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Tue Nov 18 19:44:53 2008
X Arm Cavity "Negative" FSRs Measured
Previous measurements on the X arm cavity revealed a shift of the frequencies of the cavity resonances from where one would expect these to be by just looking at integer multiples of the cavity FSR. In particular, plotting the resonant frequencies versus the order of their occurrences while sweeping the laser frequency (in our case that of the beat between the two lasers), the linear fit of the data contained an unwanted offset:
resonant_frequency = n x FSR + offset
In part, we attributed this offset to the local oscillator of the PLL, the Marconi, which was not referred to an absolute frequency clock.
For that reason, I connected the Marconi to the RS FS275 which uses the 1PPS from the GPS to generate a 10 MHZ reference signal, and then scanned the cavity again. This time I started from negative beat frequencies, that happen when the frequency of the secondary laser is smaller than the main laser's, to positive frequencies. The way I made sure of the sign of the frequency was looking at the effect of changing the temperature of the NPRO. I decided that negative frequencies where those for which an increase in temperature lowered the beat frequency and positive frequencies those for which increasing the temperature made the beat frequency go up.
I then plotted the data and obtained the attached plot.
The offset was reduced to about 80 Hz (from more than 200 in the previous measurements). I think the residual offset has to do with something that happens in the cavity, something, as Koji found out, related to the alignment of the mirrors.
Thanks to the more data points, the measurement of the FSR improved to (3897627 +/- 5) Hz, which would let us know the measure of the cavity length with an error of 50um, if it weren't for the offset. I have to understand whether and how to take this into account to determine the precision in the cavity length. I guess it depends on whether it is real or it is still a systematic error due to the measurements.