The amount of offsets in the LSC signals due to the RFAMs have been estimated by an Optickle simulation.
The next step is to think about what kind of effects we get from the RFAMs and estimate how much they will degrade the performance.
(Motivation)
We have been having relatively big RFAM sidebands ( #5616), which generally introduce unwanted offsets in any of the LSC demodulated signals. The motivation was that we wanted to estimate how much offsets we've been having due to the RFAMs.
The extreme goal is to answer the question : 'How big RFAMs do we allow for operation of the interferometer?'.
Depending on the answer we may need to actively control the RFAMs as already planed ( #5686). Since the response of the interferometer is too complicated for analytic works, so a numerical simulation is used.
(Results : Offsets in LSC error signals)
Figure: Offsets in unit of meter in all the LSC demodulated signals. Y-axis is the amount of the offsets and the X-axis represents each signal port.
In each signal port, the signals are classified by color.
(1) Offsets in the PRCL signal. (2) Offsets in the MICH signal. (3) Offsets in the SRCL signal.
Roughly the signals showed offsets at a 0.1 nm level.
The numerical error was found to be about 10-10 nm by running the same simulation without the AM sidebands.
Here is a summary of the amount of the offsets:
| |
offsets [nm] (1f signal port) |
offsets [nm] (3f signal port) |
biggest offsets [nm] (signal port) |
| PRCL |
0.3 (REFL11) |
0.2 (REFL33) |
1 (REFL55) |
| MICH |
0.00009 (AS55) |
0.8 (REFL33) |
7 (POP11) |
| SRCL |
0.1 (REFL55) |
0.1 (REFL165) |
40 (POX11) |
In the SRCL simulation REFL11I, REFL11Q, POP11I, POP11Q and POX11I didn't show any zero crossing points within 100 nm range around the resonance.
It is because that the SRCL doesn't do anything for the 11MHz sidebands. So it is the right behavior.
However POX11 was somewhat sensitive to the SRCL motion and showed a funny signal with a big offset.
(Simulation setup)
I applied the current PM/AM ratio according to the measurement ( #5616, #5519) The modulation indices used in the simulation are :
+ PM index in 11MHz = 0.17
+ PM index in 55MHz = 0.14
+ AM index in 11MHz = 0.17 / 200 = 8.5x10-4
+ AM index in 55MHz = 0.14 / 200 = 7.0x10-4
Note that the phases of the AM and PM sidebands are the same.
For clarity, I also note the definition of PM/AM ratio as well as how the first order upper sideband looks like.
The optical parameters are all at ideal length although we may want to check the results with more realistic parameters:
+ No arm cavities
+ PRCL length = 6.75380
+ SRCL length = 5.39915
+ Schnupp asymmetry = 3.42 cm
+ loss in each optic = 50 ppm
+ PRCL = resonant for 11 and 55MHz
+ MICH = dark fringe
+ SRCL = resonant for 55 MHz
The matlab script will be uploaded to the cvs server.
| Quote from #5686 |
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8. In parallel to those actions, figure out how much offsets each LSC error signal will have due to the current amount of the RFAMs.
=> Optickle simulations.
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