TABLE OF CONTENTS A planar array is capable of steering the beam in two dimensions. In a spherical-coordinate system the two coordinates ? and ? define points on the surface of a unit hemisphere. As shown in Fig. 7.8, ? is the angle of scan measured from broadside and ? is the plane of scan measured from the x axis. Von Aulock46 has presented a simplified method for visualizing the patterns and the effect of scanning. He considers the projection of the points on a hemisphere onto a plane (Fig. 7.9); the axes of the plane are the direction cosines cos ? x, cos ? y. For any direction on the hemisphere the direction cosines are
| cos ? x | = sin ? cos ? |
| cos ? y | = sin ? sin ? |
The direction of scan is indicated by the direction cosines cos ? xs, cos ? ys. Here the plane of scan is defined by the angle ? measured counterclockwise from the cos ? x axis and is given by
The angle of scan ? is determined by the distance of the point (cos ? xs, cos ? ys) from the origin. This distance is equal to sin ?. For this reason a representation of this sort is called sin ? space. A feature of sin ? space is that the antenna pattern...
