Apache Point Observatory Lunar Laser-ranging Operation - Principles of Operation

Principles of Operation

APOLLO is based on measuring the time-of-flight of a short-pulse laser reflected from a distant target—in this case the retroreflector arrays on the Moon. Each burst of light lasts 100 picoseconds (ps). One millimeter in range corresponds to only 6.7 ps of round-trip travel time. However, the retroreflectors on the Moon introduce more than one mm of error themselves. They are not usually at an exact right angle to the incoming beam, so the different corner cubes of the retroreflectors are at different distances from the transmitter. This is because the Moon, although it keeps one face to the Earth, does not do so exactly—it wobbles from side to side and up and down, by as much as 10° in magnitude. (There is a nice animated GIF of this on the libration page.) These librations occur since the Moon rotates at constant speed, but has an elliptical and inclined orbit. This effect may seem small, but it is not only measurable, it forms the largest unknown in finding the range, since there is no way to tell which corner cube reflected each photon. The biggest array, the 0.6 m Apollo 15 reflector, can have a corner-to-corner range spread of ≈ 1.2 tan(10°) m, or 210 mm, or about 1.4 ns of round-trip time. The root-mean-square (RMS) range spread is then about 400 ps. To determine the distance to the reflector to 1 mm precision, or 7 ps, by averaging, the measurement needs at least (400/7)2 ≈ 3000 photons. This explains why a much larger system is needed to improve the existing measurements—the current 2 cm RMS range precision requires only about 10 photons, even at the worst-case orientation of the retroreflector array.

APOLLO attacks this problem by using both a bigger telescope and better astronomical seeing. Both are considerably improved over existing systems. Compared to McDonald Observatory ranging station, the Apache Point telescope has a factor of 20 greater light-collecting area. There is also a big gain from better seeing—the APO site and telescope combined can often achieve one arcsecond seeing, compared to the ∼ 5 arcseconds typical for MLRS. The better seeing helps two ways—it both increases the laser beam intensity on the Moon and reduces the lunar background, since a smaller receiver field-of-view may be used, gathering light from a smaller spot on the Moon. Both effects scale as the inverse square of the seeing, so that the signal-to-noise ratio of the lunar return is inversely proportional to the fourth power of the seeing. APOLLO should therefore gain about 20 (from the bigger telescope) × 25 (for better seeing) = 500 × in return signal strength over MLRS, and additional factor of 25 in signal-to-noise (from fewer stray photons interfering with the desired ones). Likewise APOLLO should get a signal about 50 times stronger than the OCA LLR facility, which has a 1.5 m telescope and seeing of about 3 arcsec.

The increased optical gain brings some problems due to the possibility of getting more than one returned photon per pulse. The most novel component of the APOLLO system is the integrated array of Single-Photon Avalanche Diodes (SPADs) used the detector. This technology is needed to deal with multiple photon returns within each pulse. Most single photon detectors can only record the time of the first photon if another arrives very soon thereafter (This effect is called dead time.). This means that if more than one photon comes back in a single pulse, a conventional single-photon detector would record the arrival time of only the first photon. However, the important quantity is the centroid of the time of all returned photons (assuming the pulse and reflectors are symmetrical), so any system that can return multiple photons per pulse must record the arrival times of each photon. In APOLLO, the incoming photons are spread over an array of independent detectors, which reduces the chance that two or more photons hit any one of the detectors.