# Sensitivity and Performance of the Advanced LIGO Detectors in the Third
Observing Run

A. Buikema  LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139,
USA  LIGO Livingston Observatory, Livingston, LA 70754, USA  C. Cahillane
LIGO, California Institute of Technology, Pasadena, CA 91125, USA  LIGO
Hanford Observatory, Richland, WA 99352, USA  G. L. Mansell  LIGO Hanford
Observatory, Richland, WA 99352, USA  LIGO, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA  C. D. Blair  OzGrav, University of
Western Australia, Crawley, Western Australia 6009, Australia  LIGO Livingston
Observatory, Livingston, LA 70754, USA  R. Abbott  LIGO, California Institute
of Technology, Pasadena, CA 91125, USA  C. Adams  LIGO Livingston Observatory,
Livingston, LA 70754, USA  R. X. Adhikari  LIGO, California Institute of
Technology, Pasadena, CA 91125, USA  A. Ananyeva  LIGO, California Institute
of Technology, Pasadena, CA 91125, USA  S. Appert  LIGO, California Institute
of Technology, Pasadena, CA 91125, USA  K. Arai  LIGO, California Institute of
Technology, Pasadena, CA 91125, USA  J. S. Areeda  California State University
Fullerton, Fullerton, CA 92831, USA  Y. Asali  Columbia University, New York,
NY 10027, USA  S. M. Aston  LIGO Livingston Observatory, Livingston, LA 70754,
USA  C. Austin  Louisiana State University, Baton Rouge, LA 70803, USA  A. M.
Baer  Christopher Newport University, Newport News, VA 23606, USA  M. Ball
University of Oregon, Eugene, OR 97403, USA  S. W. Ballmer  Syracuse
University, Syracuse, NY 13244, USA  S. Banagiri  University of Minnesota,
Minneapolis, MN 55455, USA  D. Barker  LIGO Hanford Observatory, Richland, WA
99352, USA  L. Barsotti  LIGO, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  J. Bartlett  LIGO Hanford Observatory, Richland, WA
99352, USA  B. K. Berger  Stanford University, Stanford, CA 94305, USA  J.
Betzwieser  LIGO Livingston Observatory, Livingston, LA 70754, USA  D.
Bhattacharjee  Missouri University of Science and Technology, Rolla, MO 65409,
USA  G. Billingsley  LIGO, California Institute of Technology, Pasadena, CA
91125, USA  S. Biscans  LIGO, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  LIGO, California Institute of Technology, Pasadena,
CA 91125, USA  R. M. Blair  LIGO Hanford Observatory, Richland, WA 99352, USA
N. Bode  Max Planck Institute for Gravitational Physics (Albert Einstein
Institute), D-30167 Hannover, Germany  Leibniz Universität Hannover, D-30167
Hannover, Germany  P. Booker  Max Planck Institute for Gravitational Physics
(Albert Einstein Institute), D-30167 Hannover, Germany  Leibniz Universität
Hannover, D-30167 Hannover, Germany  R. Bork  LIGO, California Institute of
Technology, Pasadena, CA 91125, USA  A. Bramley  LIGO Livingston Observatory,
Livingston, LA 70754, USA  A. F. Brooks  LIGO, California Institute of
Technology, Pasadena, CA 91125, USA  D. D. Brown  OzGrav, University of
Adelaide, Adelaide, South Australia 5005, Australia  K. C. Cannon  RESCEU,
University of Tokyo, Tokyo, 113-0033, Japan.  X. Chen  OzGrav, University of
Western Australia, Crawley, Western Australia 6009, Australia  A. A. Ciobanu
OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia  F.
Clara  LIGO Hanford Observatory, Richland, WA 99352, USA  S. J. Cooper
University of Birmingham, Birmingham B15 2TT, UK  K. R. Corley  Columbia
University, New York, NY 10027, USA  S. T. Countryman  Columbia University,
New York, NY 10027, USA  P. B. Covas  Universitat de les Illes Balears,
IAC3—IEEC, E-07122 Palma de Mallorca, Spain  D. C. Coyne  LIGO, California
Institute of Technology, Pasadena, CA 91125, USA  L. E. H. Datrier  SUPA,
University of Glasgow, Glasgow G12 8QQ, UK  D. Davis  Syracuse University,
Syracuse, NY 13244, USA  C. Di Fronzo  University of Birmingham, Birmingham
B15 2TT, UK  K. L. Dooley  Cardiff University, Cardiff CF24 3AA, UK  The
University of Mississippi, University, MS 38677, USA  J. C. Driggers  LIGO
Hanford Observatory, Richland, WA 99352, USA  P. Dupej  SUPA, University of
Glasgow, Glasgow G12 8QQ, UK  S. E. Dwyer  LIGO Hanford Observatory, Richland,
WA 99352, USA  A. Effler  LIGO Livingston Observatory, Livingston, LA 70754,
USA  T. Etzel  LIGO, California Institute of Technology, Pasadena, CA 91125,
USA  M. Evans  LIGO, Massachusetts Institute of Technology, Cambridge, MA
02139, USA  T. M. Evans  LIGO Livingston Observatory, Livingston, LA 70754,
USA  J. Feicht  LIGO, California Institute of Technology, Pasadena, CA 91125,
USA  A. Fernandez-Galiana  LIGO, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  P. Fritschel  LIGO, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA  V. V. Frolov  LIGO Livingston
Observatory, Livingston, LA 70754, USA  P. Fulda  University of Florida,
Gainesville, FL 32611, USA  M. Fyffe  LIGO Livingston Observatory, Livingston,
LA 70754, USA  J. A. Giaime  Louisiana State University, Baton Rouge, LA
70803, USA  LIGO Livingston Observatory, Livingston, LA 70754, USA  K. D.
Giardina  LIGO Livingston Observatory, Livingston, LA 70754, USA  P. Godwin
The Pennsylvania State University, University Park, PA 16802, USA  E. Goetz
Louisiana State University, Baton Rouge, LA 70803, USA  Missouri University of
Science and Technology, Rolla, MO 65409, USA  S. Gras  LIGO, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  C. Gray  LIGO Hanford
Observatory, Richland, WA 99352, USA  R. Gray  SUPA, University of Glasgow,
Glasgow G12 8QQ, UK  A. C. Green  University of Florida, Gainesville, FL
32611, USA  E. K. Gustafson  LIGO, California Institute of Technology,
Pasadena, CA 91125, USA  R. Gustafson  University of Michigan, Ann Arbor, MI
48109, USA  J. Hanks  LIGO Hanford Observatory, Richland, WA 99352, USA  J.
Hanson  LIGO Livingston Observatory, Livingston, LA 70754, USA  T. Hardwick
Louisiana State University, Baton Rouge, LA 70803, USA  R. K. Hasskew  LIGO
Livingston Observatory, Livingston, LA 70754, USA  M. C. Heintze  LIGO
Livingston Observatory, Livingston, LA 70754, USA  A. F. Helmling-Cornell
University of Oregon, Eugene, OR 97403, USA  N. A. Holland  OzGrav, Australian
National University, Canberra, Australian Capital Territory 0200, Australia
J. D. Jones  LIGO Hanford Observatory, Richland, WA 99352, USA  S. Kandhasamy
Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India  S.
Karki  University of Oregon, Eugene, OR 97403, USA  M. Kasprzack  LIGO,
California Institute of Technology, Pasadena, CA 91125, USA  K. Kawabe  LIGO
Hanford Observatory, Richland, WA 99352, USA  N. Kijbunchoo  OzGrav,
Australian National University, Canberra, Australian Capital Territory 0200,
Australia  P. J. King  LIGO Hanford Observatory, Richland, WA 99352, USA  J.
S. Kissel  LIGO Hanford Observatory, Richland, WA 99352, USA  Rahul Kumar
LIGO Hanford Observatory, Richland, WA 99352, USA  M. Landry  LIGO Hanford
Observatory, Richland, WA 99352, USA  B. B. Lane  LIGO, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  B. Lantz  Stanford
University, Stanford, CA 94305, USA  M. Laxen  LIGO Livingston Observatory,
Livingston, LA 70754, USA  Y. K. Lecoeuche  LIGO Hanford Observatory,
Richland, WA 99352, USA  J. Leviton  University of Michigan, Ann Arbor, MI
48109, USA  J. Liu  Max Planck Institute for Gravitational Physics (Albert
Einstein Institute), D-30167 Hannover, Germany  Leibniz Universität Hannover,
D-30167 Hannover, Germany  M. Lormand  LIGO Livingston Observatory,
Livingston, LA 70754, USA  A. P. Lundgren  University of Portsmouth,
Portsmouth, PO1 3FX, UK  R. Macas  Cardiff University, Cardiff CF24 3AA, UK
M. MacInnis  LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139,
USA  D. M. Macleod  Cardiff University, Cardiff CF24 3AA, UK  S. Márka
Columbia University, New York, NY 10027, USA  Z. Márka  Columbia University,
New York, NY 10027, USA  D. V. Martynov  University of Birmingham, Birmingham
B15 2TT, UK  K. Mason  LIGO, Massachusetts Institute of Technology, Cambridge,
MA 02139, USA  T. J. Massinger  LIGO, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  F. Matichard  LIGO, California Institute of
Technology, Pasadena, CA 91125, USA  LIGO, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA  N. Mavalvala  LIGO, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  R. McCarthy  LIGO Hanford
Observatory, Richland, WA 99352, USA  D. E. McClelland  OzGrav, Australian
National University, Canberra, Australian Capital Territory 0200, Australia
S. McCormick  LIGO Livingston Observatory, Livingston, LA 70754, USA  L.
McCuller  LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139,
USA  J. McIver  LIGO, California Institute of Technology, Pasadena, CA 91125,
USA  T. McRae  OzGrav, Australian National University, Canberra, Australian
Capital Territory 0200, Australia  G. Mendell  LIGO Hanford Observatory,
Richland, WA 99352, USA  K. Merfeld  University of Oregon, Eugene, OR 97403,
USA  E. L. Merilh  LIGO Hanford Observatory, Richland, WA 99352, USA  F.
Meylahn  Max Planck Institute for Gravitational Physics (Albert Einstein
Institute), D-30167 Hannover, Germany  Leibniz Universität Hannover, D-30167
Hannover, Germany  T. Mistry  The University of Sheffield, Sheffield S10 2TN,
UK  R. Mittleman  LIGO, Massachusetts Institute of Technology, Cambridge, MA
02139, USA  G. Moreno  LIGO Hanford Observatory, Richland, WA 99352, USA  C.
M. Mow-Lowry  University of Birmingham, Birmingham B15 2TT, UK  S. Mozzon
University of Portsmouth, Portsmouth, PO1 3FX, UK  A. Mullavey  LIGO
Livingston Observatory, Livingston, LA 70754, USA  T. J. N. Nelson  LIGO
Livingston Observatory, Livingston, LA 70754, USA  P. Nguyen  University of
Oregon, Eugene, OR 97403, USA  L. K. Nuttall  University of Portsmouth,
Portsmouth, PO1 3FX, UK  J. Oberling  LIGO Hanford Observatory, Richland, WA
99352, USA  Richard J. Oram  LIGO Livingston Observatory, Livingston, LA
70754, USA  B. O’Reilly  LIGO Livingston Observatory, Livingston, LA 70754,
USA  C. Osthelder  LIGO, California Institute of Technology, Pasadena, CA
91125, USA  D. J. Ottaway  OzGrav, University of Adelaide, Adelaide, South
Australia 5005, Australia  H. Overmier  LIGO Livingston Observatory,
Livingston, LA 70754, USA  J. R. Palamos  University of Oregon, Eugene, OR
97403, USA  W. Parker  LIGO Livingston Observatory, Livingston, LA 70754, USA
Southern University and A&M College, Baton Rouge, LA 70813, USA  E. Payne
OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800,
Victoria, Australia  A. Pele  LIGO Livingston Observatory, Livingston, LA
70754, USA  R. Penhorwood  University of Michigan, Ann Arbor, MI 48109, USA
C. J. Perez  LIGO Hanford Observatory, Richland, WA 99352, USA  M. Pirello
LIGO Hanford Observatory, Richland, WA 99352, USA  H. Radkins  LIGO Hanford
Observatory, Richland, WA 99352, USA  K. E. Ramirez  The University of Texas
Rio Grande Valley, Brownsville, TX 78520, USA  J. W. Richardson  LIGO,
California Institute of Technology, Pasadena, CA 91125, USA  K. Riles
University of Michigan, Ann Arbor, MI 48109, USA  N. A. Robertson  LIGO,
California Institute of Technology, Pasadena, CA 91125, USA  SUPA, University
of Glasgow, Glasgow G12 8QQ, UK  J. G. Rollins  LIGO, California Institute of
Technology, Pasadena, CA 91125, USA  C. L. Romel  LIGO Hanford Observatory,
Richland, WA 99352, USA  J. H. Romie  LIGO Livingston Observatory, Livingston,
LA 70754, USA  M. P. Ross  University of Washington, Seattle, WA 98195, USA
K. Ryan  LIGO Hanford Observatory, Richland, WA 99352, USA  T. Sadecki  LIGO
Hanford Observatory, Richland, WA 99352, USA  E. J. Sanchez  LIGO, California
Institute of Technology, Pasadena, CA 91125, USA  L. E. Sanchez  LIGO,
California Institute of Technology, Pasadena, CA 91125, USA  T. R. Saravanan
Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India  R.
L. Savage  LIGO Hanford Observatory, Richland, WA 99352, USA  D. Schaetzl
LIGO, California Institute of Technology, Pasadena, CA 91125, USA  R. Schnabel
Universität Hamburg, D-22761 Hamburg, Germany  R. M. S. Schofield  University
of Oregon, Eugene, OR 97403, USA  E. Schwartz  LIGO Livingston Observatory,
Livingston, LA 70754, USA  D. Sellers  LIGO Livingston Observatory,
Livingston, LA 70754, USA  T. Shaffer  LIGO Hanford Observatory, Richland, WA
99352, USA  D. Sigg  LIGO Hanford Observatory, Richland, WA 99352, USA  B. J.
J. Slagmolen  OzGrav, Australian National University, Canberra, Australian
Capital Territory 0200, Australia  J. R. Smith  California State University
Fullerton, Fullerton, CA 92831, USA  S. Soni  Louisiana State University,
Baton Rouge, LA 70803, USA  B. Sorazu  SUPA, University of Glasgow, Glasgow
G12 8QQ, UK  A. P. Spencer  SUPA, University of Glasgow, Glasgow G12 8QQ, UK
K. A. Strain  SUPA, University of Glasgow, Glasgow G12 8QQ, UK  L. Sun  LIGO,
California Institute of Technology, Pasadena, CA 91125, USA  M. J.
Szczepańczyk  University of Florida, Gainesville, FL 32611, USA  M. Thomas
LIGO Livingston Observatory, Livingston, LA 70754, USA  P. Thomas  LIGO
Hanford Observatory, Richland, WA 99352, USA  K. A. Thorne  LIGO Livingston
Observatory, Livingston, LA 70754, USA  K. Toland  SUPA, University of
Glasgow, Glasgow G12 8QQ, UK  C. I. Torrie  LIGO, California Institute of
Technology, Pasadena, CA 91125, USA  G. Traylor  LIGO Livingston Observatory,
Livingston, LA 70754, USA  M. Tse  LIGO, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA  A. L. Urban  Louisiana State University,
Baton Rouge, LA 70803, USA  G. Vajente  LIGO, California Institute of
Technology, Pasadena, CA 91125, USA  G. Valdes  Louisiana State University,
Baton Rouge, LA 70803, USA  D. C. Vander-Hyde  Syracuse University, Syracuse,
NY 13244, USA  P. J. Veitch  OzGrav, University of Adelaide, Adelaide, South
Australia 5005, Australia  K. Venkateswara  University of Washington, Seattle,
WA 98195, USA  G. Venugopalan  LIGO, California Institute of Technology,
Pasadena, CA 91125, USA  A. D. Viets  Concordia University Wisconsin, 2800 N
Lake Shore Dr, Mequon, WI 53097, USA  T. Vo  Syracuse University, Syracuse, NY
13244, USA  C. Vorvick  LIGO Hanford Observatory, Richland, WA 99352, USA  M.
Wade  Kenyon College, Gambier, OH 43022, USA  R. L. Ward  OzGrav, Australian
National University, Canberra, Australian Capital Territory 0200, Australia
J. Warner  LIGO Hanford Observatory, Richland, WA 99352, USA  B. Weaver  LIGO
Hanford Observatory, Richland, WA 99352, USA  R. Weiss  LIGO, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  C. Whittle  LIGO,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA  B. Willke
Leibniz Universität Hannover, D-30167 Hannover, Germany  Max Planck Institute
for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover,
Germany  C. C. Wipf  LIGO, California Institute of Technology, Pasadena, CA
91125, USA  L. Xiao  LIGO, California Institute of Technology, Pasadena, CA
91125, USA  H. Yamamoto  LIGO, California Institute of Technology, Pasadena,
CA 91125, USA  Hang Yu  LIGO, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Haocun Yu  LIGO, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA  L. Zhang  LIGO, California Institute of
Technology, Pasadena, CA 91125, USA  M. E. Zucker  LIGO, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  LIGO, California Institute
of Technology, Pasadena, CA 91125, USA  J. Zweizig  LIGO, California Institute
of Technology, Pasadena, CA 91125, USA

