Noise Cancellation for Gravitational Wave Detectors

To everyone at the LIGO sites, thank you for being accommodating when I visited and putting up with things like orange cones and sensors all over the floors. To my parents, grandparents, brothers and the rest of my family, thank you for supporting me in everything I do.

Introduction

In preparation for the noise cancellation that will be required in the future, simulations were performed to determine the sensitivity requirements for Newtonian noise in order to suppress it below quantum noise levels. The last section of this chapter describes in detail the future work that needs to be done before Newtonian noise cancellation can be implemented in our interferometers.

Gravitational waves and astrophysical motivations

Gravitational waves

We assume that the dominant term in the metric of the universe is a flat Minkowski metric,η. We now want to evaluate the integral to determine how the phase of the light changes with the spacetime perturbation.

Figure 2.1 shows an example of the inspiral phase of a waveform for a pair of 1.4 solar mass (1.4 M ) neutron stars 1 Mpc from Earth

Motivations for low frequency sensitivity improvement

Early part of neutron star / neutron star inspiral
Pulsars
Intermediate mass black holes
Better background for unmodeled burst searches

Errors in the data stream from non-Gaussian events contaminate the background of these searches significantly. Many non-linearities exist in physical systems and can be the cause of technical errors in the data.

Motivations for mid-frequency sensitivity improvement

A common example of this from Initial and Enhanced LIGO is Barkhausen noise in the ferromagnets used to actuate LIGO's mirrors [24]. Reducing the overall movement of the mirrors will reduce the amount of changing scattered light in the system, thereby mitigating this broadband noise increase.

LIGO interferometers

Measuring gravitational waves

Michelson interferometers

PDLaser

ETMY

BS ETMX

Fabry-P´erot arm cavities

Since the gravitational wave signal is related to the voltage δLL of the distance L between the test masses rather than just the absolute difference, we increase the sensitivity of the detectors directly by increasing the length of the arms. The addition of these extra mirrors creates Fabry-P´erot optical cavities in the arms of the Michelson.

ITMY

ITMX

Power recycling

An additional mirror is placed between the laser and the beam splitter at the symmetrical gate, as shown in Figure 3.4. Clearly, we cannot change the topology of the interferometer without changing the effect of the signals at the different locations in the detector.

ITMXPRM

Initial and Enhanced LIGO noise

The mirrors absorb some of the energy in the laser beam, which heats up the mirrors. The overall sensitivities of the initial and improved generation LIGO detectors are shown in Figure 3.7 compared to the sensitivity of the original design.

Figure 3.5: Comparison of the common mode (CARM) and differential mode (DARM) transfer functions between ETM motion and the detection photodiode in the Fabry-P´erot Michelson (FPMI) configuration versus the power recycled Fabry-P´erot Michelson (PRFPMI) co

Increasing measurement sensitivity: Advanced LIGO

Signal recycling

ETMXBS

Improved seismic isolation

One of the major infrastructure changes between Initial LIGO and Advanced LIGO is the improvement of low frequency seismic isolation. Note that at the resonance frequencies of the extra stages some isolation is lost, although at 10 Hz the quadruple pendulum provides a factor of 106 more isolation than the single pendulum.

Mechanical design

Increased laser power
Output mode cleaner
Total Advanced LIGO noise

The fundamental quantum noises that most closely constrain the LIGO sensitivity curve are related to the main laser power (more specifically, the power stored in the Fabry-P´erot arm cavities, which is related to the main laser power). This is particularly important for angular control of cavities, where the torque is due to radiation pressure.

Figure 3.12: Advanced LIGO sensitivity as a function of input laser power, calculated using the LIGO Collaboration’s Gravitational Wave Interferometer Noise Calculator, GWINC.

Input optics

Input mode matching
Input pointing tilt versus translation orthogonality

Suspended optics
Recycling cavities
Locking: acquiring control

Auxiliary green locking
Frequency dependent error signal blending

The red trace shows the angular movement of the energy recycling mirror due to seismic motion. The rest of the signal is split in two, with one part (the Q phase) delayed 90° out of phase with respect to the other (the I phase).

Figure 4.1: Schematic (not to scale) layout of the 40 m Lab’s optical components. Note that the topology is similar to Advanced LIGO (and Figure 3.8), and has many of the same sensors and actuators

This scheme does not require slow reduction of the CARM offset, or using DC transmission

During the lock acquisition, we monitor the energy-recycled Michelson vertex with the 3f2 (165 MHz) IR PDH signals. However, the rate is so small that it is possible to insert the PDH CARM error signal at a CARM offset of zero without breaking the lock. This scheme does not require a slow reduction of the CARM offset or the use of DC transmission.

