andomly distributed with a root mean square (r.m.s.) surface error, the efficiency is given by equation 9.54. This is a function of frequency and falls off rapidly above a certain value, which means that the upper frequency for which a reflector can be used is always given by the surface errors. The effect on the radiation pattern of random surface errors is to fill in the nulls and to scatter energy in all directions SO that the far-out sidelobes are uniformly raised. (9.54) Dual Symmetric Reflector Antennas The performance of a large reflector antenna can be improved and the design made more flexible by inserting a subreflector into the system (see Figure 9.11). There are two versions: the Cassegrain, where the subreflector is a convex hyperboloid of revolution placed on the inside of the parabola focus, and the Gregorian, where a concave elliptical subreflector is Reflective Antenna Types Fig. 9.11 Dual-reflector antennas: (a) Cassegrain; (b) Gregorian. placed on the outside of the parabola focus. In symmetric reflectors the Cassegrain is more common because it is more compact, but the electrical performance is similar for both systems. The advantages of dual reflectors are as follows: 1. The feed is in a more convenient location. 2. Higher-performance feeds can be used because the subtend angle is such that wide aperture diameter feeds are needed. 3. Spillover past the subreflector is directed at the sky, which reduces the noise temperature. 4. The depth of focus and field of view are larger. The study of radiation characteristics and efficiency dual reflectors is similar to that of the prime-focus reflector. Analysis of the radiation patterns depends partly on the size of the subreflector. If it is small then physical optics or GTD must be used. The main reflector is usually large, SO geometric optics are adequate. The limiting factor to obtaining high efficiency in a standard parabola is the amplitude taper across the aperture due to the parabola's feed pattern and the space loss (i.e., the illumination eff