Today, I turned the input and output mirrors round 90 degrees to take a displacement noise spectrum on our table. There were several steps:
- Turn the mirrors
- Block one input beam path (I chose to use the simpler CCW beam so that I didn't have to have the AOM running, etc., so I blocked the CW path)
- Rearrange the setup at the output (in as minimally invasive a way as possible) so that I was looking directly at the power emerging from the two directions. I set up two PDA100A's since they are wide-area and we don't need anything too fast for this.
- Ideally, this measurement is done with 50/50 splitters at the input and output, so that the contrast is 100% when the beams are overlapped. Our mirrors are very reflective, so I rotated the input polarization from S to P to take advantage of the fact that the mirrors' R-to-T ratios are not quite as high for P light. I also had the EOM off to avoid adding extra AM and other junk.
I routed the outputs of the PDs to the DAQ, and acquired:
- The PD signal with the best contrast. (One output beam has a twice reflected beam plus a twice transmitted beam, while the other has two beams that have each been reflected and transmitted once. If the input and output mirrors had the same R's and T's, then this emerging beam would have 100% contrast. They don't, so it doesn't, but it's better than the other.)
- The sum, so that I could normalize the signal in (1) to reject AM.
I then fine-tuned the alignment so that the output was sitting roughly halfway between a bright fringe and a dark one (so that the power was roughly linear with displacement) and took data.
I wanted to normalize the data to the sum as mentioned above, but I don't know of a good way to do it with DTT or the like short of using Simulink to build a divider block and acquire the processed data. In any case, I ligoDV'd the data into Matlab and normalized it there, and the difference is almost unnoticeable. I can include this later if we really think it's necessary. Here is the spectrum:
It is similar in shape and of roughly the same order of magnitude as the MZ noise that Rana measured before (see the SVN NB). It is a bit lower, especially at low frequency, but it's worth noting that the low-frequency noise goes up quite a bit when the lid of our box is open (good work, Alastair).
The calibration here is a bit iffy. I have
dP/dx|_{phi=0} ~ 4 * pi * r * t * sqrt(P1 * P2) / lambda,
where r, t are the amplitude reflectivity and transmissivity, and P1&2 are the powers in the two beams reaching the output mirror from each side. There is a 50/50 splitter between the output mirror and the PD (I didn't notice this until after), so this is reduced overall by a factor of two.
The PDA100A was on its 0 dB setting, giving G_{PD} = 0.7 A/W * 1510 V/A, and I took the ADC gain to be 6.103 x 10^{-4} V/ct.
Now the iffy part. Using the powers I measured before the recombination and the r's and t's I measured some weeks ago (yes, for P), I get that the calibration is 2.06 x 10^{-10} m/ct. However, if I use the measured maximum and minimum values on the PD over full-wavelength swings of the output mirror to calculate dP/dx directly (using the cross term in the equation P_{PD} = |[rE2exp(i*phi) + itE1]|^{2} ), I get 3.45 x 10^{-11} m/ct. It is this second calibration that appears above, but it remains to be understood why there is a discrepancy. I could understand it if the contrast got worse due to imperfect overlap, which there surely was, but it appears to be better than calculated. Does not compute.
This would appear to exonerate displacement noise as our limiting noise source at the moment (we've plugged similar numbers into the budget and found that we should be orders and orders of magnitude more sensitive), but it would be either foolish or irresponsible to deny the obvious likeness of the spectrum above and that of our gyro signal. Their characteristics are nearly identical, save for some suppression from the reasonable gain of our feedback loops at lower frequencies. I think we may have to consider the possibility that displacement noise is coupling in through some other mechanism that we haven't yet considered. |