An analysis of the corrugated-surface twist polarizer which finds application in the design of scanning reflector antennas is presented. The spectraI-interation technique, a novel procedure which combines the use of the Fourier transform method with an iterative procedure is employed. The first step in the spectral-iteration method is the conversion of the original integral equation for the interface field into a form which is suitable for iteration using a method developed previously. An important feature of the technique is that it takes advantage of the discrete Fourier transform (DFT) type of kernel of the integral equation and evaluates the integral operators efficiently using the fast Fourier transform (FFT) algorithm. Thus, in contrast to the conventional techniques, e.g., the moment method, the spectral-iteration approach requires no matrix inversion and is capable of handling a large number of unknowns. Furthermore the method has a built-in check on the satisfaction of the boundary conditions at each iteration.