A Tutorial on Retroreflectors and Arrays Used in Satellite and Lunar Laser Ranging

Abstract

The present paper discusses the basics of retroreflector theory and the manner in which they are combined in arrays to service the laser tracking of artificial satellites and the Moon. We begin with a discussion of the relative advantages and disadvantages of solid versus hollow cube corners and the functional dependence of their optical cross-sections and far-field patterns on cube diameter. Because of velocity aberration effects, the design of an array for a particular space mission depends on many factors, including the desired range accuracy and the satellite’s orbital altitude, velocity, and pass geometry relative to the tracking station. This generally requires the individual retroreflectors in the array to be “spoiled” by perturbing one or more of the 90-degree angles that define a perfect cube corner, or alternatively, by adding a curved surface to a hollow cube. In order to obtain adequate return signal strengths from all points along the satellite path, the rotational orientation of the retroreflectors within the array may need to be varied or “clocked”. Possible approaches to developing millimeter-accuracy arrays with both large cross-sections and ultrashort satellite signatures are discussed, as are new designs proposed to replace aging reflectors on the Moon. Finally, we briefly discuss methods for laser ranging beyond the Moon.