Development of an integrated model and system to enable optimal efficiency of the HartRAO LLR signal path.

Abstract

The Lunar Laser Ranger (LLR) system under development at the Hartebeesthoek Radio Astronomy Observatory (Hartford) in South Africa is being built to accurately measure the Earth-Moon distance (at 1 cm level) through the use of short laser pulses, a single photon detection system, an accurate timing system and other sophisticated components. This LLR system is unique in Africa and indeed in the entire Southern Hemisphere. The system utilizes a 1 m diameter optical telescope, which was donated to the project by the Observatoire de la Côte d’Azur of France. In this work, the author discusses the development of an integrated model that will be utilized to obtain optimal efficiency of the HartRAO-LLR system. The model is used to estimate the expected number of returned photons by considering a number of parameters which affects the laser beam pulses as they traverse the atmosphere from the LLR telescope to the Moon and back to the telescope. Factors such as the apparent Earth-Moon range, atmospheric extinction, laser beam characteristics, optical path efficiencies and others, affect the estimated (predicted by software) and actual (measured) number of returned photons for the HartRAO-LLR station. The estimated average signal return rate (which is dependent on a number of factors) of the HartRAO-LLR ranges between 0 to 12 photons per minute, which is in agreement with the available data from five globally distributed LLR stations. It also correlated with the estimated returns that were obtained using least squares parameter estimations. They were in agreement by an average difference of 0.00272. Our estimated signal returns are strongly affected by two-way atmospheric extinction (atmospheric and cirrus cloud transmissions), variations in the laser beam incident angle on the retroreflectors located on the Moon as well as the varying Earth-Moon range. A new parameter, named lunar reflectivity ranging between 0 and 1, was introduced in the link budget equation to consider the effects of Moon Phases on the returned photons. Modelling the returned number of photons and comparing these to the actual number received leads to an understanding of the effects of numerous variables on the total laser path efficiency. Total system efficiency can be improved as well, as particular atmospheric conditions will not allow LLR to be successful on certain days. For these days, the system can be utilized for other purposes such as maintenance or satellite laser ranging.