On (8 months later) Off (8 months later)
5.5 Cancellation of seismically-induced angular motion in power recycling cavityrecycling cavity
To help alleviate the problems of angular motion in the power recycling cavity discussed in Sec- tion4.3, feedforward was applied in real-time at the 40 m Lab. We measure the angular motion of the cavity axis with a quadrant photodiode (QPD) located at the POP port (see Figure4.1). Note that this is done in the PRMI-only configuration (end mirrors misaligned) so that only the RF sideband is resonant in the cavity, and the QPD signal is not contaminated with information about the long arm cavity axis motion. We utilize a Trillium T-240 3-axis seismometer [129], mounted on a granite block on the ground next to the power recycling cavity, as the witness sensor for the ground motion.
As with Section5.4, we must pre-filter the witness sensor data by the actuator transfer function.
In this case, we measure this transfer function by actuating on the power recycling mirror and reading the QPD signal. This transfer function and the fit to the transfer function are shown in Figure5.16. Since the accuracy of the measurement and the fit can both limit the feedforward subtraction (see SectionA.2for details), the coherence for each data point in Figure5.16is above 0.95, and for most of the points is above 0.99.
Figure 5.16: PRMI pitch actuator transfer function, actuating on PRM and reading out at the POP QPD. Red dots are measured data points with coherence of at least 0.95, the blue trace is the fit to the transfer function, and the green trace indicates the residual mismatch between the measurement and the fit.
We then calculate the Wiener filters for each seismometer axis. Figure5.17shows an example
Wiener filter that was calculated, for the seismometer axis in the same direction as the cavity axis in the power recycling cavity. The red dots show the ideal calculated filter, and blue trace shows the fit to that filter that will be used in the real time system for the actual feedforward. The green trace indicates the residual mismatch (multiplied by a factor of ten for clarity) between the calculated filter and the fit. The coherence between the seismometer witness signal and the QPD target signal was above 0.5 for the range 0.7 Hz< f <4 Hz, and above 0.9 for the sub-range 1.2 Hz< f <3.5 Hz.
The Wiener filter’s fit is weighted by the coherence, so that frequencies of high coherence are exceptionally well fit, at the expense of frequencies of lower coherence (where the signal from this witness channel is not important). In addition to these filters, each witness channel was filtered with a 10 Hz elliptic lowpass to avoid injection of sensor noise into the system. It was found that a 0.01 Hz highpass filter was also required, although that may be due to a lack of accurate actuator measurements at lower frequencies. Future iterations of this feedforward will investigate this feature.
Figure 5.17: Example Wiener filter for PRC angular feedforward [130]. The red dots show the ideal calculated filter, and blue trace shows the fit to that filter that will be used in the real time system for the actual feedforward. The green trace indicates the residual mismatch (multiplied by a factor of ten for clarity) between the calculated filter and the fit.
Figure 5.18shows the results for the pitch degree of freedom of this feedforward applied in real-time. Both pitch and yaw feedforward were applied simultaneously. For the pitch degree of freedom, only the two horizontal axes of the seismometer are used, but for the yaw degree of freedom all three axes are used. Red traces are without the feedforward, black traces are with the
feedforward on, where both sets of measurements were taken within a few minutes of each other.
RMS values are also shown.
Figure 5.18: Suppression of angular motion in PRMI [131]. Red traces are without the feedforward and black traces are with the feedforward on. Both sets of data were taken within a few minutes of each other. RMS values are also shown.
Figure5.19shows our measured subtraction factor (blue trace) compared to the predicted noise suppression (orange trace). The predicted trace assumes noise-free actuators, as well as perfect fitting of the calculated Wiener filters. Here, a number greater than one indicates noise suppression while a number less than one indicates noise injection. We note that extra angular noise is injected below approximately 0.05 Hz. This is likely related to the need for the 0.01 Hz highpass filter, and will be investigated further in future measurements.
Interestingly, the residual intensity noise (RIN) of the cavity shown in Figure5.20decreases over a much broader band than the direct angular motion. It is expected that the power in the cavity should be more stable when the cavity axis motion is reduced. The fact that the RIN improvement is over a broader band implies that there are non-linear couplings present, such as scattered light effects.
While these results are shown in the PRMI-only configuration, they are most helpful when locking the full PRFPMI interferometer. Since the 3f locking signals are so sensitive, it is very challenging to maintain lock of the vertex degrees of freedom long enough to fully transition CARM and DARM. However, with this angular noise suppression, we are able to maintain lock of the vertex degrees of freedom quite easily for several minutes at a time, which enabled the CARM
Figure 5.19: Actual versus predicted noise suppression for pitch degree of freedom. Measured trace is the ratio of the traces from Figure5.18. A number greater than one indicates noise suppression while a number less than one indicates noise injection.
and DARM transitions and full lock of the 40 m interferometer.
Figure 5.20: RIN suppression due to improved angular noise in PRC. Red (no feedforward) and black (feedforward on) traces were measured at the same time as the traces in Figure5.18. RMS values are shown with dashed traces.