jeffrey.kissel@LIGO.ORG - posted 20:18, Friday 27 July 2012 - last comment - 08:14, Monday 06 August 2012(3642)
Calibrated Optical Lever Spectra -- Third Time's the Charm
J. Kissel, T. Vo After finally getting the optical levers aligned while the optics were aligned in a good state for the cavity, I've taken a spectra of both H2 SUS ITMY and H2 SUS ETMY in the quiet time mentioned in the isolationist data miner's dream. There're lots of fun features, differences, and similarities between the two test mass spectra, that will be good to noodle over. This will be excellent material to try to reproduce via models! If anyone wants to gather future data, this calibrated template lives here: /ligo/svncommon/SusSVN/sus/trunk/QUAD/Common/Data/2012-07-27_H2OAT_Oplev_ASDs.xml
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Please disregard the calibration in this plot. As commented by Thomas in LHO aLOG 3713, we've discovered flaws in the data analysis, in addition to some non-linearities in a step of the calibration originally posted in LHO aLOG 3614. These flaws result in the calibration scale factor being off by more than an order of magnitude in some cases. We're working on getting accurate numbers this week, thanks for your patience! Note, since there is no frequency dependence to the calibration (all analog whitening is compensated for in real time digitally), it is *only* the scale factor that is off. Details: -------- For future reference, and to give credit where credit is due, suspicion was originally raised by M. Evans and P. Fritschel, who sanity checked the numbers in the spectra with the following calculation: - The data I show here was for the cavity unlocked. They say the P motion (and even Yaw motion) of both test masses, but ETMY specifically, is "just too damn high". - I walked them through our extensive calibration technique, and they believe the methods in principle: - You've got a signal in [cts], from which you read a known translation, in [m]. - You've turned it into [rad] using the lever arm, L to (or from) from test mass. - The ratio of those two numbers, [rad] / [ct] is the calibration to which you should multiply your signal in order to get [rad] of test mass motion. But it practice, something has gone astray. - Thinking the motion was large just because the cavity was unlocked, I re-measured the cavity motion using the optical levers with our current calibration and the cavity locked (2012-08-02 04:00 UTC = 2012-08-01 9:00p PDT, a little after Alberto said he locked the cavity for the night), and compared it against cavity unlocked on 2012-07-27 02:51 UTC. See first attachment, 2012-08-02_H2OAT_Oplev_ASDs.pdf. - The motion is about the same, maybe different by a factor of 2 at most. Let's say the ETMY is moving dTheta_E = 50 urad, and ITMY is moving at dTheta_I = 5 urad at the QUADs first modes at 0.43 and 0.56 Hz, which dominate the time series (which has been confirmed, but is not shown, by *look* at the time series that formed these spectra in DTT). - Using the calculation attached from Seigmann, "LASERS" pg 768 and 769, (CavityMisalignment.pdf) and assuming the cavity stability parameters g1 = g2 = g g = 1 - L/R = 1 - (length of the cavity) / (radii of curvature of cavity mirrors) = 1 - 4e3 [m] / 2.2e3 [m] = -0.8 [ ] then that means that (from Eq 32) of attached (taking the ETM as mirror 1), the spot is jiggling on the face of the test mass by a distance, | dx | = | dTheta_E * L * g / (1 - g^2) + dTheta_I * L / (1 - g^2) | = | 50e-6 [rad] * 4e3 [m] * -0.8 [ ] / (1 - (-0.8 [])^2 ) + 5e-6 [rad] * 4e3 [m] / (1 - (- 0.8 [ ])^2) | = 0.38889 [m] ... that's 38 [cm], which is about as big as the diameter of the test mass (34 [cm])! - When you look at the spot on the ETM with the camera, while the cavity is locked, one sees the the spot moving *at most* 1 [cm] peak-to-peak in Pitch, and it *certainly* not from the top to bottom of the test mass.
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