Scalar analysis of nonsymmetrically distorted umbrella reflector

An approximation technique for analyzing nonsymmetrically distorted umbrella reflectors is presented which offers savings in computer time by a factor of twice the number of gores. The surface distortions are described by incorporating an additional path-length phase factor into the illumination function. By expanding this phase factor in a finite Fourier series and neglecting Bessel functions of large order and small argument, the field integral reduces to a compact expression integrated over only half of a gore.