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Scan Specification for Regular Uniform Arrays

The scanning phase (eq. 4) is written in terms of the scan direction . Alternatively, for a regular uniform array, the scanning phase may be written in terms of the differential phase shift between elements.

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).