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> and how "bad" the beam spread is

The spread makes the tracking easier, I suppose.

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Perhaps a little, however. Different paths through the atmosphere will perturb the phase of the signal; depending on conditions not all of that ~10m beam width is going to decode with an acceptable bit error rate.
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Tracking and actuation is nothing new or particularly challenging, IMHO. It's the laser/optical part combined with throughput at that distance that is the main area of R&D, I think.
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