Scan Specification for Regular Uniform Arrays

To develop this alternate scanning phase description, (eq. 7) is used to rewrite the expression (eq. 4) in doubly indexed form as follows:

(9)

(Let us define y_u as the differential phase between adjacent elements in the u direction. Similarly, let us define y_v as the differential phase between adjacent elements in the v direction. Then

(10)

and

(11)

The scanning phase (eq. 4) may now be rewritten in terms of y_u and y_v as

(12)

Thus in the case of a regular uniform array, the angle pair (y_u, y_v) may act as a
substitute scan definition for the more general (f₀, q₀).