What is the minimal equipment required to observe the Apollo lunar retroreflectors? It's rather well known that the Apollo lunar landings installed retroreflectors on the Moon, and that these can be used to reflect laser beams back at Earth, to measure the Earth-Moon distance to exquisite accuracy.
However, the weaselly phrase, "can be used", in that common understanding, is rarely examined in practice. So, I'd like to ask: what does it take to observe a retroreflected beam from this equipment?


*

*What is the diffraction-limited minimal width of a laser beam when it reaches the Moon if it is sent from a laser pointer? an amateur-astronomy telescope? the telescopes in actual use for this purpose?

*What is the fraction of laser power that can be effectively received back on Earth using an equivalent aperture?

*Does atmospheric seeing play a role in degrading these observations?

*What types of detectors are required to observe the beam? What laser powers are required to make the reflected beam visible to reasonable detectors?

*Is any fancy signal processing (say, shining out a burst of five pulses in a row, and looking for a matching structure in the observed image) necessary for this?

*(and, while we're here: what safety and legal concerns must be addressed when shooting laser beams at the night sky?)


I'm happy to accept a reasonably recent account of this type of observation, but I'm mostly interested in an explanation of what the minimal equipment would be to achieve it, as well as explanations of how the physical considerations in the bullet points above apply to such a setup.
 A: Some partial answers to some of your questions (a bit late, but for some reason this popped up in my feed now):
In the limit of large z (distance from beam waist), the beam radius w(z) increases linearly with z and the half-angle of the cone becomes $\theta = \frac{\lambda}{\pi n w_0}$. The total angular spread of that cone is then $\Theta = 2\theta$, and this cone contains 86% of the laser beams power (with $1/e^2$ beam waist definition). So for a beam launched from a standard laser pointer (633nm, 2mm beam diameter (probably a bit large), assuming beam waist is at laser point exit window) we'll get a divergence angle of 0.0115$^\circ$. Sounds small, but if I didn't mess up my calculation this corresponds to a beam radius on the moon of a whopping 80km moon-earth distance 400,000km). So you would want to choose a much bigger beam, and still your beam diameter would be pretty large by the time it gets to the moon.
This paper has lots of interesting details. Early laser moon ranging experiments in the 1960s used a 2.7m telescope, which resulted in a beam diameter on the moon of several kilometres. Apparently they received as little as 0.01 photons in return per pulse, so averaging of 10-45 minutes was necessary.
Seeing does definitely play a role. The return time to the moon and back is roughly 2.5s, and atmospheric seeing typically changes on the millisecond scale (hence why adaptive optics systems of big telescopes are striving for kHz rates). They also talk about seeing problems in the aforementioned paper.
In that paper they used pulsed lasers, presumably both for timing purposes and to increase the peak power. I'd say the more power, the better.
Regarding the legal issues: I know that the guide star lasers operated by the big telescopes need to be coordinated with air traffic control and they additionally operate automatic switch-off mechanisms in case a plane comes too close to the beam. Some instruments on some satellites also don't appreciate being hit by a powerful laser beam, and so as far as I'm aware the laser operators also take satellite positions relative to their lasers into account and switch off if needed. I don't know how easy it is to obtain the permits to operate a laser to shoot to the moon, but it probably helps that the large telescopes are typically in the middle of nowhere and not near a major airport.