###### Abstract

On April 1st, 2019, the Advanced Laser Interferometer Gravitational-Wave
Observatory (aLIGO), joined by the Advanced Virgo detector, began the third
observing run, a year-long dedicated search for gravitational radiation. The
LIGO detectors have achieved a higher duty cycle and greater sensitivity to
gravitational waves than ever before, with LIGO Hanford achieving angle-
averaged sensitivity to binary neutron star coalescences to a distance of
$111\text{\,}\mathrm{M}\mathrm{p}\mathrm{c}$, and LIGO Livingston to
$134\text{\,}\mathrm{M}\mathrm{p}\mathrm{c}$ with duty factors of $74.6\%$ and
$77.0\%$ respectively. The improvement in sensitivity and stability is a
result of several upgrades to the detectors, including doubled intracavity
power, the addition of an in-vacuum optical parametric oscillator for
squeezed-light injection, replacement of core optics and end reaction masses,
and installation of acoustic mode dampers. This paper explores the purposes
behind these upgrades, and explains to the best of our knowledge the noise
currently limiting the sensitivity of each detector.

###### Contents

  1. I Introduction
  2. II O3 Overview
    1. II.1 Advanced LIGO noise budgets
    2. II.2 Astrophysical range
    3. II.3 Duty cycle
  3. III Analysis of instrumental noise
    1. III.1 Quantum noise
    2. III.2 Thermal noise
    3. III.3 Seismic noise
    4. III.4 Newtonian noise
    5. III.5 Laser frequency noise
    6. III.6 Laser intensity noise
    7. III.7 Auxiliary length control noise
    8. III.8 Actuator noise
    9. III.9 Alignment control noise
    10. III.10 Beam jitter noise
    11. III.11 Scattered light noise
    12. III.12 Residual gas noise
    13. III.13 Photodetector dark noise
    14. III.14 Output mode cleaner length noise
    15. III.15 Other
  4. IV Instrument improvements
    1. IV.1 Laser power increase
      1. IV.1.1 Laser hardware changes
      2. IV.1.2 Parametric instabilities
      3. IV.1.3 Radiation pressure torque
    2. IV.2 Squeezer
    3. IV.3 Core optic replacement
    4. IV.4 Test mass discharge
    5. IV.5 Stray light control
    6. IV.6 Alignment sensing and control
      1. IV.6.1 Radiation pressure compensation
      2. IV.6.2 Alignment dither system
      3. IV.6.3 Signal-recycling cavity alignment
    7. IV.7 Lock acquisition and stability
      1. IV.7.1 Seismic controls
      2. IV.7.2 Suspension chain damping
      3. IV.7.3 CARM offset reduction
      4. IV.7.4 New VCO at Livingston
      5. IV.7.5 Increased actuator range
  5. V Interferometer characterization
    1. V.1 Correlated noise
    2. V.2 Measuring the arm power
    3. V.3 Thermal compensation
    4. V.4 Nonuniform coating absorption
    5. V.5 RF oscillator noise investigations
    6. V.6 Optic charging and stray electric fields
  6. VI Future Work
  7. VII Acknowledgements
  8. A Table of O3 Parameters

##  I Introduction

In 2015, the Advanced LIGO detectors at Hanford, Washington and Livingston,
Louisiana achieved unprecedented sensitivity to gravitational waves Martynov
_et al._ (2016); Abbott  _et al._ (2016a). On September 14th, 2015, LIGO first
detected gravitational waves from a binary black hole merger Abbott  _et al._
(2016b). During the first observing run (O1), which ran from September 2015 to
January 2016, two more binary black hole detections were made Abbott  _et al._
(2016c, d). The second observing run (O2), which ran from November 2016 to
August 2017, detected seven binary black hole mergers, and one binary neutron
star merger Abbott  _et al._ (2019a, 2017a, 2017b, 2017c, 2017d, 2017e, b).
The third observing run (O3), which ran from April 1 to September 30, 2019
(O3a) and from November 1, 2019 until March 27, 2020 (O3b), has been the most
successful search for gravitational waves in history, with greater sensitivity
and the permanent addition of the Advanced Virgo detector Abbott  _et al._
(2018). During this run, 56 candidate gravitational-wave signals, including at
least one new compact binary coalescence in the binary neutron star mass range
Abbott  _et al._ (2020a) and a system with record mass ratio Abbott  _et al._
(2020b), were announced gra . The increase in the detection rate is due to the
improved performance of the detectors, which is the subject of this paper.

Figure 1:  Simplified optical layout of the aLIGO detectors for O3. At the
input port is the pre-stabilized laser (PSL) and the phase modulating electro-
optic modulator (EOM) with three radio frequencies used for length and angular
control. The spatial profile, polarization, jitter, and frequency noise of the
beam is cleaned by the triangular input mode cleaner (IMC) cavity. Arm
cavities are formed from input test masses (ITMs) and end test masses (ETMs).
The power- and signal-recycling mirrors (PRM and SRM, respectively) together
with the beamsplitter (BS) and input test masses form the power- and signal-
recycling cavities. Light at the pick-off of the power-recycling cavity (POP)
and interferometer reflection (REFL) ports are used for sensing and control of
auxiliary degrees of freedom. The output Faraday isolator (OFI) prevents back-
reflected light from entering the interferometer from the antisymmetric port
(AS) and is used to inject squeezed light from the optical parametric
oscillator (OPO). The output mode cleaner (OMC) cleans the output spatial mode
and separates the carrier light for the output photodiodes (DCPDs) on
transmission of the OMC. These photodiodes measure the differential arm length
(DARM), which is sensitive to gravitational waves.

The Advanced LIGO detectors are dual-recycled Fabry-Pérot Michelson
interferometers. Figure 1 shows the full interferometer layout. Ultra stable
laser light at $1064\text{\,}\mathrm{n}\mathrm{m}$ Kwee  _et al._ (2012);
Thies  _et al._ (2019) enters the interferometer and circulates in the
$4\text{\,}\mathrm{k}\mathrm{m}$ arms, each with Fabry-Pérot cavities to
increase the light interaction time with a gravitational wave. The power-
recycling cavity, formed by the power-recycling mirror and the input test
masses, increases the laser power circulating in the interferometer Meers
(1988). The signal-recycling cavity, formed with the signal-recycling mirror
and the input test masses, broadens the detector bandwidth Mizuno  _et al._
(1993); Buonanno and Chen (2001). Key parameters for both interferometers are
summarized in Table 3. Improvements made between observing runs bring the
detectors closer to the final design sensitivity Aasi  _et al._ (2015).

Gravitational waves passing through the interferometer produce a metric
disturbance that results in an effective differential change in the arm
lengths. The change in effective arm length imparts a phase shift to the
electromagnetic fields circulating in the arms. This causes a change in
optical power at the antisymmetric port via the interference between the
fields from the two arms. The gravitational-wave readout is a measure of the
differential arm length, or DARM.

The lengths of these key optical cavities, and other auxiliary optical
cavities like the input and output mode cleaners, are controlled using the
length sensing and control system Abbott  _et al._ (2010); Izumi and Sigg
(2016). Most cavity lengths are sensed using radio frequency phase modulation
sidebands, added to the main beam by the electro-optic modulator, via the
Pound-Drever-Hall laser stabilization technique Drever  _et al._ (1983).
Exceptions are the output mode cleaner, which uses a dither scheme described
in Section III.14, and DARM, which uses a DC readout scheme Fricke  _et al._
(2012). The beat between carrier and sidebands present at the various ports of
the interferometer—on reflection of the power-recycling mirror, at the pick-
off of the power-recycling cavity, or at the antisymmetric port—is measured on
photodetectors, filtered through a combination of analog and digital
electronics, and then fed back to the relevant actuators via the LIGO real-
time digital control system Bork  _et al._ (2020).

Calibration is the process of characterizing the response of the detector to
gravitational waves. The DARM control loop and interferometer sensitivity are
referenced to a photon-calibrator, which induces a known displacement on an
end test mass via radiation pressure Karki  _et al._ (2016). The uncertainty
in the detector response to gravitational waves is 7% in magnitude and 4
degrees in phase between 20 and $2000\text{\,}\mathrm{H}\mathrm{z}$ Sun  _et
al._ (2020); Cahillane  _et al._ (2017); Viets  _et al._ (2018); Tuyenbayev
_et al._ (2016).

The alignment of optics in the interferometer is controlled by the alignment
sensing and control system Barsotti  _et al._ (2010). Three separate
techniques are used: radio frequency wavefront sensors Fritschel  _et al._
(1998), beam pointing onto quadrant photodiodes, and dither alignment
described in Section III.9. Controlled degrees of freedom include the
alignment of the input mode cleaner, input beam pointing, power- and signal-
recycling cavities, Michelson, output mode cleaner, squeezer beam pointing,
and the arm cavities.

The interferometer must first be “locked” to be sensitive to gravitational
waves. Locking is the process of bringing the detector into a regime where
maximum power buildup is achieved in the arm cavities and all interferometer
degrees of freedom are controlled Staley  _et al._ (2014); Martynov (2015).
First, green lasers at each end station are locked to each arm cavity length.
Then, the green transmission beams through each arm are combined with local
oscillator light on photodetectors that produce signals to control the common
and differential arm cavity lengths. Next, the power-recycling cavity, signal-
recycling cavity and Michelson lengths are locked to the infrared laser via
Pound-Drever-Hall error signals.

In this phase all main degrees of freedom are controlled but there is no
infrared light in the arm cavities. To transition to full infrared control,
first the power-recycling, signal-recycling, and Michelson error signals are
transitioned from using the first-order radio-frequency sidebands to using the
third-order sidebands Arai  _et al._ (2000). This is done because the first-
order sideband error signals become zero as the arms are brought from
antiresonance to resonance. Then, the green common arm length is brought from
infrared antiresonance to the side of an infrared fringe, where control is
handed off to infrared transmission through the arms. Next, the infrared light
is brought to resonance, where both differential and common arm lengths are
transferred to Pound-Drever-Hall error signals Drever  _et al._ (1983). For
the DC readout scheme, a $10\text{\,}\mathrm{p}\mathrm{m}$ length offset is
applied to the DARM degree of freedom to allow some carrier light to leave the
antisymmetric port and act as a local oscillator for light carrying the
gravitational wave signal.

At this stage the entire interferometer sensing is performed via the main
infrared light. The input power is increased, low-noise controls are engaged,
and squeezed light is injected to achieve maximum sensitivity to gravitational
waves. At this point the locking process is complete and the interferometer is
ready for observing.

The steps taken to acquire lock are done automatically using a state machine
called Guardian Rollins (2016). Because the locking sequence is not
deterministic and can be hindered by poor environmental conditions, there is
some variability of the lock acquisition time. The locking sequence takes
approximately 30 minutes in good environmental conditions and with good
initial alignment. Much of this time is used to allow various slow drift
control loops to settle, allow optics to thermalize, and smoothly and reliably
move between different control and actuation configurations. Improvements to
the lock acquisition are covered in Section IV.7.

A “lock loss” occurs when the detector falls out of the sensitive linear
regime and control systems are unable to return to this state. Lock losses are
caused by strong earthquakes, controls and sensor saturations, drifting
misalignment, control loop instabilities, and glitches of known and unknown
origin. The cause of lock losses are monitored, and if possible mitigated, to
improve detector duty cycle, as described in Section II.3.

Section II summarizes detector performance during O3. Section III describes
the technical and fundamental noise sources limiting gravitational-wave
sensitivity for both LIGO detectors. Section IV reports the detector upgrades
prior to O3. Section V discusses additional investigations at each detector.

