Remarkably, the five lunar retroreflector arrays are still visible and producing useful data after 40 years of exposure to the lunar environment. During that time, the precision of the range measurements has improved each time the ground stations were upgraded to the most advanced ranging technology at the time. This is despite the fact that the efficiency of the arrays appears to have degraded by a factor of 10 . Incredibly, it has taken nearly 40 years for the ground stations to catch up with the potential capability of the retroreflector arrays.
The first LLR measurements had a precision of about 20 cm. Since 1969, several stations have successfully ranged to the lunar retroreflectors and have increased the range accuracy by a factor of 10 to the level of a few centimeters. Poor detection rates have historically limited LLR precision (not every laser pulse sent to the Moon results in a detected return photon). However, the relatively new APOLLO system uses the large collecting area of the Apache Point telescope, a tightly collimated beam, good atmospheric image quality, and has very efficient avalanche photodiode arrays such that thousands of detections are recorded (even multiple detections per pulse) leading to a statistical uncertainty of about 1 mm for timescales of less than 10 minutes [6, 43].
The dominant random uncertainty per photon received by APOLLO stems from the physical size of the arrays and their changing orientation due to the lunar librations. The incoming pulse from APOLLO will illuminate an entire array, but only one (sometimes a few) of the photons will be detected upon return. APOLLO cannot determine what area of the array contributed most of the returned light, so the tilt of the array with respect to the Earth spreads out the distribution of laser pulses. The typical array dimension (Apollo 11 and 14) of 0.5 m and a typical libration angle of 6 degrees translates to a full-width pulse-spread of about 330 ps in the round-trip time. As the Moon librates, the amount of spreading changes since the array is also changing its orientation with respect to the ground station.
Modest improvements in the ranging technology will not significantly improve the range precision as the array tilt will continue to dominate the error budget for the foreseeable future. In addition, new arrays with more (or less) cubes of the same size would result in no gain: doubling the physical dimension doubles the random uncertainty requiring four times as many photons, exactly what doubling the linear array dimension provides. Likewise, the reduction in return photons would eliminate any benefit of going with a smaller array.
To maintain the advantage that multiple cubes provide in response, but eliminate the issues with orientation, one can separate the cubes far enough that their responses do not overlap when seen by the Earth stations. A range separation of about 10 cm between the cubes should be sufficient to distinguish them in the data. Since the typical (for APOLLO) 5 microradian laser beam covers a 2 km spot on the moon, any reasonable spacing will result in illumination of the entire set of reflectors at once. The cubes could be coarsely surveyed individually to provide enough information to be acquired by the lower energy Earth laser stations, or the initial acquisition from the ground could be performed with the higher laser energy / larger telescope lunar laser ranging Earth stations, which will have good signal-to-noise ratios.
Large single cube corners can also be made to provide similar return rates as the Apollo arrays without significant pulse spreading. The response from a 7.6 cm cube would be 16 times larger than that of the Apollo 3.8 cm cubes. However, simply making solid cubes larger increases their weight by the ratio of the diameters cubed. The additional size also adds to thermal distortion effects and decreases the return beam divergence: a very narrow divergence can cause the return spot to completely miss the station due to velocity aberration. Spoiling (making the dihedral angles of the cube different from 90 degrees) can compensate for the velocity aberration but reduces the effective cross section.
Solid cube corner retroreflectors (up to 11 cm) have flown on over a hundred missions, for both satellites and lunar laser ranging. Recent tests of the 10 cm cube shown in Figure 7 has demonstrated it meets relevant requirements for the lunar environment . Designs for the housing are still in development .
The main disadvantage of large solid cubes is that the thermal requirements become very challenging because of the temperature dependence of the cube material’s index of refraction. A promising alternative is to use hollow (open) cube corners. Since hollow cubes are reflective, the index of refraction problem goes away. They also potentially weigh less, have smaller thermal distortions, and do not introduce significant polarization effects. Therefore, they can be made larger without sacrificing as much in optical performance. Hollow cubes have flown on a few missions, but are generally not used on satellites for laser ranging because of a lack of test data and some indications of instabilities at high temperatures. A recent program at NASA Goddard Space Flight Center is looking at applying advanced bonding techniques for space optics that have the potential for mitigating these problems.
Isolation from ground motion and thermal changes are also key for going beyond the Apollo array capabilities. Each reflector should be rigidly grounded to directly sense lunar body motion and be located far enough away from normal human activity to prevent vibration and contamination (dust) from affecting the cubes. To provide thermal stability, the retroreflectors could be thermally coupled to the ground below the surface layer. As shown in Figure 8, measurements from the Apollo 15 and 17 heat flow probes indicate that the large diurnal temperature fluctuations are negligibly small at depths below 0.8 meters [32, 28]. To take advantage of this stability, one could drill a hole about a meter deep and insert a rod with high conductivity and a low coefficient of thermal expansion to stabilize the retroreflector temperature. The retroreflector package would be mounted to the exposed end of the rod. A thermal blanket positioned over the lunar surface around and below the retroreflector would also reduce the thermal fluctuations induced from the surrounding regolith.
Living Rev. Relativity 13, (2010), 7
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