Much Work Remains to be Done

Initially, the common (CARM) and differential (DARM) arm lengths are controlled by the common and differential green laser beatnote (ALS) signals. Due to issues with vertex sensing, we are currently working with the signal recycling cavity misaligned.). The ALS length noise is two or three times larger than the CARM linewidth, so it is not possible to keep the armpits on IR resonance. Both the common (CARM) and the differential (DARM) arm lengths have been mixed in this way before.

Figure 4-13 shows the two individual loop gains, as well as the combined total loop gain, halfway through the transition. We initially mix the IR PDH signal with a crossover around 1 Hz and pre-filter it with an integrator at 20 Hz.

Best of both worlds

Within 40ms, the cavity is returned to its fully resonant state. Perhaps

Typical Error Signal Blending Feedforward Compensated Blending

Dual recycled Michelson with Fabry-Perot arms

Optical configuration of the 40m prototype

Abstract

Two modulations at harmonic frequencies - 11MHz and 55MHz modulation sidebands

Harmonic demodulation

Interferometer path length sensing

Arm length stabilization with auxiliary beam injection [5][6]

532nm beams are generated and locked to the arm cavities

Modulation Phase Effects

Lock Acquisition Strategies

RF Signal Transition Directly from ALS - Error Point Blending - Used to Realize Full RF Control of the 40m PRFPMI

Relative phase of f1 and f2 sidebands

3f1 signal sensitive to many field products

Feedforward compensation of PDH Actuation – “ALS Fool”

Benefit from wide ALS dynamic range, low PDH sensing noise

Why are the MICH and PRCL signals so degenerate?

LIGO-G1500318 – March 2015 LVC Meeting – Pasadena, CA

Feedforward decoupling of loops

We see in the blue trace that the two paths to the summing node (via AREFLPALSSALS or via Dcpl) fit well together, as the magnitude of the ratio is very close to 0 dB. We find that it is possible to increase the gain of the Refl loop and the system remains stable. We see in the blue trace that the two paths to the summing node (via AREFLPALSSALS or via Dcpl) fit well together, as the magnitude of the ratio is very close to 0 dB.

Figure 4.14: Time series of transition from ALS to IR PDH control. The error signals are taken from the “total error” point for each system, after the blend

Characterization of the 40m interferometer

Initial displacement noise spectra of an early blocking 40 m prototype interferometer, in power-recycled Fabry-Perot. Subtracting this prediction from the ALS error point "cheats" the ALS loop by not seeing the effects of the IR loop. So far, we have demonstrated successful cancellation of the IR control signal in the ALS error signal of a single cavity Fabry-Perot 40m wing.

Figure 4.20: Measured CARM loop, near unity gain frequency, for the 40 m’s PRFPMI configuration.

Global seismic noise cancellation

Wiener filters
Seismic noise cancellation applied to triangular ring cavity
Estimated impact for Enhanced LIGO
Static implementation for Enhanced LIGO

When the relative motion of the mirror and the other surfaces in the scattering path is greater than the laser wavelength (λ-1µm), the phase noise introduced by this scattered light is experienced not only at the frequency of the motion, but as broadband noise up to a cutoff frequency determined by the relative speed [115]. In Figure 5.3 we show that the differential ground motion over the length of the cavity is not much greater than the instrument noise from the seismometers. The limit to the performance of the feed-forward subtraction seems to be a combination of

Figure 5.1 shows the locations of the witness sensors relative to the cavity mirrors. The mirrors of the cavity are suspended as pendulums with a resonance of ∼ 1 Hz to mechanically filter high frequency noise, with the suspensions sitting on vibration iso

Magnitude [dB]

40 Measurement Fit

Frequency [Hz]

Measurement Fit

Control Signal [m/√Hz]

On On (rms)

On Off

On (8 months later) Off (8 months later)

Cancellation of seismically-induced angular motion in power recycling cavityrecycling cavity

We measure the angular movement of the cavity axis with a quadrant photodiode (QPD) located at the POP port (see Figure 4.1). 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. Interestingly, the residual intensity noise (RIN) in the cavity shown in Figure 5.20 falls over a much wider band than the direct angular motion.

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

Least mean squared adaptive noise cancellation

We use the leaky modification by incorporating a factor of (1−τ) to decrease the filter's response over time. We use the normalized modification of the algorithm so that the size of µ with respect to ~x does not change. This variant recognizes that phase delays exist in the path of the target signal that cannot be approximated by the LMS method alone [137].