##  II O3 Overview

###  II.1 Advanced LIGO noise budgets

Both detectors are sensitive to gravitational waves across a broad frequency
band from $20\text{\,}\mathrm{H}\mathrm{z}$ to
$5\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$. The sensitivity of a detector is
limited by the collection of noises coupled to the gravitational-wave readout.
To improve the sensitivity of a detector, typically a source of noise or noise
coupling is identified and mitigated. The noise budget is a tool used in this
process.

The noise budget is displayed as an amplitude spectral density of the
equivalent differential arm motion for the various noise sources, and is shown
in Figure 2. Figure 2 also shows comparisons of the total measured noise in
the three observing runs. The most dramatic improvements made for O3 are due
to the injection of squeezed light into the antisymmetric port (Section IV.2)
and the increase of resonating laser power inside the interferometer (Section
IV.1.1), both of which improve the high-frequency sensitivity.

The noise budgets show the current understanding of the limiting noise sources
at each observatory. The black solid trace in each plot represents the sum of
all known contributing noise sources. There is excellent agreement between the
modeled and measured noise above roughly $100\text{\,}\mathrm{H}\mathrm{z}$,
but there remain additional noise sources below
$100\text{\,}\mathrm{H}\mathrm{z}$ that are not understood. The noise budget
is not used to explain narrow spectral features such as the violin resonant
modes of the fused silica fibers at $500\text{\,}\mathrm{H}\mathrm{z}$ and
harmonics, mains power at $60\text{\,}\mathrm{H}\mathrm{z}$ and many others
explained in Covas  _et al._ (2018). While the detectors are nominally
physically identical, slight differences in optical properties, control loop
settings, and local environments mean that the noise budgets are not
identical, particularly for sources that do not limit DARM sensitivity. We
discuss each limiting noise source in Section III.

(a) LHO

(b) LLO

Figure 2:  Full noise budget of LABEL:sub@fig:LhoNb LIGO Hanford Observatory
(LHO) and LABEL:sub@fig:LloNb LIGO Livingston Observatory (LLO). Calculated
noise terms are given as solid lines, while measured contributions are given
as dots. Also included are the instrument noise floors for previous observing
runs, as originally presented in Martynov  _et al._ (2016) and Driggers  _et
al._ (2019). The O2 noise spectrum for LHO has several lines and independently
witnessed noises subtracted. Individual noises are discussed in Section III.
Both sites are broadly limited by the same noise sources, with some notable
differences, including beam jitter coupling (Section III.10), laser noise
couplings (Sections III.5 and III.6), and residual gas noise (Section III.12).

###  II.2 Astrophysical range

Recent upgrades and improved understanding of the limiting noise sources have
produced record sensitivity. A useful metric for understanding the sensitivity
of a detector is the _binary neutron star inspiral range_ , or simply _range_.
The range reported is the luminosity distance at which a detector is sensitive
to an angle-averaged merger of two neutron stars for a canonical SNR of 8 Finn
and Chernoff (1993); Finn (1996); Chen  _et al._ (2017). The angle average is
over the orientation of binary systems and position relative to the detector
antenna patterns. As such the range does not represent a strict maximum
distance at which a binary neutron star merger can produce a significant
signal. The LIGO Livingston Observatory (LLO) has achieved a binary neutron
star range of around $134\text{\,}\mathrm{M}\mathrm{p}\mathrm{c}$, while the
LIGO Hanford Observatory (LHO) has achieved a range of around
$111\text{\,}\mathrm{M}\mathrm{p}\mathrm{c}$. The detector sensitivity to
heavier binary black holes extends much further than binary neutron stars.

The range is calculated every minute from the online calibrated strain power
spectral density; Figure 3 shows the range of each observatory during O3.

(a)

(b)

Figure 3: The angle-averaged sensitivity of each detector (as determined by
the binary neutron star inspiral range; see main text for definition) as
LABEL:sub@subfig:rangevstime a function of time and LABEL:sub@subfig:rangehist
a fraction of observing time. The time dependence is largely caused by changes
in anthropogenic noise, which can increase scattered light noise. Additional
variations are due to changes in the interferometer configuration. The break
in the horizontal axis corresponds to the month-long observing break in
October 2019. Brief but significant drops in the range at both sites are
caused by instrumental _glitches_ of unknown origin (Section III.15).

###  II.3 Duty cycle

During O3 both detectors were operational a greater percentage of the time
compared to the past two observing runs, with LHO and LLO achieving
observation duty cycles of $74.6\%$ and $77.0\%$, respectively, with
coincident observation $62.2\%$ of the time. Time not observing is spent
either acquiring lock, unlocked and undergoing maintenance, unlocked due to
unfavorable environmental conditions (earthquakes, wind, storms), or locked
and in a state of commissioning, where improvements are made to the detectors.
Improvements to the automated lock acquisition sequence, which places the
detector in a detection-ready state, are outlined in Section IV.7. While some
parts of lock acquisition are faster, new features have been added such that
overall the lock acquisition time has not changed significantly from run to
run.

Section IV.7 discusses improvements to detector robustness and stability that
result in less frequent lock losses, longer lock durations, and improved
observation duty cycle (Table 1).

Observatory | O1 | O2 | O3a | O3b
---|---|---|---|---
LHO |  |  |  |
Mean (hr) | $9.8$ | $9.4$ | $12.4$ | $14.9$
Median (hr) | $7.2$ | $4.7$ | $8.8$ | $8.9$
Duty cycle (%) | $62.6$ | $70.6$ | $71.2$ | $78.8$
LLO |  |  |  |
Mean (hr) | $5.7$ | $5.5$ | $10.2$ | $14.5$
Median (hr) | $1.9$ | $2.9$ | $6.5$ | $9.3$
Duty cycle (%) | $55.3$ | $65.8$ | $75.7$ | $78.6$
Table 1:  Mean and median times of low-noise lock segments for each observing
run and overall observing run duty factor. Large transients or unfavorable
weather and seismic conditions can knock the interferometers out of lock,
reducing the total observing time. In addition to improved sensitivity, both
detectors have improved resistance to large disturbances.

Figure 4 shows the integrated time-volume sensitivity to binary neutron stars
for both sites over the three observing runs. The increase in sensitivity
combined with the higher duty factor have resulted in a dramatic increase in
the observed time-volume integral, and a roughly proportional increase in
gravitational-wave event candidates gra ; nas .

Figure 4: Integrated observation time-volume for both LHO and LLO over the
durations of the three observing runs. The observing volume is calculated as a
sphere with radius equal to the binary neutron star inspiral range, a proxy
for the sensitivity of each detector (see text for definition). The rapid
increase in this metric during O3 is due to improvements in interferometer
sensitivity and duty cycle. The vertical dashed lines indicate the planned
breaks between the three runs.

##  III Analysis of instrumental noise

Figure 2 shows the current understanding of the limiting noise sources at each
observatory. These are produced using two sets of noise terms: those that are
calculated based on interferometer optical and material properties gwi , and
projections of noises from auxiliary channels.

The most common type of projection is made by inferring a coupling function
$G(f)$ between a witness channel $w$ and DARM at frequency $f$. The
contribution of noise in this channel to DARM is given by

$S_{w\rightarrow d}(f)=G(f)S_{w,0}(f).$ (1)

Here $S_{w,0}$ is the power spectrum of witness channel $w$ under normal
operating conditions, assumed not to be limited by sensing noise. For most
auxiliary channels, the coupling function is estimated according to

$G(f)=\frac{S_{d,\textrm{exc}}(f)-S_{d,0}(f)}{S_{w,\textrm{exc}}(f)-S_{w,0}(f)}.$
(2)

Here $S_{x,\textrm{exc}}$ is the power spectrum of channel $x$ with an
external excitation applied, while $S_{x,0}$ is the same spectrum in ambient
conditions. $w$ and $d$ refer to the witness channel and DARM, respectively.
$G(f)$ is set to zero where such excitations do not produce an appreciable
signal in the witness channel or DARM. Because typical witness channels have
low coherence with DARM, this is _not_ equivalent to taking the transfer
function between channels; see the example in Section III.7. These injections
are performed at a number of different amplitudes to confirm that $G(f)$ does
not depend on the amplitude of the witness signal. However, this coupling can
be modulated or up-converted from other channels and will depend on the
amplitude of those signals.

Several projections presented in Figure 2 are more complicated. In some cases,
the coupling to DARM is nonlinear (such as the output mode cleaner length
noise, Section III.14). In other cases, it can be challenging to perform an
excitation that mimics and is measured by witness sensors in the same way as
ambient disturbances; this is especially problematic for jitter and scattered
light noise estimates (Section III.11).

What follows is a brief discussion of each noise term shown in Figure 2.

###  III.1 Quantum noise

Fluctuations of the vacuum electric field at the interferometer readout port
impose a fundamental limit to the interferometer sensitivity Caves (1980,
1981); Braginsky  _et al._ (1992); Buonanno and Chen (2001). Quantum noise
appears as shot noise and quantum radiation pressure noise (QRPN).

Shot noise arises from statistical fluctuations in the arrival time of photons
at the interferometer output. As the intracavity power is increased, the
displacement signal-to-shot-noise ratio increases. Shot noise dominates the
high-frequency region of the spectrum.

QRPN is displacement noise arising from amplitude fluctuations of the electric
field in the arms. These amplitude fluctuations produce a fluctuating momentum
on the optics via radiation pressure, inducing displacement noise. As the
intracavity power is increased, this displacement noise also increases. QRPN
is attenuated by the free-mass response of the test masses and so is more
important at low frequencies. QRPN never dominates the gravitational-wave
spectrum.

In O3, shot noise is reduced by the use of squeezed vacuum injected through
the antisymmetric port of the interferometer Tse  _et al._ (2019). Injecting
vacuum squeezed in the phase quadrature reduces the power fluctuations seen by
the antisymmetric port photodiodes, lowering the shot noise floor. However,
due to the uncertainty principle, squeezing the phase quadrature leads to
anti-squeezing in the amplitude quadrature, raising the QRPN floor.

The increase in laser power and installation of the squeezer has decreased the
shot noise contribution. These improvements come with a corresponding increase
in QRPN, which is acceptable because QRPN does not dominate the low frequency
gravitational-wave spectrum. However, QRPN is close to limiting the current
gravitational-wave noise floor Yu  _et al._ (2020).

Signal-recycling mirror reflectivity also impacts quantum noise by modifying
the interferometer response to gravitational waves. The increase in signal-
recycling mirror reflectivity discussed in section IV.3 slightly broadened the
region of low quantum noise while slightly increasing the minimum quantum
noise. This had a small effect on binary neutron star inspiral range.

###  III.2 Thermal noise

Thermal motion in the test mass suspension, substrate, and optical coating
cause displacement noise in DARM Braginsky and Vyatchanin (2003); Levin
(1998); Yam  _et al._ (2015). Generally thermal noise increases with
mechanical loss or loss angle, as related by the fluctuation-dissipation
theorem Callen and Greene (1952); Saulson (1990). The test mass quadruple
suspension system has been designed to limit thermal noise in the measurement
band Aston  _et al._ (2012). The fused silica substrate material is chosen for
low mechanical loss and has a small contribution to the thermal noise. A minor
contribution to the thermal noise is due to the addition of acoustic mode
dampers (Section IV.1.2) Biscans  _et al._ (2019). The thermal noise
contribution from these dampers is estimated to degrade interferometer
sensitivity by less than 1%.

Brownian motion of the optic dielectric coatings is the dominant noise in the
LLO noise budget from
$40\text{\,}\mathrm{H}\mathrm{z}100\text{\,}\mathrm{H}\mathrm{z}$. Advanced
LIGO test masses have titania-doped tantala/silica coatings
($\mathrm{TiO}_{2}$-doped $\mathrm{Ta}_{2}\mathrm{O}_{5}/\mathrm{SiO}_{2}$),
with 25% titania in the tantala layers and varying layer thicknesses to reduce
thermal noise Harry  _et al._ (2006); Granata  _et al._ (2020). The coating
thermal noise contribution is estimated based on recent optical measurements
of aLIGO end test mass witness samples Gras and Evans (2018). The correlated
noise measurements in Section V.1 approach the thermal noise limit as the
dominant known noise source around $200\text{\,}\mathrm{H}\mathrm{z}$. The
coating thermal noise can be reduced with low-loss optical coatings or
cryogenic optics Steinlechner (2018).

###  III.3 Seismic noise

The Advanced LIGO test masses form the bottom stage of a quadruple pendulum
chain Aston  _et al._ (2012). The purpose of this chain is to reduce coupling
of ground motion (characterized at the LIGO sites in Daw  _et al._ (2004)) to
the test mass. These pendulums are suspended from seismic isolation platforms
Matichard  _et al._ (2015) which themselves are supported by hydraulically
actuated pre-isolation structures Wen  _et al._ (2014).

This arrangement ensures that the seismic noise contribution at the bottom of
the chain sits far below the DARM noise curve. However this seismic noise
contribution only accounts for linear coupling to the DARM degree of freedom;
coupling can become nonlinear when motion is large, up-converting into the
gravitational-wave band. There are circuitous paths by which seismic motion
can couple to the interferometer output, such as through angular degrees of
freedom (Section III.9), auxiliary cavity length degrees of freedom (Section
III.7), or scattered light (Section III.11). Earthquakes, high microseism, and
windy conditions—which can confuse isolation systems by tilting building
floors near wind-driven walls—generate additional motion that can increase
scattered light coupling, cause lock loss, and hinder lock reacquisition.

###  III.4 Newtonian noise

Newtonian noise is produced by direct gravitational coupling of test masses to
fluctuating mass density fields, such as produced by seismicity and
atmospheric pressure fluctuations Harms (2015); Driggers  _et al._ (2012);
Coughlin  _et al._ (2016, 2018). Newtonian noise, dominated by seismic surface
waves called Rayleigh waves, is predicted to limit the design sensitivity of
the Advanced LIGO detectors from
$10\text{\,}\mathrm{H}\mathrm{z}20\text{\,}\mathrm{H}\mathrm{z}$ Saulson
(1984); Hughes and Thorne (1998). Newtonian noise has not been detected in
Advanced LIGO, and is predicted to be below O3 sensitivity levels Harms  _et
al._ (2020).

###  III.5 Laser frequency noise

Frequency noise refers to the fluctuations in the instantaneous frequency of
the laser. Frequency noise can appear as differential phase fluctuations in
the arms, masking the gravitational-wave signal.

The common-mode rejection of the interferometer ensures most frequency noise
does not reach the antisymmetric port. Asymmetries in the interferometer allow
frequency noise to appear at the dark port, including the DARM offset and
Schnupp asymmetry purposefully introduced for interferometer control, and
unintentional mismatch in the arm reflectivity, losses, cavity pole, power
buildup, and transverse mode content Izumi  _et al._ (2015); Somiya  _et al._
(2006); Camp  _et al._ (2000); Cahillane  _et al._ (2020).

