Abstract

Precise measurements, such as those made with interferometric gravitational-wave detectors, require the measurement device to be properly controlled so that the sensitivity can be as high as possible. Mirrors in the interferometer are to be located at specific operation points to isolate laser noise and to accumulate the signal in resonant cavities. On the other hand, rigid control of an auxiliary degree of freedom may result in imposing sensing noise of the control on the target object as excess force noise. Evaluation of this so-called loop noise is important in order to design a decent control scheme of the measurement device. In this paper, we show the method to calculate the level of loop noise, which has been recently implemented in simulation tools that are broadly used for designing gravitational-wave detectors.

© 2010 Optical Society of America

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2009 (2)

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

The Virgo Collaboration, “Advanced Virgo baseline design,” VIR-027A-09 (2009), https://pub3.ego-gw.it/itf/tds/.

2008 (1)

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

2007 (2)

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

S. Sato, S. Kawamura, K. Kokeyama, F. Kawazoe, and K. Somiya, “Diagonalization of the length sensing matrix of a dual recycled laser interferometer gravitational wave antenna,” Phys. Rev. D 75, 082004 (2007).
[CrossRef]

2006 (3)

O. Miyakawa, “Calculation of loop noise for Advanced LIGO using Optickle engine,” internal report (2006), http://lhocds.ligo-wa.caltech.edu:8000/advligo/Loopnoise results.

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
[CrossRef]

K. Somiya, O. Miyakawa, P. Fritschel, and R. Adhikari, “Length sensing and control for AdLIGO,” Tech. Rep. LIGO-T060272-00-I (2006), https://dcc.ligo.org/

2005 (1)

2004 (1)

K. Somiya, “Investigation of radiation pressure effect in a frequency-detuned interferometer and development of the readout scheme for a gravitational-wave detector,” Ph.D. dissertation (University of Tokyo, 2004); Sec. 3.9.

2003 (1)

2001 (1)

M. Ando and TAMA Collaboration, “Stable operation of a 300 m laser interferometer with sufficient sensitivity to detect gravitational-wave events within our galaxy,” Phys. Rev. Lett. 86, 3950–3954 (2001).
[CrossRef] [PubMed]

1997 (1)

H. Lück and the GEO600 Team, “The GEO600 project,” Class. Quantum Grav. 14, 1471–1476 (1997).
[CrossRef]

1992 (1)

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

1990 (1)

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Abbott, B.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Abbott, R.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Abramovici, A.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Adhikari, R.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

K. Somiya, O. Miyakawa, P. Fritschel, and R. Adhikari, “Length sensing and control for AdLIGO,” Tech. Rep. LIGO-T060272-00-I (2006), https://dcc.ligo.org/

Aguirregabiria, J.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Althouse, W.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Ando, M.

M. Ando and TAMA Collaboration, “Stable operation of a 300 m laser interferometer with sufficient sensitivity to detect gravitational-wave events within our galaxy,” Phys. Rev. Lett. 86, 3950–3954 (2001).
[CrossRef] [PubMed]

Arai, K.

Ballmer, S.

S. Ballmer, “Interferometer sensing and control,” presented at the LSC meeting, Hannover, LIGO-G070687-00-I (22–25 October 2007).

Barone, F.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Barron, D.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Bel, H.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Beyersdorf, P.

Bonazzola, S.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Bork, R.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Bradaschia, C.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Brillet, A.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Capozzi, M.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Chelkowski, S.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

Chen, Y.

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
[CrossRef]

Collaboration, The Virgo

The Virgo Collaboration, “Advanced Virgo baseline design,” VIR-027A-09 (2009), https://pub3.ego-gw.it/itf/tds/.

Cregut, O.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Damour, T.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Danzmann, K.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

Degallaix, J.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

Del Fabbro, R.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Di Fiore, L.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Di Virgilio, A.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Drever, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Duruisseau, J.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Evans, M.

M. Evans, “Optickle,” http://ilog.ligo-wa.caltech.edu:7285/advligo.

Freise, A.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

A. Freise, “FINESSE,” http://www.gwoptics.org/finesse/.

Fricke, T.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Fritschel, P.

K. Somiya, O. Miyakawa, P. Fritschel, and R. Adhikari, “Length sensing and control for AdLIGO,” Tech. Rep. LIGO-T060272-00-I (2006), https://dcc.ligo.org/

Frolov, V.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Fuligni, F.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Giazotto, A.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Gourghoulon, Y.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Grote, H.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

Gürsel, Y.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Heefner, J.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Hello, P.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Hewitson, M.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

Hild, S.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

Holloway, L.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Hough, J.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

Iafolla, V.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Ivanov, A.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Kautzky, H.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Kawamura, S.

