In measuring small microwave reflections back to the transmitting antenna, a finite reflecting surface which simulates the reflection of an infinite plane is desirable for calibration. Treating a flat reflecting surface by the methods of physical optics, the reflection can be represented as the sum of the contributions of Fresnel zones. Owing to the slow rate of decrease of reflections from successive zones, the shape of the surface has considerable effect on the accuracy with which its reflection simulates that of an infinite plane. By means of the calculus of variations, an optimum shape is designed which, for a given antenna pattern, reflector size, and range of antenna to reflector distances, will give the closest simulation of the reflection of an infinite plane. Such an optimum surface of 23 wavelengths extreme dimensions has been constructed for use at 25 wavelengths from a dipole antenna. The maximum simulation error was calculated to be ±3 percent. The reflection from this surface has been measured and is within ±4 percent of that of an infinite plane over the range of 15 to 35 wavelengths from the antenna.
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