A frequency stabilization servo (FSS) is employed both to lock the laser to
the extremely narrow common-arm linewidth and to suppress the free-running
frequency noise of the main laser Fritschel  _et al._ (2001). There are three
hierarchical control loops. The first stage is the reference cavity, a
$20\text{\,}\mathrm{c}\mathrm{m}$ fixed-length cavity to which the laser
frequency is initially stabilized Kwee  _et al._ (2012). The second stage is
the input mode cleaner, where the laser is stabilized to the
$33\text{\,}\mathrm{m}$ suspended cavity. The third stage is the common-arm
cavity, where the laser is stabilized to the $4\text{\,}\mathrm{k}\mathrm{m}$
arm length, with coupled cavity pole of $0.6\text{\,}\mathrm{H}\mathrm{z}$.
All three stages together suppress the frequency noise so it does not limit
the gravitational-wave spectrum.

Two upgrades to the frequency stabilization loop were performed at LIGO
Hanford. First, a second photodetector was added to detect the light reflected
from the interferometer, where the common-arm length degree of freedom is
sensed. This allows for the two photodetectors to be used in an in-loop, out-
of-loop configuration to directly measure the sensing noise in the loop.
During operation, both photodetectors are used in-loop to reduce the risk of
saturations.

Second, the power on the input mode cleaner reflection photodetector was
increased by a factor of seven. This improved the optical gain of the second
stage of the FSS, reducing the frequency noise incident on the interferometer.
Figure 5 shows the current frequency noise budget after these changes.

Frequency noise couplings to the gravitational-wave spectrum were found to
change significantly with the thermal state of the interferometer, likely due
to changing transverse mode content Cahillane  _et al._ (2020). These
couplings were partially mitigated via the thermal compensation system
(Section V.3).

Figure 5:  LIGO Hanford laser frequency noise budget. The upper trace is the
out-of-loop witness of frequency noise incident on the interferometer, which
is dominated by shot noise. This trace is projected into the gravitational-
wave spectrum in Figure 2a. The in-loop frequency noise is limited by shot
noise from the input mode cleaner (lower trace). During operation, the
reflection shot noise is a factor of 2 lower than plotted here as both
reflection photodiodes are in-loop, doubling the common-arm length signal.

###  III.6 Laser intensity noise

Intensity fluctuations of the laser appearing at the interferometer dark port
can mask gravitational-wave signals. Similar to frequency noise, the common-
mode rejection of the interferometer is not enough by itself to avoid sensing
intensity fluctuations in DARM. Advanced LIGO employs an intensity
stabilization servo (ISS) made of two hierarchical control loops to suppress
the laser intensity fluctuations incident on the interferometer. Both ISS
loops feed back to a single-pass acousto-optic modulator (AOM) that actuates
on the laser power.

The ISS first loop stabilizes the total laser power out of one port of the
bow-tie pre-mode cleaner on the pre-stabilized laser table with a bandwidth of
$80\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$. The second ISS loop stabilizes
the total power transmitted through the input mode cleaner cavity. A pick-off
of this cavity transmission goes to an in-vacuum array of eight photodiodes.
Four of the eight photodiodes are used for the second loop sensor. This
control signal is filtered and summed with the control signal from the first
loop and sent to the AOM. The other four photodiodes are out-of-loop witnesses
of intensity noise. The ISS second loop has a bandwidth of around
$28\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$.

Figure 6 illustrates the laser intensity stability at Hanford. Intensity noise
RMS is dominated by input mode cleaner angular control peaks between 1 and
$4\text{\,}\mathrm{H}\mathrm{z}$. Between 4 and
$30\text{\,}\mathrm{H}\mathrm{z}$, jitter in the beam path after the input
mode cleaner causes apparent intensity fluctuations on the ISS photodiode
array, as witnessed by the ISS quadrant photodiode. The shot noise floor of
the second loop is attained between $30\text{\,}\mathrm{H}\mathrm{z}$ and
$1\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$. Unsuppressed intensity noise
dominates above $1\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$, where the
intensity servo is gain-limited.

The large difference between the Hanford and Livingston intensity noise
contributions to DARM at low frequencies, as seen in Figure 2, is likely due
to an increased radiation pressure coupling due to a larger arm power mismatch
at Hanford. The circulating arm powers for both sites are discussed in Section
V.2.

Figure 6:  LIGO Hanford laser intensity noise budget. The uppermost trace
represents the out-of-loop witness of intensity noise incident on the
interferometer. This trace is projected into the gravitational-wave spectrum
in Figure 2a. Seismic motion causes intensity fluctuations below
$1\text{\,}\mathrm{H}\mathrm{z}$, and input mode cleaner suspension resonances
dominate the intensity RMS. Beam jitter dominates from 4 to
$30\text{\,}\mathrm{H}\mathrm{z}$, the shot noise limit is attained from 30 to
$1000\text{\,}\mathrm{H}\mathrm{z}$, and the intensity stabilization servo is
gain-limited above $1\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$.

###  III.7 Auxiliary length control noise

The gravitational-wave readout is orders of magnitude more sensitive to
differential arm cavity length (DARM) than to the lengths of the power-
recycling cavity, signal-recycling cavity, or the Michelson degree of freedom
(beam splitter position relative to the arm input mirrors). However, each of
these auxiliary degrees of freedom must be controlled to keep the
interferometer in its sensitive configuration, and DARM readout is still
marginally sensitive to each. Each has an individual readout scheme Izumi and
Sigg (2016) that is less sensitive than the main DARM readout.

The gains of each auxiliary loop are chosen to be high enough to always
control the interferometer while being as low as possible to minimize re-
injected sensing noise. Even with this gain optimization, sensing noise from
the Michelson and signal-recycling cavity loops can couple to DARM and would
limit interferometer sensitivity if not for feedforward cancellation.

Figure 7:  The contribution of the signal-recycling cavity length (SRCL)
control signal to the gravitational-wave readout channel (DARM) at LLO. The
coherent contribution is determined by the magnitude-squared coherence between
DARM and SRCL, while the total contribution is estimated as described at the
beginning of Section III. By using a feedforward signal from the SRCL control
to DARM, the coherent contribution is significantly reduced, but there remains
a component that cannot be removed with simple feedforward.

Feedforward is a technique of real-time noise subtraction in DARM. Re-injected
sensing noise in the auxiliary length loops is measured and known to limit
DARM. The transfer functions from the auxiliary loop to DARM and the
feedforward actuation path to DARM are first measured and fit using software
tools such as IIRrational iir . The output signal of this auxiliary loop is
injected into DARM with this transfer function and opposite sign, cancelling
the auxiliary noise that normally would appear in DARM. Such feedforward loops
have reduced the magnitude-squared coherence between these channels and DARM
to below $10^{-2}$ above $10\text{\,}\mathrm{H}\mathrm{z}$. Figure 7 shows how
a feedforward filter between the signal-recycling length control signal and
DARM reduces the coherent contribution of this noise source to DARM, defined
as Bendat and Piersol (2011)

$\frac{\left|S_{wd}(f)\right|^{2}}{S_{w}(f)}=\gamma_{wd}^{2}(f)S_{d}(f),$ (3)

where $S_{w}(f)$ and $S_{d}(f)$ are the power spectral densities of the
auxiliary (witness) channel and DARM, respectively, and $\gamma_{wd}^{2}(f)$
and $S_{wd}(f)$ are the magnitude-squared coherence and cross-spectral density
between these channels, respectively.

As seen in Figure 7, the contribution of these auxiliary channels to the DARM
noise is larger than expected based on coherence alone, suggesting nonlinear,
bilinear, and/or non-stationary coupling to DARM. Non-stationary coupling has
already been observed due to modulation from motion of the angular degrees of
freedom, and can be partially removed offline Vajente  _et al._ (2020); Mukund
_et al._ (2020). Additional work is required to understand this type of
contribution to the interferometer noise floor.

###  III.8 Actuator noise

The position of the LIGO optics is controlled with digital-to-analog
converters (DACs) and either electromagnetic coils or electrostatic actuators.
Analog electronics filter the output of the DACs and allow conversion between
a high-range configuration for lock acquisition and a low-noise configuration
for normal operation. Upper suspension stages have larger actuation range but
due to the suspension response have less control authority—and therefore,
lower noise coupling—at frequencies above the pendulum response Aston  _et
al._ (2012). As such, the test mass and penultimate mass actuators are most
important for direct noise coupling in the gravitational-wave band.

Operating with higher actuator range minimizes instrument susceptibility to
saturations and lock loss, which can significantly negatively affect observing
duty cycle. However, this generally comes at the cost of increased noise
injection. Improvements to the actuators and digital-to-analog converters have
helped both to move this noise contribution safely below the current
sensitivity and improve duty cycle. These are discussed in Section IV.7.5.

###  III.9 Alignment control noise

The alignment sensing and control (ASC) system controls the alignment of
interferometer optics. The mirrors must be actively aligned to suppress motion
from external disturbances, maximize optical power coupling, and counteract
instabilities from radiation pressure Dooley  _et al._ (2013). During lock
acquisition, large increases in optical power result in radiation pressure
that can push the optics out of alignment. During low-noise operation, slow
drifts in alignment must be corrected and radiation pressure torques on the
optics must be compensated to maintain stable operation Aasi  _et al._ (2015).

Below $25\text{\,}\mathrm{H}\mathrm{z}$ the angular arm controls are the
largest known source of noise contribution to DARM. As described in Barsotti
_et al._ (2010) and in Martynov  _et al._ (2016), any residual angular motion
is expected to couple to the longitudinal degrees of freedom of the cavities
through both static and dynamic mis-centering of the beams, leading to linear
and nonlinear coupling.

Centering the beams on the suspensions by adjusting the spot position on the
optic or by digitally compensating the position of the rotation point is a
critical step in reducing the ASC noise contribution to DARM. The centering of
the beams is discussed in Section IV.6.2.

Changes in cavity alignment are primarily sensed with dedicated
interferometric sensors called wavefront sensors. These quadrant
photodetectors, with radio-frequency demodulation on each segment, rely on the
relative alignment of carrier and sidebands inside the interferometer Anderson
(1984); Morrison  _et al._ (1994). The sensing of the residual angular motion
above $10\text{\,}\mathrm{H}\mathrm{z}$ is limited by the noise of these
sensors. To filter this noise and achieve low-noise operation, aggressive low-
pass filters in the ASC control loops are engaged. This critical step in the
lock acquisition sequence reduces the angular control gain above
$10\text{\,}\mathrm{H}\mathrm{z}$, and therefore produces orders of magnitude
reduction in angular control noise coupling to DARM. However, this also
reduces the phase margin of the loops to close to few tens of degrees. While
acquiring lock, the low-pass filters are not engaged: the ASC loops are
operated with larger phase margins to cope with large radiation pressure
transients. More details on the ASC control scheme are given in Section
IV.6.1.

The wavefront sensors can also be affected by spurious local noise coupling.
At both sites, the sensing of one of the arm common angular modes is
contaminated by the vertical motion of the in-vacuum table where the sensors
are located. A feedforward scheme has been implemented at LLO that reduces the
impact of this effect. At LHO, the wavefront sensors signals are blended with
local reference sensors (quadrant photodiodes) in the transmission of the arms
that are free of this coupling.

In the low-noise configuration, the contributions from ASC are the dominant
known source of noise below $25\text{\,}\mathrm{H}\mathrm{z}$. The
contribution is currently smaller at LLO than LHO. The coherence between the
ASC signals and DARM is low, suggesting that this coupling is primarily
nonlinear. Upgrades to the ASC system for O3 are discussed in Section IV.6 and
high-power alignment control issues are discussed in Section IV.1.3.

###  III.10 Beam jitter noise

Alignment fluctuations of the beam at the interferometer input couple
additional noise to DARM via the changing coupling of the fundamental optical
transverse mode to the arm cavities Mueller (2005); Hardwick (2019). The beam-
position-dependent absorption introduced by point absorbers on the input test
masses (Section V.4) is also believed to couple jitter noise to DARM by
breaking the symmetry of the arms.

During the first two observing runs, the most severe jitter noise originated
from the LHO pre-stabilized laser, where vibration from the water cooling
system of the high-power oscillator produced multiple peaks between 100 and
$900\text{\,}\mathrm{H}\mathrm{z}$ in DARM. These peaks were associated with
resonances of optic mounts on the pre-stabilized laser table, which are
identified by individually exciting each mount while monitoring spectra of
beam jitter sensors.

Before O3 the high-power laser oscillator was replaced (see Section IV.1.1),
allowing a reduction in cooling water flow. In addition, several optical
mounts on the pre-stabilized laser table were mechanically damped. Removal of
the high-power oscillator is also thought to be responsible for reduction of
the broad peak between 250 and $800\text{\,}\mathrm{H}\mathrm{z}$ by reducing
fluctuations in beam size.

Figure 8 shows the jitter noise improvement between O2 and O3 in the LHO DARM
spectrum as well as in estimates of the angular jitter noise contribution to
DARM based on acoustic and mechanical vibration injections at the pre-
stabilized laser table. The most severe peaks around
$300\text{\,}\mathrm{H}\mathrm{z}$ at LHO show a reduction in amplitude of
approximately an order of magnitude. The jitter noise was lower at LLO during
O2, where the high-power oscillator was bypassed Hardwick (2019).

Figure 8: Jitter noise from the pre-stabilized laser, measured at LHO. Data
from O2 (O3) is the upper (lower) dotted trace. Current total displacement
sensitivity (solid) is compared to the O2 displacement sensitivity (dashed).
Peaks in the spectrum are mechanical resonances coupled to DARM via beam
jitter. At some frequencies jitter noise is over- or under-estimated because
the accelerometers used to compare ambient and injected motion are near but
not on the optics that produce the beam jitter.

There are several remaining jitter peaks at LHO and LLO which are just below
DARM and originate from within the pre-stabilized-laser room. Further
reductions in water flow may reduce their amplitude. Note that the linearly
coupled component of jitter can be removed in post-processing, as in the LHO
O2 trace in Figure 2 Driggers  _et al._ (2019).