S. Sato, S. Kawamura, K. Kokeyama, F. Kawazoe, and K. Somiya, “Diagonalization of the length sensing matrix of a dual recycled laser interferometer gravitational wave antenna,” Phys. Rev. D 75, 082004 (2007).
[CrossRef]

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
[CrossRef]

K. Somiya, P. Beyersdorf, K. Arai, S. Sato, S. Kawamura, O. Miyakawa, F. Kawazoe, S. Sakata, A. Sekido, and N. Mio, “Development of a frequency-detuned interferometer as a prototype experiment for next-generation gravitational-wave detectors,” Appl. Opt. 44, 3179–3191(2005).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Kawazoe, F.

S. Sato, S. Kawamura, K. Kokeyama, F. Kawazoe, and K. Somiya, “Diagonalization of the length sensing matrix of a dual recycled laser interferometer gravitational wave antenna,” Phys. Rev. D 75, 082004 (2007).
[CrossRef]

K. Somiya, P. Beyersdorf, K. Arai, S. Sato, S. Kawamura, O. Miyakawa, F. Kawazoe, S. Sakata, A. Sekido, and N. Mio, “Development of a frequency-detuned interferometer as a prototype experiment for next-generation gravitational-wave detectors,” Appl. Opt. 44, 3179–3191(2005).
[CrossRef] [PubMed]

Kokeyama, K.

S. Sato, S. Kawamura, K. Kokeyama, F. Kawazoe, and K. Somiya, “Diagonalization of the length sensing matrix of a dual recycled laser interferometer gravitational wave antenna,” Phys. Rev. D 75, 082004 (2007).
[CrossRef]

Le Denmat, G.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Li, C.

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

Longo, M.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Lops, M.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Lück, H.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

H. Lück and the GEO600 Team, “The GEO600 project,” Class. Quantum Grav. 14, 1471–1476 (1997).
[CrossRef]

Man, C.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Manh, P.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Marck, J.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Marraud, A.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Mason, J.

McKenzie, K.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Milano, L.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Mio, N.

Miyakawa, O.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

O. Miyakawa, “Calculation of loop noise for Advanced LIGO using Optickle engine,” internal report (2006), http://lhocds.ligo-wa.caltech.edu:8000/advligo/Loopnoise results.

K. Somiya, O. Miyakawa, P. Fritschel, and R. Adhikari, “Length sensing and control for AdLIGO,” Tech. Rep. LIGO-T060272-00-I (2006), https://dcc.ligo.org/

K. Somiya, P. Beyersdorf, K. Arai, S. Sato, S. Kawamura, O. Miyakawa, F. Kawazoe, S. Sakata, A. Sekido, and N. Mio, “Development of a frequency-detuned interferometer as a prototype experiment for next-generation gravitational-wave detectors,” Appl. Opt. 44, 3179–3191(2005).
[CrossRef] [PubMed]

Montelatici, V.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Müller-Ebhardt, H.

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

Natale, G.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Passuello, D.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Pinto, I.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Prijatelj, M.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

Raab, F.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Rehbein, H.

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

Rotoli, G.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Russo, G.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Sakata, S.

Sato, S.

S. Sato, S. Kawamura, K. Kokeyama, F. Kawazoe, and K. Somiya, “Diagonalization of the length sensing matrix of a dual recycled laser interferometer gravitational wave antenna,” Phys. Rev. D 75, 082004 (2007).
[CrossRef]

K. Somiya, P. Beyersdorf, K. Arai, S. Sato, S. Kawamura, O. Miyakawa, F. Kawazoe, S. Sakata, A. Sekido, and N. Mio, “Development of a frequency-detuned interferometer as a prototype experiment for next-generation gravitational-wave detectors,” Appl. Opt. 44, 3179–3191(2005).
[CrossRef] [PubMed]

Schnabel, R.

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

Sekido, A.

Shoemaker, D.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Sievers, L.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Slagmolen, B.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Smith, J.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

Smith, M.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Somiya, K.

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

S. Sato, S. Kawamura, K. Kokeyama, F. Kawazoe, and K. Somiya, “Diagonalization of the length sensing matrix of a dual recycled laser interferometer gravitational wave antenna,” Phys. Rev. D 75, 082004 (2007).
[CrossRef]

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
[CrossRef]

K. Somiya, O. Miyakawa, P. Fritschel, and R. Adhikari, “Length sensing and control for AdLIGO,” Tech. Rep. LIGO-T060272-00-I (2006), https://dcc.ligo.org/

K. Somiya, P. Beyersdorf, K. Arai, S. Sato, S. Kawamura, O. Miyakawa, F. Kawazoe, S. Sakata, A. Sekido, and N. Mio, “Development of a frequency-detuned interferometer as a prototype experiment for next-generation gravitational-wave detectors,” Appl. Opt. 44, 3179–3191(2005).
[CrossRef] [PubMed]

K. Somiya, “Investigation of radiation pressure effect in a frequency-detuned interferometer and development of the readout scheme for a gravitational-wave detector,” Ph.D. dissertation (University of Tokyo, 2004); Sec. 3.9.

K. Somiya, “Length sensing and control of AdLIGO,” presented at the LSC meeting, Baton Rouge, LIGO-G060481-00-Z (14–17 August 2006).

