Questions first, then my rough estimations:
1) Is it possible to perform moon laser ranging with amateur motorized 114mm telescope? My calculations suggest that for 1mJ laser it should receive ~2 photons per source 1mJ laser pulse.
2) Given that we already talking about individual photons, how it was possible to perform moon laser ranging BEFORE retro-reflectors were deployed to the moon? Retroreflector sends back light in ~1arcsecond angle, while bare lunar sufrace - in ~6 archours, which means we supposed to receive signal ~(6*60*60)^2 = 4.5*10^8 weaker, i.e. even with 2.5 meter telescopes we are talking 1 photon per 250 1J pulses.
My rough estimations: Given that atmosphere turbulence limits telescope resolution to ~1 arcsecond (adaptive optics was not available when laser ranging experiments started, nor it is available now for amateurs), if we use telescope with diameter larger than ~150mm (so that we are limited by atmosphere, not diffraction) to expand the laser beam we will get ~1939x1939 meter illuminated area on the moon surface (tan(1arcsec)*400'000km). Which means only 1/(1939*1939) part of our energy will reach reflector.
Retroreflector is ~1x1 meter in size. It will reflect the light with same beam divergence - 1arcsecond. Too sad, as diffraction limit for retro-reflector of such size is ~0.2 arcsecond.
So, if our receiving telescope has area of ~1 meter^2, we will receive again 1/(1939*1939) part of what reached the moon, so total attenuation is ~ 1.4*10^13.
If we use 532nm pulse laser with 1mJ pulse energy, it will emit 2.67*10^15 photons, which means we are going to receive ~190 photons per pulse. Sounds realistic.
These calculations suggests that 114mm amateur telescope should be able to detect 2 photon per pulse - again should be detectable statistically.
Answer
Per BarsMonsters's request I'll expand my comment into an answer.
This same calculation has been done in a post on the blog Built on Facts. His conclusion is that amateur lunar ranging isn't feasible with a the lasers at his disposal. (Specs are given in the quote.)
Typical values for the lasers we use might be somewhere in the 1 milliradian range. The distance to the moon is roughly 400,000 km, so the portion of the lunar surface illuminated by our laser will be about (0.001)*(400,000 km) = 400 kilometers in diameter. This is an area of about 125 billion square meters. If the retroreflector is one square meter, only about 1 part in 10^11 of our emitted light even makes it to the reflector. Now the reflected light has to make it back to the earth. If we’re extremely optimistic, we might say that the reflector introduces no extra angular spread, and its reflected light is spread over a 400 km diameter of the earth’s surface. To a first approximation this just means the total there-and-back efficiency is about 1 part in (10^11)^2, or one photon in 10^22.
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The energy of one photon of wavelength λ is:
$$\frac{1}{A}\frac{dp}{dt}=\frac{S}{c}$$
The laser we’d likely use has a wavelength of 532 nanometers, and plugging into the equation we find that each photon has an energy of about 3.7 x 10^-19 joules. Therefore we’d need about 1000 joules per pulse to get up to the neighborhood of 10^22 photons per pulse. And we need 10^22 photons just to get one photon back per pulse on average.
We have a few compact 15 mJ/pulse q-switched Nd:YLF lasers with 1 KHz rep rates, and we even have a few not-so-compact 2 J/pulse with a 10 Hz rep rate. With a 2 second round trip time, the repetition rate isn’t so relevant since we can effectively only use one pulse per round-trip time. Even 2 joules won’t cut it unless we’re willing to do many thousands of shots worth of statistics. And that’s without even thinking about noise, which will not be inconsequential even with good filtering.
I can't answer your second question, but I can help with a few references. Linked from the above post, there is an article on The Lunar Ranging Experiment (PDF). The introduction gives some history of the retroreflector measurements, as well as the ranging experiments before the retroreflectors were placed.
In 1962, Smullin and Fiocco (3) at Massachusetts Institute of Technology succeeded in observing laser light pulses reflected from the lunar surface using a laser with millisecond pulse length. Additional measurements of this kind were reported by Grasyuk et al. (4) from the Crimean Astrophysical Observatory, and later Kokurin et al. reported successful results (5) using a Q-switched ruby laser.
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(3): L. D. Smullin and G. Fiocco, Institute of Electrical and Electronics Engineers Proceedings 50, 1703 (1962).
(4): A. Z. Grasyuk, V. S. Zuev, Yu. L. Kokurin, P. G. Kryukov, V. V. Kurbasov, V. F. Lobanov, V. M Mozhzherin, A. N. Sukhanovskii, N. S. Chernykh, K. K. Chuvaev, Soviet Physics Doklady 9, 192 (1964).
(5): Yu. L. Kokurin, V. V. Kurbasov, V. F. Lobanov, V. M. Mozhzherin, A. N. Sukhanovskii, N. S. Chernykh, Journal of Experimental and Theoretical Physics Letters 3, 139 (1966). (link)
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