M. Todd, C. Compton, S. Dwyer

This is a continuation of the last alog discussing how we can estimate thermal actuator contributions to the surface curvature to the test masses. In this I tried to layout the problem with a little more detail.

Essentially, with a few different ring heater powers and their corresponding HOM spacing measurements from OMC data, we can estimate the coupling factor of ring heater power to test mass surface defocus [D/W]. The assumption is that the cavity g-factor is linear with this ring-heater power dependence, and higher order terms are assumed to be small enough to ignore.

This fit to a premlinary dataset (one HOM data point per ring-heater power_) yields a ring-heater coupling value of 0.6483 uD/W -- note: the HOM spacing has been observed to change during the same ring heater powers over time, and these should be included in the dataset.

This value is about 65% of what we think it to be, from TCS - SIM.

We can also constrain the HOM spacing shift from self-heating alone using the intercept of this curve -- this is estimated to be about 153 Hz (from 5166Hz to 5319Hz), compared to the predicted 411Hz change.

The plots and derivations are attached in the notes pdf