Length Offsets

A truly vexing aspect of the LSC scheme described in chapter6is the inevitable presence of offsets in the various error signals, a consequence of the imbalanced sidebands that result from having a detuned signal cavity and imperfect knowledge of demodulation phase (cf. section6.3.3). These error signal offsets are different from those in a power-recycled interferometer, which are unintentional and depend on physical asymmetries, many of which can be measured and are stationary. In contrast, in a detuned interferometer, the error signal offsets depend on the microscopic state of the interferometer and on demodulation phase in a cyclical way that makes them difficult to accurately pin down. Moreover, they can vary with interferometer alignment, which is not actively controlled at the 40 m; a set of automatic alignment scripts is used during the bootstrapping (cf. section8.5) to set the DC alignment, but this is not a perfect method for a reproducible alignment. The final result is that the positions of the optics can be displaced from their nominal, designed positions by rather alarming amounts: up to a few picometers for the ETMs and a few nanometers for the BS, PRM, and SRM. Since all the RF sidebands are imbalanced, these offsets can affect any length degree of freedom. These length offsets can severely disrupt our understanding of how laser and oscillator noises can couple to the gravitational wave signal. These noises couplings can vary strongly with microscopic offsets because, in principle, the interferometer has been designed with symmetries such that these noises cancel. The offsets ruin the symmetry and thus the cancellation.

9.3.1.1 Cyclical dependencies

There is, to my knowledge, no simple way to measure the various length offsets accurately enough to remove them; because of the sensing scheme, they cannot be measured unless the interferometer is fully locked, and the detailed response of the interferometer depends on the offsets. It is thus a

chicken-and-egg problem, although not as bad the lock acquisition problem. One possible solution is of course to explore the offset space and find the place of lowest noise coupling. This is some- times done with one to two alignment degrees of freedom in initial and Enhanced LIGO. However, by adding the length offsets, we increase the dimensionality of the space that must be explored. Moreover, since the offsets can change, this process would need to be repeated regularly. This is onerous.

9.3.1.2 Mode cleaner length

In addition, the input mode cleaner may not be completely resonant for the RF sidebands, although it is always resonant for the carrier. A macroscopic length change of 100µmcan have a significant effect on noise couplings. The regular fluctuations in mode cleaner length are known to be greater than this amount, and so this represents another significant source of uncertainty. The ultimate source of this fluctuation is poorly understood, but it probably has to do with thermal expansion in the laboratory floor and the seismic stack which supports MC2 (cf. figure5.1). This does not have anything to do with the interferometer detuning; it is because the mode cleaner itself does not have long term stability, and the problem is exacerbated by the high RF modulation frequencies (thef2sidebands must pass on the mode cleaner’s 15th FSR). This problem could be circumventing

by automating a mode cleaner length measurement, and doing it once or twice a day, but this has not yet been done.

9.3.1.3 Effect on DARM calibration

It is worth commenting that all these length offsets do not significantly degrade our ability to understand how the interferometer responds to gravitational waves: that depends more on the actuators and the photodiodes, so the calibration of the device (cf. chapter7) is not really at risk. This is because unlike the noise sources, which are supposed to cancel, the signal is supposed to add; small changes thus do not have a large effect. In any case, for the conduction of searches for gravitational waves it is necessary for the calibration to be continuously tracked and measured regularly. We could track the noise couplings in the same manner as the calibration is tracked, but this would unnecessarily take up either observation time or observation bandwidth, an unattractive proposition.

9.3.2

Simulation

The simulation in this configuration is using the looptickle extension for Optickle (see appendixF), which includes linear control loops. The loops have proved crucial to understanding the noise couplings, as the pure optical coupling (analytically described in appendixC) does not explain any

of the measured couplings.

9.3.2.1 Feedback and Offsets

The simulations are closed loop; the DARM offset is actually set by the simulation (its nominal value is 25 pm), by ensuring that the OMC transmitted power is near its actual in lock value of∼1.5 mW. The actual DARM offset then changes with the MICH offset (as it does in the real interferometer, since DARM is servo-ed to keep the OMC transmitted power constant). This actually helps explains something which was puzzling in the real interferometer: sometimes the control hand-off of DARM to DC readout would not work. It is not difficult to understand why the transition did not work if one realizes there can be carrier light at the asymmetric port which is not due to a DARM offset—the DARM length sensing based on the OMC transmitted power has too little gain and as a result the DARM loop is unstable. At the time, an offset in the RF DARM loop (in the other offset direction) was suspected, but it is now clear that a MICH offset could also have been the problem.

There are then 5 offsets which are unknown (and which can vary between each measurement trace, as they will vary from lock to lock): CARM, MICH, PRCL, SRCL, and the mode cleaner length, a five-dimensional space. In RF readout, there can also be a DARM offset, for a sixth dimension. This offset space was explored through simulation by hand in the following ranges: CARM _±3 picometers (and DARM in RF readout), _± 200 microns for the mode cleaner length, and _±3 nanometers for MICH, PRCL, and SRCL. For the short degrees of freedom, this level is determined by inspecting figure 6.2, where we can see that length offsets approximately scale as 1 nm/degree of demodulation phase error. For the 40 m with DDM signals_±3 nanometers is actually a conservative limit. Nonetheless, the simulated noise couplings vary radically (by more than an order of magnitude, with significant changes in the frequency response) for offsets of this magnitude. The control loops in the simulation are automatically compensated to keep the UGFs approximately at the actual value in the real interferometer (about 100 Hz for the short loops, 180 Hz for DARM, and several kHz for CARM). The shown simulated couplings are ‘eyeball’ fits to the data—the simulation is far too slow for an automated fitting mechanism. The simulations do not perfectly match the measured data, but they do give an indication of the likely coupling mechanisms.