On earth, fiber optics can measure the awakening of cicadas, trains, seismic events, etc.
I didn't know about the awakening of cicadas (Wired, November 30, 2023, Cicadas Are So Loud, Fiber Optic Cables Can ‘Hear’ Them hat tip to Jacob Krall) but certainly optical fiber seismology is a well-developed concept for both naturally and artificially-induced vibrations and movements. But all of those technologies depend upon imperfections in the silica fibers that cause polarization mode dispersion and micro-reflections (or other more complex phenomenon, especially right after the amplifiers when the light intensities are strongest and the multiplexed wavelengths most susceptible to nonlinear effects in the fiber).
But here you're asking about "free-space" optical communication which really means there's no artificial guiding of the waves (waveguides) but it doesn't mean that the space is necessarily empty and not full of birds, air, gases, clouds, dust, water droplets, etc. ALL OF THOSE should be able to induce detectible shifts if you go out of your way to make your system sensitive to it.
Lasers certainly are used in a surprisingly wide range of atmospheric characterization techniques. (I think "how are lasers used in a "surprisingly wide range of atmospheric characterization techniques?" would make for an excellent Earth Science SE question!)
So I would look for meteorological applications first. However, I would make sure that whatever you are measuring isn't sufficiently covered by the wide range of Earth observation satellites already placed in LEO, GEO and Sun-Earth L2 which image over a very wide range of wavelengths and shoot lots of lasers already!
Another thing; all of the commercial electro-optics and electronics developed for the fiber and free-space optical communications industries are designed to ignore and push through various phenomena (those birds, etc) and deliver the best data possible. They will have some separate data stream for reporting "link-health" for diagnostics and preventative maintenance scheduling, but there won't be the same level of sophistication, because unlike fiber with all its inherent distortions and dispersions and static micro-reflections, free-space is "a breeze". Mostly you are just looking at intensity drop-outs when it rains.
One of the biggest challenges to satellite technology giving us accurate GNSS positions is the electron content of the ionosphere and the precipitable water vapor content (i.e. the gas, not the drops) in the lower atmosphere. In fact GPS signals are used all the time to monitor water in various parts of the upper atmosphere.
The link was so long “it cut down through the atmosphere, all the way down to 30 kilometers above the surface of the Earth,” he said, before the connection broke.
So if the electronics was set up right, it could possibly be able to measure the delay of the signal, and measure deviations in the delay from what the geometrical distances would indicate and that could measure something like the integrated density of air using some model for index of refraction as a function of density, temperature and water content. I don't know if that would be sensitive-enough to be useful, nor if the Starlinks are set up to continuously record path-length induced delays to sufficient precision to later-on recover useful atmospheric-induced effects.
I would suspect that that 30 km path was a special test, and that they may not be using those longest, extreme links continuously. Your article goes on to say (near the end):
“Another really fun fact is that we held a link all the way down to 122 kilometers while we were de-orbiting a satellite,” he said. “And we were able to downstream the video.”
Source (Credit: PCMag/Michael Kan)
But for all the links outside the atmosphere, the interaction of near IR with the ionosphere should be very, very weak.
Maybe short breaks in the links or the received intensity can be linked to space junk passing through the beam... occasionally?
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