jeffrey.kissel@LIGO.ORG - posted 11:42, Monday 03 February 2020 - last comment - 16:14, Monday 03 February 2020(54868)
PCALX vs. PCAL Cancelling Line(s) Moved Temporarily to 530.1 and 503.2 Hz
J. Kissel, for R. Savage and S. Karki As we continue to explore systematic error in the calibration during the O3 run, a remaining outstanding mystery is the discrepancy seen between PCALX and PCALY at the 0.5% level as measured through the interferometer (see current inconclusive state of the analysis, e.g. LHO aLOGs 53195, 53244, and 53259). In order to get *really* good SNR on this measurement, we're going to move the line down to 530.1 and 530.2 Hz for PCALX and PCALY, respectively, for about ~4 hours. We will retain the same excitation amplitude, but the signal to noise should improve by a factor of 8 or so, which will allows us to make discriminating statements at the ~0.1% level, where -- to-date -- we have not been able to. Here will be the temporary parameters: H1:CAL-PCALX_PCALOSC9_OSC_FREQ 530.1 H1:CAL-PCALX_PCALOSC9_OSC_SINGAIN 5007.0 H1:CAL-PCALX_PCALOSC9_OSC_COSGAIN 5007.0 H1:CAL-PCALX_PCALOSC9_PHASE 0.0 H1:CAL-PCALX_PCALOSC9_OSC_TRAMP 5.0 H1:CAL-PCALX_PCALOSC9_OSC_FREQ 530.2 H1:CAL-PCALX_PCALOSC9_OSC_SINGAIN 3619.0 H1:CAL-PCALX_PCALOSC9_OSC_COSGAIN 3619.0 H1:CAL-PCALX_PCALOSC9_PHASE 0.0 H1:CAL-PCALX_PCALOSC9_OSC_TRAMP 5.0 I'll be turning this line on during the routine calibration measurement time, then we'll be going in to OBSERVATION READY for about ~4 hours, and then we'll return the PCALX / PCALY pair of calibration lines to 1153.1 and 1153.2 Hz [note *different than before*: they were at the same frequency, now they will remain 0.1 Hz apart.]
The OBSERVATION READY segment that just started at 2020-02-03 19:53:05 UTC with these lines newly moved. Attached is a screenshot of a 0.01 Hz BW, 25 average ASD and transfer function (75% overlap, Hann window). Even this preliminary result of PCALX / PCALY = PCALX/DELTAL * DELTAL/PCALY = (0.993761)^(-1) * (0.993408) = 0.999644 alone should have uncertainty of unc_X = sqrt((1-C)/2*Navg*C) = sqrt((1.0-0.999985)/(2*25*0.999985)) = 0.000548 = 0.0548% = 5.4 "HOPs" unc_Y = sqrt((1-C)/2*Navg*C) = sqrt((1.0-0.999978)/(2*25*0.999978)) = 0.000663 = 0.0663% = 5.4 "HOPs" total_unc = sqrt(unc_X^2 + unc_Y^2) = 0.000860 = 0.086% = 8.6 HOPs. Note, as usual, this assumes that the value of C/(1+G) at 530.1 Hz and 530.2 Hz doesn't change with respect to each other over the duration of the measurement. This should be sufficiently high above the DARM UGF that C*A*D = G >> 1, and the time dependence of C should be dominated by the change in optical gain and cavity pole frequency. The optical gain change, \kappa_C would be common to both frequencies, so the only concern is with cavity pole, f_cc. These time dependent parameters of C are measured independently with other PCALY line frequencies at 410.3 Hz, and they indicate that f_cc remains between 410 and 414 Hz. If one takes the ratio transfer functions with a pole at 410 Hz, and one at 414 Hz, then evalute that ratio at 530.1 Hz and 530.2 Hz, then magnitude ratio value is (C_410 / C_414)_530.1 Hz = 0.9939656567, (C_410 / C_414)_530.2 Hz = 0.9939647934, and the difference across the two frequencies is at the [[ (C_410 / C_414)_530.1Hz - (C_410 / C_414)_530.2Hz ] / (C_410 / C_414)_530.1Hz] = 8.68e-07 = 8.68e-5% level. Further detailed analysis will likely support the same conclusion with this preliminary result: there is "no" residual systematic error between the PCALs at this frequency, at this time.