The precision of the measurement is excellent. We should move on to look for systematic errors.
According to Johannes and Gautam (see T1700117_ReflectionLoss .pdf in Attachment 1), the loss in the cavity mirror is obtained by measuring the light reflected from the cavity when it is locked and when it is misaligned. From these two measurements and by using the known transmissions of the cavity mirrors, the roundtrip loss is extracted.
I write a Python notebook (AnalyzeLossData.ipynb in Attachment 1) extracting the raw data from the measurement file (data20190216.hdf5 in Attachment 1) analyzing the statistics of the measurement and its PSD.
Attachment 2 shows the raw data.
Attachment 3 shows the histogram of the measurement. It can be seen that the distribution is very close to being Gaussian.
The loss in the cavity pre roundtrip is measured to be 73.7+/-0.2 parts per million. The error is only due to the deviation in the PD measurement. Considering the uncertainty of the transmissions of the cavity mirrors should give a much bigger error.
Attachment 4 shows noise PSD of the PD readings. It can be seen that the noise spectrum is quite constant and there would be no big improvement by chopping the signal.
The situation might be different when the measurement is taken from the cavity lock PD where the signal is much weaker.