Beam jitter also couples to DARM at the output port of the interferometer.
Fluctuations in beam pointing change the coupling of the beam to the output
mode cleaner (OMC) Arai  _et al._ (2003). At LLO the beam pointing to the
output mode cleaner is controlled with an angular dither alignment scheme. In
this scheme, modulation is applied to the actuators that control the four
degrees of freedom of beam pointing to the OMC. The modulation frequencies
used in O3 were between $2.2\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$ and
$2.3\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$. Light transmitted through the
OMC is then demodulated to produce the alignment error signals. The control
loop bandwidths are less than $10\text{\,}\mathrm{H}\mathrm{z}$. Residual
motion from this control is projected to DARM with a technique that uses the
root mean square level of beam motion to provide the linear coupling factor.
Output jitter projections at LLO are estimated using the quadrature sum of the
contributions from the four angular degrees of freedom.

At LHO the beam pointing to the OMC is controlled with a quadrant
photodetector scheme. The beam is actively aligned onto two quadrant
photodetectors on a pick-off of the light incident on the OMC. The position of
the beam on the quadrant photodetectors is chosen to maximize the
interferometer optical gain. However, for one of the alignment degrees of
freedom a different beam position gave the lowest coupling of OMC angular
control noise to DARM. This suggests some unwanted light is incident on the
OMC. The projection from the OMC angular control noise to DARM at LHO was not
made for O3.

###  III.11 Scattered light noise

When light lost from the main interferometer beam reflects or scatters off a
moving surface it acquires a time-dependent phase shift. If this scattered
light re-couples to the main interferometer beam it will introduce noise to
DARM Billing  _et al._ (1979).

When the displacement of the scattering surface is small relative to the
wavelength of light, the scattered light noise couples linearly Vinet  _et
al._ (1996). When the displacement is much larger than the wavelength,
scattered light coupling is highly nonlinear. In this large-motion regime,
known as fringe wrapping, the noise is approximately flat in frequency, with
an amplitude proportional to the intensity of the scattered beam and maximum
frequency related to the speed of the scattering object as described in
Section 8 of Martynov (2015), and in Ottaway  _et al._ (2012).

During times of high ground motion, fringe wrapping can significantly degrade
detector sensitivity. This is apparent in Figure 3 where LLO was more
susceptible to scattered light for the first 30 weeks, resulting in greater
variability in the binary neutron star inspiral range. Mitigation efforts
subsequently reduced this variability Soni  _et al._ (2020). As discussed
further in Section IV.5, baffles, mechanical damping, reaction chain
actuation, and transmission monitor suspension actuation were implemented
before and during O3 to mitigate stray light noise. The contribution in Figure
2 represents the scattered light noise in times of typical ground motion and
does not include the contribution from ground motion up-conversion during
times of high microseism.

###  III.12 Residual gas noise

Residual gas in the vacuum chambers adds noise in two ways: as additional
phase noise due to the traversal of gas molecules across the arm cavity laser
beam path Zucker and Whitcomb (1996), and as damping of the test masses Dolesi
_et al._ (2011). The latter contribution has been estimated to be
significantly reduced following the installation of the annular end reaction
masses (Section IV.3).

A small intermittent vacuum leak appeared near the mid point of the X arm at
LLO several years ago, which increased the pressure from a few nanotorr to a
few tens of nanotorr. The correlated noise measurement at LLO in Section V.1
is consistent with a contribution from excess gas noise. The contribution of
this noise depends on the partial gas pressure at different points along the
arms. Large uncertainties in vacuum gauge readouts, poor spatial resolution,
and uncertainty of the residual gas constituents make it challenging to
estimate the induced phase noise along the length of the beam.

Two leaks were located in October 2019 using standard helium leak checking
techniques. The leaks appeared at corroded areas that show visual similarity
to microbial-induced corrosion Little  _et al._ (2007). Such corrosion may
have occurred in the humid environment formed by rodents and insulation that
surrounded the pipe that was installed for the initial bake to remove residual
water in the tube inner surface David  _et al._ (2019). This insulation was
removed in 2017.

After leak repair, residual gas pressure at the mid station of the X-arm
returned to a few nanotorr. For the latter half of O3, the LLO residual gas
contribution is expected to be reduced to the LHO contribution.

###  III.13 Photodetector dark noise

Photodetector dark noise refers to the noise on the gravitational-wave
photodetection chain when there is no light on the two diodes on transmission
of the output mode cleaner. This incorporates the dark noise of the diodes as
well as the associated electronics. Dark noise is a technical noise source,
roughly a factor of 5 below DARM.

###  III.14 Output mode cleaner length noise

The output mode cleaner (OMC) is a bow-tie cavity that transmits the
fundamental interferometer mode that carries the DARM information while
reflecting higher-order transverse modes and modulation sidebands. This
reflected light has relatively large phase noise and intensity noise, as it
contains light not filtered by the arm cavities. Length fluctuations of the
OMC cause fluctuations of the transmitted power that introduce noise to the
gravitational-wave readout.

The OMC length is controlled with a dither lock scheme. OMC length modulation
is applied at $4.5\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$ at LLO and
$4.1\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$ at LHO with a piezoelectric
actuator on one OMC cavity mirror. The signal from the transmitted light is
demodulated to produce an error signal used to control the cavity length via
the same actuator. The control scheme is designed to have an OMC length noise
of , safely below DARM Arai  _et al._ (2003).

The OMC length noise is more than a factor of 10 below DARM at both detectors.
There are small contributions around the frequency of the dither line, at
injected calibration lines, and mechanical resonance lines. There is also a
small low-frequency noise contribution. Differences in this contribution at
LLO and LHO are likely due to differences in the OMC length control schemes.

###  III.15 Other

The understanding of other noise sources has not changed dramatically since
previous observing runs, though the difference between measured DARM noise and
the sum of known noises has significantly decreased since O1. Narrow spectral
features are mostly understood and are either the electrical mains
($60\text{\,}\mathrm{H}\mathrm{z}$ and harmonics), single-frequency
excitations for control signals or calibration (e.g.,
10–$20\text{\,}\mathrm{H}\mathrm{z}$,
$410\text{/}435\text{\,}\mathrm{H}\mathrm{z}$, and
$1083\text{\,}\mathrm{H}\mathrm{z}$), or suspension violin-mode resonances
($\sim 300\text{\,}\mathrm{H}\mathrm{z}$ and harmonics for beam splitter,
$\sim 500\text{\,}\mathrm{H}\mathrm{z}$ and harmonics for test masses). These
narrow spectral features do not appreciably affect compact binary coalescence
detection, although they can affect searches for continuous gravitational-wave
sources Covas  _et al._ (2018), and at sufficiently high amplitude can
introduce nonlinear effects.

Large transients in the gravitational-wave channel are still observed
regularly, affecting the sensitivity as seen in Figure 3. Such transients—also
called “glitches” Powell  _et al._ (2017); Zevin  _et al._ (2017); Cabero  _et
al._ (2019)—reduce the amount of clean data, decrease the significance of real
gravitational wave signals, and, if they occur during a real signal, can
complicate parameter estimation Pankow  _et al._ (2018). While there has been
progress in reducing whistle glitches (Section IV.7.4), the causes of other
types of glitches are poorly understood. Preliminary evidence suggests that
_tomte_ -type glitches may be caused by charge transfer on the high-voltage
ESD actuators (Section V.6).

##  IV Instrument improvements

This section will discuss the instrument upgrades that facilitated the
increase in sensitivity and duty cycle for O3, focusing on hardware upgrades
to the interferometers.

###  IV.1 Laser power increase

Increasing the laser power reduces instrument noise at high frequency where
the sensitivity is shot-noise-limited but comes with operational challenges.
Hardware upgrades to the pre-stabilized laser and core optics allowed for an
increase in average circulating power in the arm cavities to
$201\text{\,}\mathrm{k}\mathrm{W}$ at LHO and
$239\text{\,}\mathrm{k}\mathrm{W}$ at LLO for O3 (see Table 2).

The major technical challenges of operating a high-power interferometer are
caused by radiation pressure inducing instabilities and absorption of the test
masses. These instabilities are discussed in Section IV.1.2 and the angular
controls system is discussed in Section IV.6. Thermal distortion of the test
masses due to optical absorption is discussed in Section V.3.

####  IV.1.1 Laser hardware changes

The original aLIGO pre-stabilized laser (PSL) design Kwee  _et al._ (2012)
took the output of a Nd:YAG non-planar ring oscillator (NPRO) operating at
$1064\text{\,}\mathrm{n}\mathrm{m}$ and successively amplified the output to
above $150\text{\,}\mathrm{W}$. The original amplifier chain consisted of a
$35\text{\,}\mathrm{W}$ solid-state amplifier (“front end”) followed by a
high-power injection-locked ring oscillator. In addition to operational
challenges, the latter high-power oscillator and its high coolant flow
produced fluctuations of the beam size and pointing angle Hardwick (2019).
This beam jitter noise is further discussed in Section III.10.

For O3 the high-power oscillator was replaced at both observatories with a
smaller single-pass solid-state amplifier (neoLASE neoVAN-4S) that requires
less coolant flow. The new amplifier produces roughly $70\text{\,}\mathrm{W}$
of stable output power during the run. After input optics and mode-cleaning
cavities, this provides up to $50\text{\,}\mathrm{W}$ at the power-recycling
mirror.

The reduced coolant flow and damping and tuning of problematic optic mounts
has reduced the amplitude of angular beam jitter. The higher input power, in
addition to the squeezer (Section IV.2), lead to improved sensitivity above
$100\text{\,}\mathrm{H}\mathrm{z}$.

####  IV.1.2 Parametric instabilities

High circulating power in the arm cavities can excite the internal acoustic
modes of the test masses via radiation pressure. When a test mass acoustic
mode overlaps with a higher-order optical mode, light can be scattered into
this higher-order mode. This will further amplify the mechanical motion,
increasing the scatter rate, eventually becoming a runaway process. This is
known as a parametric instability, and has been previously observed at both
sites Evans  _et al._ (2010, 2015).

Before O3, acoustic mode dampers were installed on all test masses to mitigate
parametric instabilities Biscans  _et al._ (2019). These small passive
piezoelectric devices are bonded directly to the barrels of the test masses,
reducing the Q-factor of test mass mechanical modes and lowering the
parametric gain below unity. In previous observing runs, parametric
instabilities required active damping using the test mass electrostatic drives
Blair  _et al._ (2017). With the addition of acoustic mode dampers the
circulating power in the arm cavities has been increased by a factor of two.
The acoustic mode dampers increase the thermal noise contribution to DARM by
less than 1%.

Parametric instabilities have been observed at
$10.2\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$ and
$10.4\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$ at LHO during O3 Biscans  _et
al._ (2019). These frequencies are lower than the main target range of the
acoustic mode dampers. The instabilities were suppressed by tuning the end
test mass ring heater (see Section V.3) to shift the arm cavity higher-order-
mode spacing away from the test mass acoustic mode. Modeling of the arm cavity
suggests that the overlap between the optical mode and acoustic mode is
exacerbated by beam mis-centering on the test mass. The beam is deliberately
off-center to avoid known absorption features on the corresponding input test
mass, as discussed in Section V.4.

####  IV.1.3 Radiation pressure torque

As the power circulating in the arm cavities increases, torques exerted on the
test masses due to radiation pressure also increase. These torques can produce
instability when their magnitude approaches the restoring torque of the
pendulum Sidles and Sigg (2006); Hirose  _et al._ (2010); Dooley  _et al._
(2013). While O3 power levels are still far from producing this instability
condition, the torque modifies the dynamics of the suspended mirrors
significantly and couples the angular motion of the cavity mirrors. This
requires angular control compensation filters to be modified as the optical
power in the arm cavities increases. This is discussed in Section IV.6.

###  IV.2 Squeezer

For O3 an in-vacuum squeezer was installed at each site to inject squeezed
vacuum into the interferometers and reduce shot noise. A full description of
the new squeezer can be found in Tse  _et al._ (2019). In contrast to previous
squeezers for gravitational-wave detection Aasi  _et al._ (2013); Abadie  _et
al._ (2011); Grote  _et al._ (2013), the squeezed vacuum source (an optical
parametric oscillator) is placed inside the vacuum envelope on a separate
suspended platform Álvaro Fernández-Galiana  _et al._ (2019). This reduces
squeezing ellipse phase noise and backscattered light noise Oelker  _et al._
(2016). The squeezer has been fully integrated into the automated lock
acquisition sequence.

While Section IV.1 discussed increasing the input power to the interferometer,
which increases interferometer sensitivity by enhancing the gravitational-wave
signal, injecting squeezed vacuum improves the signal-to-noise ratio by
decreasing the interferometer noise. In this sense
$\sim$$3\text{\,}\mathrm{d}\mathrm{B}$ of squeezing is equivalent to doubling
the intracavity power to $\sim$$450\text{\,}\mathrm{k}\mathrm{W}$. The
detector sensitivity is therefore closer to the Advanced LIGO design
sensitivity, which specified $750\text{\,}\mathrm{k}\mathrm{W}$ intracavity
power and did not include squeezing.

Above $50\text{\,}\mathrm{H}\mathrm{z}$ the interferometer sensitivity is
increased by $2.0{}\text{\,}\mathrm{d}\mathrm{B}$ and
$2.7{}\text{\,}\mathrm{d}\mathrm{B}$ at LHO and LLO, respectively. This
provides a 12% and 14% increase in binary neutron star inspiral range at each
respective site.

Below $50\text{\,}\mathrm{H}\mathrm{z}$, injecting frequency-independent
squeezed vacuum, as is done during O3, increases the quantum radiation
pressure noise. The low-frequency noise at LLO is small enough that this
increase in quantum radiation pressure noise is detrimental to sensitivity and
binary neutron star inspiral range. The current squeezing level at LLO cannot
be further increased without causing a reduction in range Tse  _et al._
(2019). The squeezing angle is therefore set to $7{}^{\circ}$ from the optimal
high-frequency configuration. This increases range by reducing low-frequency
radiation pressure noise at the expense of a
$0.5\text{\,}\mathrm{d}\mathrm{B}$ increase in shot noise at high frequencies.
This effect is more fully explored in Yu  _et al._ (2020).

Detuning of the signal-recycling cavity also produces frequency-dependent
squeezing. This effect was used to identify and correct a
2–$3\text{\,}\mathrm{n}\mathrm{m}$ detuning in the signal-recycling cavity
length locking point at LLO. Signal-recycling cavity detuning was then also
exploited to maximize binary neutron star inspiral range.

###  IV.3 Core optic replacement

Several of the core optics were replaced before O3 to improve detector
sensitivity, stability, and lock acquisition performance. The motivation and
performance benefit of each replacement is presented here.

