Phased Arrays - MATLAB Simulations for Radar Systems Design - page 338

Eq. (8.56) can be expressed in terms of the directional cosines

u θφ =

v θφ

sin cos

(8.57a)

= sin sin

u

--  

φ = atan

(8.57b)

u 2 v 2

θ = asin +

The visible region is then defined by

u 2 v 2

+ ≤ 1

(8.58)

It is very common to express a planar arrayÓs ability to steer the beam in
space in terms of the

UV , space instead of the angles θ φ , . Fig. 8.21 shows

how a beam steered in a certain θφ , direction is translated into UV , space.

V

1

U

θ

φ

Figure 8.21. Translation from spherical coordinates into U,V space.