Arm lengths were measured using ALS

X arm length = 37.79 +/- 0.05 m

Y arm length = 37.81 +/- 0.01 m

Whats and whys

We want to measure the arm length with an accuracy of say a mm.

This would mean a measurement precision of 1e-3/40=25ppm. (1mm in 40m)

So the required measurement resolution on the spectrum analyser is 25ppm*4MHz=100Hz (assuming the cavity FSR is roughly 4MHz). 

Although the spectrum analyser does not limit the measurement precision, we are limited by the noise in ALS at 1000Hz rms. So we can use ALS only to measure arm length precise to the order of a few mm.

RXA: Not that we really need to right now, but even with an ALS noise of 1000 Hz, we can can do better just by averaging at each resonance point. And fitting a line as you have already done gets even better:

http://en.wikipedia.org/wiki/Propagation_of_uncertainty

The Spectrum analyser was reference locked to the rubidium clock @10MHz for these measurements.

The FSRs of the arms

X arm = 3.9671e+06 +/- 4.8535e+03 Hz

Y arm = 3.9648e+06 +/- 1.1064e+03 Hz

Attachments:

1&2. Plots representing the arm scans showing the beat frequency for which IR resonates in the arm vs the ALS offset (position of the ETM).

3. Data and code (zip file)

P.S. We had trouble scanning the arms using ALS. This was because the slow servo was not enabled. Hence ALS was losing its PDH lock everytime we scanned past a couple of FSRs.