Figure 5.22: Online Adaptive Filter performance: the spectral density of the cavity length fluctua- fluctua-tions are shown with the feed-forward on (lower black trace) and off (upper red trace) [138]

Newtonian gravitational noise cancellation

Estimating Newtonian gravitational impact on Advanced LIGO

Vibration of outer walls
Building tilt
Air pressure fluctuations
Air handler fans
Seismic noise

Here the Newtonian noise contribution of the tilting of the buildings is calculated in much the same way as for the wall panels. Perhaps one of the formerly most concerning Newtonian sound candidates is air pressure fluctuations (since it is very difficult to subtract them if they are significant). The Newtonian sound acceleration of the test mass in the horizontal direction can be written as.

Figure 6.2: Seismic 90th percentile Newtonian noise estimates for the LIGO Livingston (LLO) and Hanford (LHO) sites (green and red lines), third generation strain noise model (blue line), and additional Newtonian noise estimates from vibrations of walls (c

Optimal seismic arrays

Simulation of seismic Newtonian noise
Sensor array optimization

The test mass is suspended 1.5 m above the ground, which is approximately the height of the LIGO test masses. The sum over grid points in Equation 6.17 is used to determine the time series of the Newtonian noise at the test mass. The spectral histogram for the Hanford site is very similar for the frequencies plotted here.

Figure 6.7: Histogram of one year of unaveraged 128 s seismic spectra measured during the 6th LIGO science run inside the corner station of the Livingston detector

Distance [m]

Along interferometer arm [m]

O ffl ine post-subtraction
Online feedforward subtraction
Comments on the possibility of suppressing the gravitational wave signal through subtractionwave signal through subtraction
Study of ground vibration content at the LIGO Hanford site
Work remaining before Newtonian noise subtraction can be implementedimplemented

Measurement and analysis of seismic field at each test mass
Newtonian noise budget improvements
Analysis of seismic shielding via excavations
Newtonian noise cancellation using mass actuators

The input consists of the seismometer channels, and the single-filter output is the Newtonian noise estimate. The size of the peak on each map is due to the array's finite resolution. Wave travels in the direction of the gray arrows (upward for body waves, and to the right for surface waves).

Figure 6.11: Subtraction residual as defined in Equation 6.18 vs. frequency for the array shown in Figure 6.10, and three different spiral configurations.The ‘N=10, r=8 m’ array is shown in Figure 6.13, and the ‘N=10, r=2 m’ array is the same, but with all

Conclusion

Appendix A

Control theory

Feedback controls

Calculating effect of feedback

Note that this cancellation of the error signal means that the loop will inject any sensor noise (eg electronics noise) into the loop. Obviously, this does not remain true if the device changes drastically (such as a sign reversal in the optical device of interferometers, as described in Section 4.4). The location bi is called the loopback failure point and the location is the loop control point.

Figure A.1: Cartoon of how feedback control works. Sense disturbance after the plant, use a controller (designed by the user) to decide how to actuate on the plant.

Feedforward controls

A challenge with the feedforward control topology is that it requires a very precise knowledge of the system. The ability to measure this transfer function can be a limiting factor in the forward system's ability to subtract the noise. So if we measure the actuator only to 10%, we can only subtract about a factor of 10 from the noise.

Figure A.2: Cartoon of how feedforward control works. The disturbance directly affects the plant, but it is also sensed by an external “witness” sensor

Appendix B

Review of Pound-Drever-Hall locking

To maintain generality, we must multiply by sine or cosine to extract all the information from Vrefl. This difference in notation is due to the choice to use sine as the modulation in Equation B.2 instead of cosine. If the phase of the local oscillator is set correctly, the Q-phase signal will disappear and all the information about the cavity length with respect to the laser frequency will be contained in the I-phase signal.

Appendix C

Layout of the 40 m Interferometer

In-vacuum optical tables

The output mode cleaner (and associated optical path) is not used; however, this table includes one of the curved entry modes to match telescoping mirrors, as well as control to direct the main beam in and out of the vacuum envelope. In addition to the X-arm input test mass, this table houses a power recycling cavity folding mirror and optics to extract the power recycling cavity pick-off beam ("POP"). This table contains the signal recycling mirror and a signal recycling cavity folding mirror, as well as the output path control optics and input test mass for the Y-arm.

Figure C.3: Detail of input mode cleaner table. MC1 and MC3 sit on this table, while the curved mode cleaner mirror, MC2, sits 13.5 m away (not shown, to the right).

In-air optical tables

Bibliography

Predictions for the rate of compact binary mergers detectable by ground-based gravitational wave detectors.Class. Studies of laser interferometer design and a vibration isolation system for interferometric gravitational wave detectors. Forward reduction of the microseismic disturbance in a long-baseline interferometric gravitational wave detector. Rev.