Temperature control for an intra-mirror etalon in interferometric gravitational wave detector fabry–perot cavities

The sensitivity of interferometric gravitational wave detectors is optimized, in part, by balanced finesse in the long Fabry–Perot arm cavities. The input test mass mirrors of Advanced Virgo feature parallel faces, which creates an etalon within the substrate, adding variability in the total mirror reflectivity, in order to correct imbalanced finesse due to manufacturing tolerances. Temperature variations in mirror substrate change the optical path length primarily through varying the index of refraction and are tuned to correct for a finesse imbalance of up to 2.8% by a full etalon fringe of 0.257 K. A negative feedback control system was designed to control the mirror temperature by using an electrical resistive heating belt actuator for a heat transfer process modeled as a two-pole plant. A zero controller filter was designed which achieves temperature control within 2.3% of the etalon fringe and recovers to within 10% of the working point within 32 hours after a step input of one etalon fringe. A preliminary unlock condition control designed to compensate when the interferometer unlocks shows that the control remains stable even after a drastic change in the plant due to the absence of the laser heating. Further improvements to the control must also consider the full heat transfer mechanisms by using modern control state space models.