At both sites the two end test masses were replaced. To improve the lock
acquisition sequence, the optical coatings on the O3 end test masses have
lower scatter loss and increased reflectivity for
$532\text{\,}\mathrm{n}\mathrm{m}$ laser light. This increased the green arm
cavity finesse from 15 to 70 at LHO and to 100 at LLO (more values in Appendix
A). This improves the reliability of the early stages of lock acquisition,
where control of each arm length is transitioned from green to infrared error
signals Staley (2015).

The $\sim$$10\text{\,}\mathrm{p}\mathrm{p}\mathrm{m}$ reduction in scatter
loss has resulted in improved power-recycling gain at both sites. However when
increasing the circulating power in the arm cavities, the power-recycling gain
has not increased as expected due to nonuniform absorption on the optics
increasing scatter losses in the arm cavities; see Section V.4.

The X-arm input test mass at LHO was replaced before O3 following the
identification of a point absorber in the coating. The presence of the point
absorber limited high-power operation and coupled jitter noise from the pre-
stabilized laser to DARM. The new input test mass shows no significant
absorbers. Similar defects have been found on several other test masses
currently installed; these are further discussed in Section V.4.

The signal-recycling mirror (SRM) at both sites was replaced. The previous SRM
was an aluminum and fused-silica composite with a 2” diameter optic that
allowed for easy mirror replacement. The composite SRM introduced thermal
noise due to internal modes of the composite system with high mechanical loss.
The replacement SRM is monolithic fused silica,
$150\text{\,}\mathrm{m}\mathrm{m}$ diameter, with no measurable thermal noise
contribution to DARM. To maximize the binary neutron star inspiral range, the
SRM transmission should be reduced with increasing circulating optical power.
For O3, the SRM transmission was reduced from 37% to 32%.

The reaction masses, which are suspended in a separate pendulum chain behind
the end test masses, provide high-frequency actuation via the electrostatic
drive Aston  _et al._ (2012). The proximity of the reaction mass to the end
test masses can increase the damping noise due to residual gas bouncing
between the test mass and reaction mass. This noise is known as squeezed film
damping Dolesi  _et al._ (2011). Before O3 the reaction masses were replaced
with annular reaction masses with cored out centers that retained the original
electrode pattern. These annular end reaction masses are expected to have
reduced the squeezed film damping noise by a factor of 2.5 below
$100\text{\,}\mathrm{H}\mathrm{z}$ Evans  _et al._ (2011).

###  IV.4 Test mass discharge

Charge that builds up on the test masses or changes in charge distribution
around the test masses can result in electric field noise coupling to test
mass motion, as discussed in Section V.6. Several changes have been made to
reduce charge build-up, discharge or depolarize the test masses, and monitor
sources of electric field noise.

A likely source of test mass charge in O1 and O2 was ionization from UV light
emanating from the ion pumps that are part of the vacuum system. These pumps
were relocated and baffled to prevent incident UV radiation on the test mass.
The electrostatic drive applies a large bias voltage
$\sim$100\text{\,}\mathrm{V}$$ between electrodes. Even with the
aforementioned changes to ion pumps the effective charge on the test masses
(witnessed by the electrostatic drive actuation force) changes slowly over
time due to charge migration resulting in polarization Hewitson  _et al._
(2007); Prokhorov and Mitrofanov (2010). This change in effective charge has
predictable rate and direction. Therefore the polarity of the electrostatic
drive bias voltage is reversed periodically, reversing the direction of charge
build up, thereby limiting the effective charge on the test mass.

The removal of polymer First Contact, which is used to clean test mass
surfaces before a vacuum chamber is closed, results in triboelectric charging
on the test mass surface. A discharge procedure has been developed where
ionized dry nitrogen gas is used to discharge the optic after the removal of
First Contact Campsie  _et al._ (2011). Additionally, a test mass discharge
system has been installed and demonstrated to effectively discharge with
optics without opening the vacuum tanks. This system again uses ionized
nitrogen to flood the chamber up to
$30\text{\,}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{r}$. This results in up to
an order of magnitude reduction in charge as interrogated by the electrostatic
actuation force on the test mass.

Finally, electric field meters were installed in the chamber of the Y end test
mass of LLO and the X end test mass of LHO. This electric field meter is
designed to witness any time-varying electric field in the chamber that could
induce a large enough force on a charged test mass to impact interferometer
sensitivity.

###  IV.5 Stray light control

Light that scatters out of the main interferometer beam can pick up time-
varying phase relative to the main beam by reflecting or scattering again off
moving surfaces. If this scattered light is re-coupled to the main beam, it
can produce noise in DARM, as discussed in Section III.11.

Observations of stray light in video monitors at LLO, and observations of
anthropogenic ground motion coupling to DARM at LHO, led to further stray
light investigations. During O2 improved dumping of “ghost” beams and damping
of resonances of a stray-light baffle reduced scatter noise in DARM. Based on
this experience, multiple baffles were added or modified between O2 and O3.

Scattering mitigation activities continued during the break in O3, including
additional baffle installation. During the first half of O3, fringe wrapping
noise was often observed at LLO when ground motion below
$10\text{\,}\mathrm{H}\mathrm{z}$ was large. Drops in binary neutron star
inspiral range visible in Figure 3 were a daily feature at LLO. Baffles
installed around a transmitted light monitor at an end station at LLO reduced
scattering noise from anthropogenic vibrations during the day.

An in-vacuum window traversed by the output beam was removed at LHO to
mitigate scattered light coupling. During O3, accelerometer tests at LHO
localized a scattering site causing a $48\text{\,}\mathrm{H}\mathrm{z}$ peak
in DARM to a particular vacuum chamber. A beam dump installed outside a
viewport to the chamber dumped a stray beam and significantly reduced this
noise contribution. Late in the O3 run, transients from scattered light were
greatly reduced at both sites by actuating on the reaction chain to reduce
micron-scale relative motion between test masses and reaction masses. The
likely scattering path involved multiple reflections between the gold traces
of the electrostatic drive on the reaction mass and the high-reflectivity
coating on the test mass Soni  _et al._ (2020).

###  IV.6 Alignment sensing and control

In this section upgrades to the alignment sensing and control (ASC) scheme are
reviewed. Recent upgrades accommodate increased optical power, reduce noise
injection to DARM, and produce more robust angular control.

These modifications to the alignment sensing and control scheme have produced
the most robust angular noise control to date. However, as discussed in
Section III.9, the overall noise contribution from angular controls is still
the most significant source of noise in DARM below
$20\text{\,}\mathrm{H}\mathrm{z}$. Ongoing research aims to reduce angular
control noise further Mow-Lowry and Martynov (2019).

####  IV.6.1 Radiation pressure compensation

The radiation pressure dynamically links the angular motion of the test masses
of each arm together via the mis-centering of the beam spots. The angular
modes of the cavity thereby created are called “hard” and “soft” modes
Barsotti  _et al._ (2010), since they respectively increase or decrease the
stability of the resonant cavity. The changes in system dynamics due to
radiation pressure on the test masses require control filters to be modified
as the power is increased.

The hard mode ASC control loop bandwidths must be sufficiently large to
suppress arm cavity motion to maintain stable operation. The unity gain of
these loops is currently set at $3\text{\,}\mathrm{H}\mathrm{z}$, above the
resonance of the Sigg-Sidles hard modes Sidles and Sigg (2006) at the
circulating power. Each site has adopted a different approach for the control
of these degrees of freedom.

At LLO, hard mode filters optimized for plant dynamics up to
$25\text{\,}\mathrm{W}$ incident on the power-recycling mirror are used for
the initial part of the lock acquisition sequence. Just after reaching full
input power, the control filters are switched to control filters optimized for
$40\text{\,}\mathrm{W}$ operation. Cutoff filters, carefully tuned to minimize
noise when used in conjunction with the high-power angular control
compensation filters, are then engaged in the final stages of the lock
acquisition sequence.

At LHO, an adaptive hard mode filter design has been implemented that allows
continuous variation of the control filters for a range of input powers Yu
(2019). The filter is designed to correct for the radiation pressure torque
effects, returning the plant dynamics back to that of a lower circulating
power, chosen to correspond to $10\text{\,}\mathrm{W}$ input power to account
for uncertainties in the compensation. There is then only one control filter
design for all power levels.

The soft mode controls mainly damp an instability around
$0.5\text{\,}\mathrm{H}\mathrm{z}$ using the quadrant photodetectors in
transmission of the arms as the error signal. The
$0.5\text{\,}\mathrm{H}\mathrm{z}$ pitch oscillation can be explained by a
spurious dependence of the circulating power on the beam spot position that in
turns creates an additional torque through the length-to-pitch cross-coupling
of the suspensions. Controlling this instability has been a challenge towards
operation at high power.

####  IV.6.2 Alignment dither system

Changes in spot positions on core optics between locks have been shown to
significantly alter the angular optical-mechanical plant. To make the locking
process more consistent, both sites have adopted a dither alignment system.

Dithering is an intentional angular injection into an optic at a specific
frequency. Angular modulation is injected by actuation on the core optic
penultimate masses. For LLO the dithering frequencies are chosen outside of
the detection band, below 10 Hz, whereas they are between
$15\text{\,}\mathrm{H}\mathrm{z}20\text{\,}\mathrm{H}\mathrm{z}$ for LHO. The
relevant length motion signal is demodulated at the same frequency to produce
a measure of the angle-to-length coupling. This signal is minimized by slowly
adjusting the optic angle so that the rotation point coincides with the beam
position.

The preferred beam position on each test mass is first determined in terms of
minimum power losses in the cavities. Each optics rotation point is digitally
set to match these positions. The error signals are then used to control the
spot positions on the input and end test masses with bandwidths on the order
of $0.01\text{\,}\mathrm{H}\mathrm{z}$. This alignment dither system provides
more repeatable spot positioning compared to quadrant photodetector error
signals. Being a reliable way to scan the surface of the mirrors for minimum
losses, it also allowed the precise beam locations to be chosen to avoid point
absorbers (Section V.4).

####  IV.6.3 Signal-recycling cavity alignment

Before O3, the angular control of the signal-recycling cavity proved
challenging due to the lack of a good sensor. Previously, the alignment error
signal of the signal-recycling cavity was formed from the beat note between
the $9\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ and the
$45\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ sidebands. This
$36\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ beat note was detected by
wavefront sensors at the antisymmetric port, using the
$9\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ TEM00 as the reference beam and
$45\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ TEM01 and TEM10 modes as the
misalignment signals.

This signal-recycling alignment error signal was problematic. The signal is
weak due to inefficient transmission of the
$9\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ sideband to the dark port. Because
the beat note is formed from two sidebands, the
$36\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ error signal is not zero when the
cavity is well aligned. This results in some degeneracy with the beam
centering on the wavefront sensor. Additionally, higher-order modes generated
by thermal distortions in the test masses can produce competing beat note
signals that dramatically change the
$36\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ error signal response to signal-
recycling cavity misalignment.

To generate a cleaner signal-recycling alignment error signal a new RF phase
modulation sideband was injected into the interferometer at
$118\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$, the 13th harmonic of the
$9\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ signal. The new alignment error
signal is derived from the beat note at
$72\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ between the
$118\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ TEM00 transverse mode and the
$45\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ TEM01/01 transverse modes. The
$118\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ sideband is more efficiently
transmitted to the dark port than the
$9\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ sideband due to the Schnupp
asymmetry. While the $118\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ sideband
also suffers thermal distortions and
$72\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ is also formed from two sidebands,
these effects are manageable with a stronger signal. The
$72\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ beat note provides a robust signal
for signal-recycling alignment control Yu (2019).

###  IV.7 Lock acquisition and stability

This section highlights instrument improvements that affect detector duty
cycle. Sections IV.7.1, IV.7.2, and IV.7.5 provide examples of stability
improvements. Section IV.7.3 is an example that makes the lock acquisition
sequence more robust and hence faster. This compensates additional features,
such as squeezing, that have made lock acquisition slower. The result is a
minimal change in average lock acquisition time. Section IV.7.4 is an example
of the mitigation of large transients that can make data unusable. The
resulting improvement in the detector duty cycle was discussed in Section
II.3.

####  IV.7.1 Seismic controls

Core and auxiliary optic suspensions are mounted on isolation platforms that
serve to decouple the optic motion from the ground. Different types of
platform are used for the core and auxiliary optics, but the general concept
is identical for all of them. Each platform provides a combination of passive
and active isolation to bring the platform motion down to $\sim$ at
$10\text{\,}\mathrm{H}\mathrm{z}$ Matichard  _et al._ (2015). Between O1 and
O3, hardware and software changes have improved the seismic configurations at
both sites, with improved lock stability in the presence of increased ground
motion.

Beam rotation sensors, which measure ground tilt, were installed at both end
stations (LHO) and the end and corner stations (LLO); these facilitate tilt-
corrected ground motion measurements Venkateswara  _et al._ (2017); Ross  _et
al._ (2020). This is relevant below $0.1\text{\,}\mathrm{H}\mathrm{z}$ where
seismometer signal is contaminated by ground tilt, which is exacerbated under
windy conditions. In the corner station at LHO, tilt-free ground motion is
measured by a seismometer at the center of the building, where ground tilt is
reduced compared to the edges of the building. Effective cancellation of
ground motion between 0.1 and $1\text{\,}\mathrm{H}\mathrm{z}$ is performed by
feedforward from seismometers Matichard  _et al._ (2015). This can inject
excess noise at out-of-band frequencies. With tilt removed, a more aggressive
control configuration is possible, allowing the interferometers to have better
resilience to windy or high microseism conditions. Tilt cancellation is the
main upgrade to the seismic system between O1 and O2 for LHO, and O2 and O3
for LLO.

Elevated ground motion in the 0.03 to $0.1\text{\,}\mathrm{H}\mathrm{z}$ band
during an earthquake can overwhelm seismic isolation platforms and unlock the
interferometer. During an earthquake the end stations and corner station
predominantly experience common ground motion. For O3 an experimental sensor
configuration was implemented upon an early-warning earthquake trigger,
calculating the common motion by averaging seismometer signals from the corner
and end stations, and then subtracting this from local ground sensors to
produce feedforward signals Lantz (2018); Coughlin  _et al._ (2017); Biscans
_et al._ (2018); Schwartz  _et al._ (2020). This system has improved the
detector duty cycle by allowing the interferometers to remain locked through
moderate earthquakes.

####  IV.7.2 Suspension chain damping

The test masses are suspended by a main quadruple suspension chain. Each of
these main chains is accompanied by a quadruple stage reaction chain, which
sits behind the test masses. The suspension chains are designed to have low
mechanical loss to minimize thermal noise, hence the resonant modes of the
suspension chain have high quality factors. Sensing and actuation for local
damping of these modes occurs at the top mass of each chain Strain and Shapiro
(2012). This limits the injection of local sensing noise into the
gravitational-wave readout through three stages of mechanical filtering at the
cost of reduced actuation authority at the test mass.

