Spherical retrodirective array

This paper derives the characteristics of a spherically-shaped retrodirective space array. The array can receive an incoming signal over 4\pi steradians, amplify, frequency translate, and modulate this signal, and then return it in the direction of the incident wave. The directivity of the array for every angle of incidence corresponds to the area illuminated by the incoming wave. In the array the retrodirective characteristic is obtained by a phase inversion technique that is realized in tunnel-diode image frequency converters. A circular cross section of the spherically-shaped retrodirective array is analyzed. The analysis is extended to the spherically-shaped array. It is shown that the effective aperture of a spherical array is smaller than the illuminated area. This reduction occurs because of a tapered amplitude distribution and a symmetrical phase error proportional to the frequency difference between incident wave and reradiated wave at the image frequency. The output spectrum of the converters in the array contains not only the image frequency signal but additional frequency components as well. Because of the phase characteristics of the spectral components, only the image frequency signal when reradiated by the array elements will add coherently in direction of the incident wave. The reradiation of the other frequency components is not collimated.