Phase scanning of one-dimensional pattern

A method of determination of phase function required for scanning a one-dimensional pattern is presented. Analysis reveals that the one-dimensional pattern is produced in the meridian plane of a two-dimensional aperture by application of nonlinear phase in the directions along and parallel to this plane. Scanning is produced by application of a linear phase progression in the perpendicular direction. The shape of the linear phase progression is different for different positions along the direction of nonlinear phase distribution. Expressions giving the variation of this slope along the length of the array for various amplitude distributions and desired radiation patterns are derived.