Interferometric control signals, which are more sensitive than local damping
signals, are applied as actuation between the main and reaction chains. These
control signals can introduce energy into the modes of both suspension chains.
While the fundamental vertical (bounce) and roll modes of the test masses were
actively damped in O1 and O2, these are now passively damped with tuned mass
dampers Robertson  _et al._ (2017). Many of the fundamental, second, and third
harmonics of the transverse (“violin”) modes of the fused silica fibers
supporting the test masses were actively damped at LLO and LHO during O3. In
the future these modes may be passively damped as significant time is lost
when they are excited either through control system failure or excitation from
earthquakes. During O3, the amplitude of a pitch mode of the input test mass
reaction chain became unstable at LLO, producing excess motion at
$3.3\text{\,}\mathrm{H}\mathrm{z}$. To address this issue, local signals from
the penultimate stage of the suspensions are filtered and applied to the
reaction chain’s top mass, enhancing energy extraction.

####  IV.7.3 CARM offset reduction

Reducing the common arm length (CARM) offset to bring the arms onto resonance
with the carrier field has historically been a fragile point of the LLO lock
acquisition sequence. This was due to a handoff between a CARM error signal
derived from the carrier field transmitted from the arm cavities to an error
signal derived from the $9\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ field
reflected from the power-recycling cavity. This handoff was historically
performed with the common arm lengths detuned
$10\text{\,}\mathrm{p}\mathrm{m}$ from resonance. Near this point, the gain of
the $9\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ signal passes through zero
Martynov (2015). Non-ideal conditions during this handoff would result in the
wrong sign control gain, departure from the fringe, and lock loss. In O3, the
transmission lock is left engaged while engaging the
$9\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ lock, then a reduction in CARM
offset is applied just before ramping down the transmission loop gain. This
nudge pushes the $9\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ signal into the
regime where the $9\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ gain is
increasing, ensuring it reaches the correct set point and significantly
increasing the CARM offset reduction stability.

####  IV.7.4 New VCO at Livingston

The LIGO detector characterization group identified a type of loud transient
signal (“glitch”) known as a whistle glitch Walker (2017). The glitch
morphology is a narrow spectral line rapidly moving in frequency that often
appears to “reflect” off zero. Whistle glitches are thought to be the result
of radio frequency lines crossing each other, beating to produce a signal in
the gravitational-wave measurement band. This type of glitch is particularly
problematic as the “whistle” can produce signals similar to those produced by
coalescing astrophysical binaries. Investigations at LLO identified a voltage
controlled oscillator (VCO) that is at least in part responsible for producing
whistle glitches. This VCO produces an offset frequency between the laser
light going to a reference cavity that is used for laser frequency noise
suppression and the light going to the interferometer. The VCO was replaced at
LLO prior to the run and ongoing investigations during the run resulted in
several changes. The change in VCO resulted in a dramatic reduction in the
occurrence of whistle glitches. However some interim solutions suffered from
increased laser frequency noise. Frequency noise represented in Figure 2b is a
later iteration with less impact on high-frequency sensitivity. Even in
earlier iterations frequency noise had minimal impact on binary neutron star
inspiral range.

At LHO whistle glitches appear when this VCO crosses certain frequencies. No
spectral features could be found at these frequency crossing points so the
source of the second frequency line is unknown. The VCO frequency is therefore
chosen to avoid these crossing points. However during periods of high ground
motion, frequency excursions can become large resulting in whistle glitches.
Whistle glitches contaminate roughly 1% of the data from LHO. This was similar
to LLO during the first two observing runs.

####  IV.7.5 Increased actuator range

A number of changes have been made to the test mass actuators that improve
detector duty cycle while limiting injected noise.

Before O3 all suspension actuators used 18-bit DACs (General Standards 18AO8)
that suffer from a _zero-crossing_ issue. When the digital signal crosses zero
counts the output voltage may contain an impulse that can get worse in time
without periodic re-calibration of the DAC. This impulse injects broadband
noise. Additionally, the nominal noise has been found to depend on drive
amplitude, DC offset, and the DAC channel used. The actuators on the lower
stages have been partially replaced with 20-bit DACs (General Standards
20AO8C500K), which have slightly lower noise and do not have this zero-
crossing issue.

To better understand DAC noise, _in situ_ monitors were partially installed to
measure the noise while removing the large optic control signal at low
frequencies. This allows for sensitive real-time monitoring of the control
signal noise in the gravitational-wave band without saturation of the monitor
due to low-frequency control signals.

The test-mass actuator analog electronic filter was also modified to provide
greater actuation range above $15\text{\,}\mathrm{H}\mathrm{z}$ without
injecting significant noise. Preliminary results suggest this modification has
improved detector resilience against fast large transients that can unlock the
interferometer.

These improvements have helped to move the actuator noise contribution safely
below the current sensitivity and have produced more robust interferometer
control.

##  V Interferometer characterization

The noise budget presented in Section III is one tool used to present and
understand the interferometer noise floor. In parallel, commissioning
activities seek to characterize and optimize the detector, and search for new
noise sources. This section details some of the commissioning investigations
which occurred before and during O3. Section V.1 discusses a cross-correlation
measurement which reveals noise below shot noise, Section V.2 explains a new
method of measuring the circulating power in the interferometer arms, Sections
V.3 and V.4 discuss the thermal compensation system and nonuniform coating
absorption. Section V.5 discusses an investigation into radio frequency
oscillator noise, and Section V.6 discusses test mass charging and stray
electric fields.

###  V.1 Correlated noise

In DC-readout operation, the two DC photodetectors (DCPDs) at the
antisymmetric port are summed together to measure the DARM degree of freedom.
By cross correlating the DCPD signals—and compensating for the additional
correlation induced by the DARM control system—the sensing noise is averaged
out and the correlated noise beneath can be revealed Izumi (2017). Note that
both shot noise and photodetector dark noise are averaged out. This
measurement is taken without squeezed light injection because this induces
correlated quantum shot noise between the DCPDs McCuller (2018).

Figure 9 shows the results of this measurement. Sufficient averages were taken
to reach below statistical noise across the entire range.

The mirror coating thermal noise is the limiting correlated noise source
around $200\text{\,}\mathrm{H}\mathrm{z}$. This represents a fundamental limit
to the sensitivity improvement we can expect from lowering the quantum shot
noise via increased squeezing and increased laser power.

This measurement provides some confirmation of the increased gas noise
contribution at LLO. Without the gas noise contribution, the expected
correlated noise between $400\text{\,}\mathrm{H}\mathrm{z}$ and
$1\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$ deviates significantly from the
measurement. The excess gas noise at LLO is the result of a leak around the
mid point of the X arm vacuum enclosure. The leak has been fixed since the
time of this measurement, as explained in Section III.12.

At frequencies above $3\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$, laser
frequency and intensity noise dominate the correlated noise budget. The poor
match between predicted and measured correlated noise above
$2\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$ at LLO is thought to be due to the
coupling function of laser (frequency and intensity) noise to DARM being non-
stationary.

The origin of the correlated noise at
$1\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}2\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$
is unknown, but is a factor of five below DARM sensitivity. The origin of the
correlated noise below $100\text{\,}\mathrm{H}\mathrm{z}$ is also unknown, and
is likely the same noise that limits DARM sensitivity at
$40\text{\,}\mathrm{H}\mathrm{z}$ in Figure 2.

(a) LHO

(b) LLO

Figure 9:  Correlated displacement noise at the antisymmetric port, measured
as described in Section V.1. The total expected correlated noise is shown in
black. The dominant expected contribution to the correlated noise curve is
thermal noise from
$60\text{\,}\mathrm{H}\mathrm{z}900\text{\,}\mathrm{H}\mathrm{z}$. The upper
two traces show the DARM noise around the time of the correlation measurement
with and without squeezed light injection. The differences in beam jitter
coupling is covered in Section III.10. To average away uncorrelated sensing
noise between the DCPDs, the LHO measured correlated noise trace used
$20\,000$ averages over $10\,000$ seconds of data, while LLO used $21\,600$
averages over $10\,800$ seconds of data.

###  V.2 Measuring the arm power

The circulating laser power in the arm cavities governs the amplitude of the
interferometer response to gravitational-wave signals. The arm power is
difficult to estimate precisely due to large uncertainty in the power on the
beamsplitter and optical gain of the arm cavities. Uncertainties are dominated
by photodetector calibration and interferometer optical loss uncertainty.

The arm powers in a power-recycled interferometer with a 50:50 beamsplitter
should follow

$P_{\mathrm{arm}}=\frac{1}{2}P_{\mathrm{in}}G_{\mathrm{PR}}G_{\mathrm{arm}},$
(4)

where $P_{\mathrm{arm}}$ is the power in an arm, $P_{\mathrm{in}}$ is the
input power, $G_{\mathrm{PR}}$ is the power-recycling gain, and
$G_{\mathrm{arm}}$ is the arm power gain.

The input power $P_{\mathrm{in}}$ is the power incident on the power-recycling
mirror, and is estimated from a pick-off just before entering the
interferometer. The power on the beamsplitter $P_{\mathrm{BS}}$ is estimated
directly from a pick-off of the power-recycling cavity. The power-recycling
gain is estimated from the ratio of the power incident on the beamsplitter
over the input power: $G_{\mathrm{PR}}=P_{\mathrm{BS}}/P_{\mathrm{in}}$.
Finally, the arm power gain $G_{\mathrm{arm}}$ is estimated from the input and
end mirror transmissions, as well as the round-trip loss.

Photodetector power uncertainty originates from uncertainty in calibration,
losses along beam path combined with beam size mismatch and misalignment. We
have assumed a total uncertainty of 5% in power estimated from pick-off
photodetectors, $P_{\mathrm{in}}$ and $P_{\mathrm{BS}}$. The arm gain
$G_{\mathrm{arm}}$ at Livingston is assumed to be $265$ with uncertainty of
5%. The Hanford X-arm gain is $262$, while the Y-arm gain is $276$; the 5%
gain difference is due to the slightly different transmissions of the input
test masses at Hanford (see Appendix 3). Results are shown in Table 2.

A technique to measure the arm powers using radiation pressure was developed
prior to O3 Cahillane (2019); Izumi  _et al._ (2015). The length of the
signal-recycling cavity is modulated, creating audio sidebands on the carrier
laser in the signal-recycling cavity. The audio sidebands enter the arm
cavities producing a light power modulation that has opposite sign in each arm
cavity, causing a signal to appear in DARM.

The power estimate is derived from the ratio of measurements of the relative
intensity noise in transmission of the arms and the DARM signal. Many
complexities, such as the amplitude of the signal-recycling sideband,
photodetector calibration and optical losses between interferometer and
photodetector, appear in the numerator and denominator and divide out in this
measurement. For frequencies below $100\text{\,}\mathrm{H}\mathrm{z}$
radiation pressure moving the test masses dominates the DARM signal, and the
transfer function between arm transmitted power relative intensity and DARM
has a simple expression:

$\frac{L_{\mathrm{DARM}}}{\mathrm{RIN}_{\mathrm{arm}}}(f)=\frac{2P_{\mathrm{arm}}}{mc\pi^{2}f^{2}}=\frac{\alpha}{f^{2}},$
(5)

where $L_{\mathrm{DARM}}=L_{x}-L_{y}$ is the differential arm displacement,
$\mathrm{RIN}_{\mathrm{arm}}$ is the relative intensity of the arm
transmission, $m$ is the mass of the final stage of the quadruple pendulum,
and $P_{\mathrm{arm}}$ is the power in the arm.

By fitting the $\alpha/f^{2}$ slope of the relative intensity of the arm power
transmission to DARM transfer function, the power in each arm can be estimated
according to

$P_{\textrm{arm}}=\frac{1}{2}\alpha mc\pi^{2}.$ (6)

Each arm power estimate relies on the relative intensity response of quadrant
photodetectors on transmitted beams from each arm. Each quadrant’s relative
intensity response can be distorted by poor alignment, as small changes in
alignment can result in one or more quadrants becoming saturated with light.
The spot positions on the arm cavity optics and transmission monitor table
drift can affect the alignment onto the quadrant photodetectors. These effects
can bias the arm power estimate, and must be monitored to ensure the accuracy
quoted in Table 2.

Table 2 reports the measured arm powers during O3. Measurements derived from
signal-recycling cavity length modulation are consistent and more precise
compared with measurements derived from test masses’ reflectivity (Table A)
and beam power measurements.

Power | Symbol | LHO | LLO | Units
---|---|---|---|---
Input | $P_{\mathrm{in}}$ | 34 $\pm$ 2 | 38 $\pm$ 2 | W
Power-Recycling Gain | $G_{\mathrm{PR}}$ | 44 $\pm$ 3 | 47 $\pm$ 3 | W/W
X-arm via Eq. 4 | $P_{X}$ | 190 $\pm$ 14 | 240 $\pm$ 18 | kW
X-arm via Eq. 6 | $P_{X}$ | 194 $\pm$ 2 | 232 $\pm$ 15 | kW
Y-arm via Eq. 4 | $P_{Y}$ | 200 $\pm$ 15 | 240 $\pm$ 18 | kW
Y-arm via Eq. 6 | $P_{Y}$ | 207 $\pm$ 2 | 245 $\pm$ 5 | kW
Table 2:  Highest measured laser power levels during O3. Input power is
estimated via a pick-off from the light incident on the power-recycling
mirror. Power-recycling gain is estimated from the pick-off of the power-
recycling cavity, using a ratio of power on the beamsplitter and input power.
Arm powers are estimated in two ways. The first method is via input power and
gain estimates, Eq. 4. Arm power uncertainties for Eq. 4 are propagated from
uncertainty in the input power, power-recycling gain, and loss in the arms.
The second method is via radiation-pressure relative intensity noise to DARM
transfer function, Eq. 6. Arm power uncertainties for Eq. 6 are derived from
the coherence of the measured transfer function. Typical arm power levels at
LLO were about 5% lower over the course of the run.

###  V.3 Thermal compensation

The thermal compensation system (TCS) is designed to measure and actuate on
the thermal lenses and radii of curvature of the core optics Brooks  _et al._
(2016). The operational target for the TCS is to correct optical aberration
induced by absorption in core optics and to correct any static lens
discrepancies.

