Matthew B.

As part of the calibration group's search for the source of the unexplained feature at low frequency in the sensing function inferred from PCAL and DARM open loop measurements, we decided to examine the possibility of PCAL mis-centering. A mis-centering of the PCAL beam on the test mass can cause a torque leading to rotation. This rotation can then couple to DARM via mis-centering of the main interferometer beam causing an extra signal when measuring the sensing function.

I used Brett Shapiro's QuadModel Matlab model to generate length-to-length, pitch-to-pitch, and yaw-to-yaw transfer functions for ETMY. These were used to estimate the uncertainty in a measurement of DARM over the PCAL displacement following the process detailed in P1500248 and P1500249 using the modeled transfer functions rather than 1/f^2 approximations. This percent error takes the form of the dot product of the PCAL and interferometer beams multiplied by the ratio of the length-to-length transfer function to the angle-to-angle transfer function.

Attached is the spectrum of this error using either the pitch-to-pitch or yaw-to-yaw transfer functions for the angle-angle coupling. Here, I used a cavity power of 180kW, a PCAL offset of +10mm, and an interferometer beam offset of -15.7mm for pitch and +13.2mm for yaw. It should be noted that the PCAL offset was just an estimate based on prior observations. The actual value could vary leading to slightly larger or smaller error values. This mis-centering theory seems insufficient as the model does not yield any notable spikes above ~3 Hz, settling to an error of around 1% above this point.

The model I used can be found in /ligo/svncommon/SusSVN/trunk/QUAD/Common/MatlabTools/QuadModel_Production/ascPlantRP_copy.m