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This answer to What exactly is a “Next Generation Lunar Reflector”? Difference in design and performance? quotes Next Generation Lunar Retroreflectors Should Fly Soon (published in the magazine Forbes) and another section of that article says:

The Apollo retroreflectors are made up of either 100 or 300 individual glass corner cube retroreflectors (CCRs) attached to a metal frame, says Currie. But this Apollo-era design isn’t a good fit with today’s more precise, thermally-stable, state-of-the-art laser and timing technology, says Currie, who helped design the Apollo retroreflectors.

Earth-based lasers hit only one of these Apollo-era corner cubes and it’s impossible to know which one. That leads to uncertainty in the cube’s exact location on the Moon. Thus, timing of the laser ‘returns’ from the Moon to Earth using the old Apollo retroreflectors is hamstrung in their precision.

My question is not if it is a good idea to learn about Physics by reading articles in Forbes, it's about the physics behind the "Earth-based lasers hit only one of these Apollo-era corner cubes..." bit.

The retroreflector array is a large number of discrete reflectors, and while the astronauts took pains to align the array normal to the average direction towards Earth it's not perfect. Reflection across one reflector can be fairly coherent, but between each one and the others there will be delays of millimeters or even centimeters.

My problem is in understanding what happens when counting and measuring the arrival time of photons in this case. It's a pulsed laser and most pulses result in either zero or one photon recorded in a photomultiplier tube.

Is it really reasonable to think of the photon as having scattered from one of the many corner cubes, or should we think of the arriving photon as having been reflected from the average distance of all the cubes since the incoming wave illuminates all reflectors with the same amplitude?

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From https://space.stackexchange.com/q/14943/12102 (click for larger)

You can read more about the actual retroreflector arrays on the moon and the precision ranging measurements in

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  • $\begingroup$ Note, the linked question in Space SE has a bounty that expires in 20 hours, plus there's a 24 hour grace period. $\endgroup$ – uhoh May 29 at 6:40
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Because the size of each cube is much smaller than the diffraction-limited spot from the laser/telescope combination, and in fact because the whole array is much smaller than the diffraction- limited spot, each photon from the source is a wave function that is spread out over the whole array and beyond. That means that, as long as there is nothing to limit or measure which cube a photon can reflect from, it is quantum mechanically impossible to know which cube a photon received back on Earth was reflected from. That in turn means it was reflected from all of them.

The amount of jitter observed here is less than the duration of the laser pulse, so can be completely attributed to uncertainty re which (temporal) part of the pulse contained the received photon.

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