in which the smallest of the elements is of major dimension L and the largest of the elements is of major dimension M, which is at least 2 L, and at least a majority of the elements are of major dimension greater than L; and b) a plurality of electrical conductors, said conductors electrically connected individually to each of said piezoelectric elements.