The core TCS actuators consist of ring heaters situated around the barrel of
each test mass and CO2 lasers which heat the compensation plate behind the
input test masses (ITMs). The ring heaters create a negative thermal lens in
the test masses and reduce the radius of curvature on the high reflectivity
surface, while the CO2 lasers can create either a positive or negative lens in
the compensation plate. Other TCS actuators that have been tested include a
disk heater behind “SR3,” a reflective optic in the signal-recycling cavity,
to decrease its surface curvature, and a CO2 laser projected onto the signal-
recycling mirror (SRM). The accumulated substrate thermal lens of each test
mass is monitored using Hartmann wavefront sensors Brooks  _et al._ (2007).
The two sites use different TCS settings and TCS settings have changed during
O3.

At LLO, only ITM ring heater actuators are used. Applying a heat load to the
ITM actuators in common is expected to affect optical build up in the coupled
power-recycling cavity and also mode matching to the output mode cleaner.
Applying heat load differentially to each ITM actuator is expected to affect
the contrast defect, resulting in changes in frequency and intensity noise
coupling to DARM Brooks  _et al._ (2016) (Sections III.5 and III.6). Even
after minimizing noise coupling with the differential degree of freedom, it
was found that the common degree of freedom could further decrease laser noise
coupling.

Suboptimal laser noise coupling affected LLO binary neutron star inspiral
range more than suboptimal power in the power-recycling cavity. Therefore the
ring heaters are tuned to minimize laser noise coupling. Optimal mode matching
of the interferometer beam to the output mode cleaner was inferred to occur at
approximately the same ring heater setting as the minimum in laser noise
coupling. This inference was made based on measurements of the interferometer
response to a mechanical excitation of a test mass as a function of ring
heater power at LLO. It was also found that the ring heater settings that
minimized laser frequency noise coupling were not exactly the same as those
required to minimize laser intensity noise coupling. Therefore after the
change in voltage controlled oscillator (see Section IV.7.4), the dominant
coupling switched from frequency to intensity noise. The ITM ring heaters were
tuned differentially to minimize intensity noise coupling.

No improvement in binary neutron star inspiral range, mode matching, or noise
coupling could be achieved with the SR3 heater at LLO. By applying positive
and negative SRM thermal lens with the CO2 laser, a limit was set on the
amount an SRM lens could improve mode matching to the output mode cleaner of
$<1\%$.

At LHO, increased absorption in the Y-arm ITM (ITMY) causes a power-dependent
mismatch between the two arms. To maintain stability while increasing the
input power, the TCS is used to preheat the test masses while acquiring lock.
In this scheme, when the interferometer is acquiring lock with low input
power, the compensation plate CO2 lasers create a thermal lens that emulates
the thermal lens due to absorption in the ITM coatings at operating power.
When power builds up in the arm cavities (Table 2) the CO2 laser power is
reduced such that the thermal transient in the ITMs roughly cancels the
thermal transient in the compensation plates. At full input power the ITM CO2
and ring heater settings are tuned to minimize laser frequency noise coupling,
the dominant laser noise coupling at LHO. This ultimately resulted in an
increase in ITMX’s CO2 laser power Vo (2019).

The effect of the SR3 heater was also studied at LHO. At LHO a
$4\text{\,}\mathrm{W}$ power setting was shown to improve many parameters
including binary neutron star inspiral range. As described in Section IV.1.2,
at LHO the end test mass ring heaters were used to change arm cavity
transverse mode spacing to avoid parametric instability.

Avoiding parametric instability is complicated by changes in mirror radii of
curvature resulting from absorbed optical power in the mirror coating. This
changes the tuning condition for parametric instability and in O2 resulted in
transient instabilities occurring in the first few hours of operation. A
scheme described in Hardwick  _et al._ (2020) was demonstrated whereby
transients applied to the ring heating null the transient in mirror radii of
curvature. This allowed the optical power to be increased to
$170\text{\,}\mathrm{k}\mathrm{W}$, demonstrating precise control of the
cavity geometry. While this scheme has not been used since the installation of
acoustic mode dampers discussed in Section IV.1.2, at higher optical power it
could be useful to reduce interferometer transients and quell remaining
instabilities.

The thermal compensation tuning and noise couplings discussed above are
complicated by the presence of point absorbers in the test mass coatings
discussed in Section V.4.

###  V.4 Nonuniform coating absorption

Increasing optical power on the interferometer power-recycling mirror from
$25\text{\,}\mathrm{W}$ to $\sim$$40\text{\,}\mathrm{W}$ did not result in a
proportional increase in optical power in the power-recycling cavity. The loss
of optical buildup cannot be recovered with adjustments to the thermal
compensation actuators described in Section V.3. When the input power is
increased the power-recycling gain degrades with a time constant of
$\sim$$100\text{\,}\mathrm{s}$, while the time constant of a uniform
absorption thermal lens is $\sim$$1000\text{\,}\mathrm{s}$. These features
indicate nonuniform absorption resulting in increased optical loss.

Moving the beam position on the test masses showed a position-dependent
optical loss. Figure 10 shows the measured relation between input power and
recycling power with two traces for two different beam positions. The
difference between the expected and measured power at the beamsplitter could
be reduced with adjustments to the beam spot position on the test masses,
moving the spot position away from an area of high absorption.

Figure 10:  Power incident on the beam splitter as a function of
interferometer input power at LLO. The dashed line is the expected power if
losses are independent of power, while other traces are the measured power at
the pick-off port. Point absorbers thermally distort the test masses and
increase optical loss through scattering, resulting in the lower trace. Moving
the beam spot on the end test masses to avoid these absorbers and maximize the
recycling gain can partially mitigate these losses, leading to the upper
measured trace.

The Hartmann wavefront sensors at both sites revealed nonuniform localized
absorption or point absorbers on several optics in O2 and O3. In O3 they are
present on LLO’s ETMX and ETMY and LHO’s ITMY and ETMX. They have been
unaffected by attempts to clean them from the optic surfaces. Figure 11 shows
a microscope image and Hartmann wavefront sensor image of a point absorber
which was present on LHO’s ITMX during O2; this optic was replaced for O3. The
Hartmann wavefront sensor image is taken _in situ_ , while the microscope
image is taken after removal from the interferometer.

Simulation and analysis presented in Brooks  _et al._ (2020) broadly confirm
the level of observed optical loss is that expected from point absorbers. The
mechanism for optical loss is thermo-elastic expansion distorting the test
mass surface resulting in light being scattered from the fundamental cavity
mode.

Figure 11:  Point absorbers imaged using dark field microscopy (top) and _in
situ_ with the Hartmann wavefront sensor (bottom). The top image shows the
point absorber on LHO’s ITMX for O1 and O2. The absorber is
$155\text{\,}\mathrm{\SIUnitSymbolMicro m}$ across the bright center. The
bottom image is a Hartmann wavefront sensor image of the same optic in the
interferometer. The main interferometer beam uniformly heats a region roughly
$5\text{\,}\mathrm{c}\mathrm{m}$ in radius and illuminates the defect, causing
a point distortion in the wavefront. There is an uncertainty of about $\pm
1\text{\,}\mathrm{c}\mathrm{m}$ in the location of the origin of the Hartmann
wavefront sensor coordinate system. The largest contour ring represents a
$20\text{\,}\mathrm{n}\mathrm{m}$ optical distortion and the contour spacing
is $20\text{\,}\mathrm{n}\mathrm{m}$.

Microscopic analyses of mirror coatings on spare test masses are ongoing.
Features identified on test masses that have been removed from the
interferometer have been compared to features identified on test masses that
have not yet been installed. These investigations suggest that the point
absorbers are likely due to contamination introduced during the coating
process and are therefore present before installation. They may be altered by
the intense laser power they experience in the arm cavity. Efforts are ongoing
to image potential absorbers using thermal cameras and Hartmann wavefront
sensors before test mass installation.

###  V.5 RF oscillator noise investigations

Radio-frequency (RF) phase modulation sidebands are imprinted on the input
beam to the interferometer to control the various longitudinal and angular
degrees of freedom. The electro-optic modulator which imprints the RF
sidebands also imprints oscillator phase and amplitude noise on the input
beam. The RF oscillator noise is not directly sensed or controlled beyond the
electro-optic modulator driver amplitude stabilization. Because the RF
sidebands are designed to not resonate in the full interferometer, the RF
oscillator noise is not filtered by the common arm cavity pole. Additionally,
the RF sidebands do not carry gravitational-wave signal but do exit the
antisymmetric port at higher overall power than the carrier in operation. The
output mode cleaner is placed at the antisymmetric port to lock onto the main
carrier light and reject the RF sidebands. The rejection is not perfect, and a
small amount of RF sideband light imprints its noise on the DARM signal. RF
oscillator noise coupling was investigated in the first observing run, see
Section III G of Martynov  _et al._ (2016).

At LHO, a 9th-order transverse optical mode was visible on the output mode
cleaner cavity transmission camera. Modeling of the output mode cleaner
suggested that this mode on the upper
$9\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ sideband could be close to co-
resonant with the carrier given the cavity geometry. The output mode cleaner
length is controlled via two piezoelectric transducers (PZTs) attached to the
two curved mirrors. The offset locking voltage of one of the PZTs was large,
possibly flexing its curved mirror and changing the cavity geometry to allow
this light to transmit through the cavity. A new PZT driver was installed for
the purpose of relieving the high offset voltage needed to lock the output
mode cleaner. Tests changing the PZT offset voltage between locks did not
yield conclusive results in the differential arm noise.

###  V.6 Optic charging and stray electric fields

Length actuation on the test mass is performed using electrostatic drivers
(ESDs) Aston  _et al._ (2012). Both _in situ_ and laboratory tests suggested
charge separation due to a water monolayer on the optic Awakuni and Calderwood
(1972); Ho  _et al._ (1967) was producing a change in actuator strength of a
few percent over weeks Prokhorov and Mitrofanov (2010); Buikema (2020).

A large earthquake in Montana in July 2017 decreased the sensitivity of LHO at
low frequencies, hypothesized to be due to charging of a test mass by rubbing
against an earthquake stop. Additionally, excess coupling between motion of
the protective cage surrounding the suspension and the test mass was observed;
subsequent discharging of the optic by ionized gas significantly reduced this
coupling and the noise. In spite of this, large actuator bias voltages
injected noise into DARM that suggested excess unexplained electric fields.

The steel vacuum chambers act as Faraday cages and largely shield the optics
from external electric fields, but in-vacuum electronics and signals entering
through uncovered viewports can still couple to DARM. As such, an electrometer
was installed at each interferometer next to an end test mass to search for
large-scale in-chamber electric fields. Measurements were consistent with the
noise floor of the instrument at at $100\text{\,}\mathrm{H}\mathrm{z}$.
Viewport injections of electric fields confirmed the electrometer as a good
witness, but the coupling to DARM was at least $100$ times below the current
DARM sensitivity. Large excitations of the suspension cage motion were not
seen in DARM. Together these suggest that net optic charge is and remains low.

Local charge separation/polarization can still affect how local electric
fields couple to optic motion. Measurements of the coupling of sources of
these fields to DARM was performed to estimate the noise contribution for
arbitrary actuator configurations Buikema (2020). It was discovered that
ground currents can produce voltage fluctuations of the ESD driver, producing
a potential difference between the ESD and the cage that is not filtered by
the driver electronics. This mechanism was likely the source of narrow
spectral features that had previously been removed by partially isolating the
ESD electronics Covas  _et al._ (2018); additional reconfiguration of these
electronics helped to eliminate other noise sources.

##  VI Future Work

Work continues on improving the sensitivity and duty cycle of the
observatories. O3 was paused for a one-month commissioning break during
October 2019 to install several upgrades including in-vacuum baffles for
mitigating scattered light noise (Section III.11). Wind fences were installed
at the Hanford end stations to reduce wind shear on the buildings and lab
floor motion in windy conditions; this is expected to improve the network duty
cycle. An extended upgrade and commissioning period will precede observing run
four (O4) Abbott  _et al._ (2018).

A goal for O4 is to improve the shot-noise-limited sensitivity, with increased
intracavity laser power. To this end, an additional free-space amplifier stage
(neoVAN-4S-HP) outputting up to $114\text{\,}\mathrm{W}$ will be installed
Thies  _et al._ (2019). The addition of the acoustic mode dampers make
operation at higher powers possible with minimal parametric instability
(Section IV.1.2) Hardwick  _et al._ (2020). The power-limiting effects of
point absorbers (Section V.4) will likely be mitigated by replacing the
affected test masses.

Various upgrades to improve the observed squeezing level are planned (Section
IV.2). These include new output Faraday isolators to reduce losses, higher
green power to increase the injected squeezing level, and deformable optics to
improve mode matching between the squeezer and interferometer.

Additional observatory upgrades are planned to prepare the site for A+, the
detector configuration that will be used after O4 Miller  _et al._ (2015);
Barsotti  _et al._ (2018). As the optical power and squeezing level increase,
quantum radiation pressure noise (Section III.1) will worsen low-frequency
sensitivity. To mitigate this effect, a $300\text{\,}\mathrm{m}$ filter cavity
for injection of frequency-dependent squeezing Evans  _et al._ (2013);
McCuller  _et al._ (2020) will be installed prior to O4.

Work continues to understand and mitigate known noise sources. Additional
stray light baffles installed where vibrational coupling has been observed
should mitigate the effect of scattered light (Section III.11). Improved
modeling of angular motion coupling to DARM and how this may be mitigated is
underway. The use of universal (as opposed to local) control on seismic
isolation platforms at the vertex, similar to the scheme used to ride out
earthquakes (Section IV.7.1), is expected to improve the nonlinear noise
coupling during times of large ground motion and also improve interferometer
duty cycle by limiting saturations. Machine learning techniques are being
developed that allow offline removal of nonlinear noise contributions Vajente
_et al._ (2020).

The challenge to discover and mitigate the sources of noise below
$100\text{\,}\mathrm{H}\mathrm{z}$ will also be critical for Advanced LIGO to
achieve design sensitivity in O4. This achievement’s potential reward is
another 40% increase in the astrophysical range of the detectors and
commensurate tripling of the expected number of detections. O3 was the most
successful search for astrophysical gravitational-wave sources in history; O4
promises even greater knowledge of the furthest reaches of the universe.

##  VII Acknowledgements

The authors gratefully acknowledge the support of the United States National
Science Foundation (NSF) for the construction and operation of the LIGO
Laboratory and Advanced LIGO as well as the Science and Technology Facilities
Council (STFC) of the United Kingdom, and the Max-Planck-Society (MPS) for
support of the construction of Advanced LIGO. Additional support for Advanced
LIGO was provided by the Australian Research Council. The authors acknowledge