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There's minimal averaging, as the signals are transient.

Depends on what you mean by averaging I suppose, but the signal is a measure of the average path length from several hundred reflections in the cavity. Furthermore, the signals are generated from the average interference of many photons. Even still, shot noise from the limited number of photons in the cavity is a major source of uncertainty.

All true.

To give perspective on where I was coming from: from the (human) perspective of looking at noise in 1/sqrt(Hz) units, the signals are actually less-than-averaged if they're less than a second in duration.

It's not like a continuous-wave source where one can integrate for months and hammer down the uncertainty to far lower strain values.

It's averaging in the sense of a long integration time. The signals of interest are glacial w/r/t speed of light, in the few Hz range, so you can integrate the optical signal over a longer period of time to improve SNR and beat shot noise.

I suppose one could rely on averaging the raw inputs of a large number of less reliable sensors, but I don't believe that's what the researchers have actually done here.

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