On grating plateaux of nonuniformly spaced arrays

This paper investigates the optimization and synthesis of nonuniformly spaced arrays with respect to the flattening of their grating plateaux. The analysis begins with the proof that the exponential spacing gives flat space-factor grating plateaux, using Poisson's sum and the stationary phase method. The theory then is generalized to include arrays of nonisotropic elements. It is found that results of the above analysis can be reduced to very simple forms. Through the use of Parseval's theorem, the theory of the space-factor gain of nonuniformly spaced arrays is also developed.