Dana, Jenne, Louis,

In alog 74477 we looked at how MICH couples to DARM (both calibrated to meters) in LHO during an excitation. In the attached figure, we compare this to LLO's MICH to DARM coupling during a similar excitation that took place on August 29th. Note: LSC feed forward was off for all measurements. We look at two different DARM channels in LLO, L1:CAL-DELTAL_EXTERNAL_DQ and L1:OAF-CAL_DARM_DQ and find they are nearly identical (see green and brown power spectrum traces). The data in all five channels plotted below had been whitened, so to calibrate we did the following:

L1: CAL-CS_MICH_CTRL_DQ - We applied a gain of 1e-6 to convert from um to m. We dewhitened by inverting the whitening transfer function, i.e., we set Poles = [1, 1, 1, 1, 1] and Zeros = [100, 100, 100, 100, 100].

H1:CAL-CS_MICH_CTRL_DQ - We applied a gain of 1e-6 to convert from um to m. We dewhitened by inverting the whitening transfer function, i.e., we set Poles = [1, 1] and Zeros = [100, 100].

L1:OAF-CAL_DARM_DQ - We applied the transfer function found within "/ligo/home/dana.jones/Documents/cal_MICH_to_DARM/L1_DARM_calibration_to_meters.txt".

L1:CAL-DETLAL_EXTERNAL_DQ - We applied the transfer function found within "/ligo/home/dana.jones/Documents/cal_MICH_to_DARM/L1_deltal_external_calib_dtt.txt".

H1:CAL-DELTAL_EXTERNAL_DQ - We applied the transfer function found within "/ligo/home/dana.jones/Documents/cal_MICH_to_DARM/H1_deltal_external_calib_dtt.txt".

For the transfer function DARM/MICH we would expect a magnitude of around 3.5e-3 m/m* starting at roughly 20 Hz. This is what we see in Livingston (green/blue trace in transfer function panel). In Hanford, however, DARM/MICH lies at around 5e-3 m/m at 20 Hz, off by roughly 40%. This means there is an increased coupling between MICH and DARM in LHO, and we are not sure exactly why.

*The expected coupling of MICH to DARM is 1/gain, where gain = (power inside the cavity) / (power outside the cavity) ≈ 2/pi * cavity finesse (this assumption hinges on the mirrors having near perfect reflectivity). Using a cavity finesse of 440, we get a gain of about 280 and thus a coupling of 3.57e-3 m/m.