Collimation of row-and-column steered phased arrays

An optically fed phased array must be provided with a means of collimation as well as with a beam steering function. The same phase shifters which are used to steer the beam can be used to collimate the beam. The use of row-and-column phase commands, while greatly simplifying the beam steering function over that required for commanding individual elements, precludes the attainment of exact collimation. A consequent phase error across the aperture results in a loss of antenna gain. For a given order of approximation to the collimation function, the minimization of the gain loss is a valid criterion for completely specifying all the parameters of the approximate collimation function. The gain loss incurred can then be determined. This paper develops the equations necessary to specify any order of approximation to the collimation function and the expression for the gain loss. Examples illustrate the differences between first- and second-order approximations and the effect of another parameter (f/D) on the gain loss of a typical antenna system.