Spero, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Strain, K.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

Taylor, R.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Thorne, K.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Tourrenc, Ph.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Vass, S.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Vinet, J.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Vogt, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Waldman, S.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Ward, R.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Weinstein, A.

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Weiss, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Whitcomb, S.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Willems, P.

Willke, B.

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

Zucker, M.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Appl. Opt. (2)

Class. Quantum Grav. (3)

H. Lück and the GEO600 Team, “The GEO600 project,” Class. Quantum Grav. 14, 1471–1476 (1997).
[CrossRef]

R. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “dc readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

S. Hild, H. Grote, J. Degallaix, S. Chelkowski, K. Danzmann, A. Freise, M. Hewitson, J. Hough, H. Lück, M. Prijatelj, K. Strain, J. Smith, and B. Willke, “DC-readout of a signal-recycled gravitational wave detector,” Class. Quantum Grav. 26, 055012 (2009).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. Man, P. Manh, A. Marraud, D. Shoemaker, J. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. Aguirregabiria, H. Bel, J. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. Marck, Y. Gourghoulon, L. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Phys. Rev. D (3)

S. Sato, S. Kawamura, K. Kokeyama, F. Kawazoe, and K. Somiya, “Diagonalization of the length sensing matrix of a dual recycled laser interferometer gravitational wave antenna,” Phys. Rev. D 75, 082004 (2007).
[CrossRef]

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

M. Ando and TAMA Collaboration, “Stable operation of a 300 m laser interferometer with sufficient sensitivity to detect gravitational-wave events within our galaxy,” Phys. Rev. Lett. 86, 3950–3954 (2001).
[CrossRef] [PubMed]

Science (1)

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Other (11)

K. Somiya, “Investigation of radiation pressure effect in a frequency-detuned interferometer and development of the readout scheme for a gravitational-wave detector,” Ph.D. dissertation (University of Tokyo, 2004); Sec. 3.9.

It has been reported that ℓm contains more information of gravitational-wave signals at low frequencies in some configurations; see Ref. 10.

A. Freise, “FINESSE,” http://www.gwoptics.org/finesse/.

M. Evans, “Optickle,” http://ilog.ligo-wa.caltech.edu:7285/advligo.

K. Somiya, “Length sensing and control of AdLIGO,” presented at the LSC meeting, Baton Rouge, LIGO-G060481-00-Z (14–17 August 2006).

O. Miyakawa, “Calculation of loop noise for Advanced LIGO using Optickle engine,” internal report (2006), http://lhocds.ligo-wa.caltech.edu:8000/advligo/Loopnoise results.

S. Ballmer, “Interferometer sensing and control,” presented at the LSC meeting, Hannover, LIGO-G070687-00-I (22–25 October 2007).

http://gw.icrr.u-tokyo.ac.jp/JGWwiki/LCGT.

DC readout is a way to obtain the signal by adding an offset on the arm-cavity control and using the carrier light that leaks through the dark port as a reference; see Refs.

K. Somiya, O. Miyakawa, P. Fritschel, and R. Adhikari, “Length sensing and control for AdLIGO,” Tech. Rep. LIGO-T060272-00-I (2006), https://dcc.ligo.org/

The Virgo Collaboration, “Advanced Virgo baseline design,” VIR-027A-09 (2009), https://pub3.ego-gw.it/itf/tds/.

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Figures (8)

Fig. 1
Fig. 1

Second-generation gravitational-wave detector.

Fig. 2
Fig. 2

Block diagram of a feedback control system with excess noise in the measurement device.

Fig. 3
Fig. 3

Schematic of the feedback control in an interferometric gravitational-wave detector.

Fig. 4
Fig. 4

First-order and second-order contributions of loop noise described in the normalized sensing matrix.

Fig. 5
Fig. 5

Block diagram that shows the mixture of sensing noise and displacement noise of other degrees of freedom into each output. Here G i k is the electric feedback-gain matrix element that sends y k into x i , and D j i is the sensing matrix element that expresses the coupling from x i into y j . We split D j i into the optical gain H j and the normalized matrix element A j i .

Fig. 6
Fig. 6

Normalized sensing matrix A and the optical-gain vector H (i.e., normalized factor) at 100 Hz in two different cases of signal sensing for a second-generation gravitational-wave detector: p and s signals are obtained with single demodulation in panel (a) and with double demodulation in panel (b). For the other degrees of freedom, the signal-extraction ports are the same for two cases: L + from the reflection port, L - from the dark port with dc readout [17, 18, 19, 20], and m from the dark port with double demodulation. Panel (a) shows poorer signal separation for the common-mode signals but higher optical gains, while panel (b) is the other way around. A small number in the top-right corner of each segment indicates the relative phase.

Fig. 7
Fig. 7

Loop-noise curves of LCGT in the two cases introduced in Fig. 6 correspond to the matrix in (a) Fig. 6a and (b) Fig. 6b.

Fig. 8
Fig. 8

Loop noise with and without feed-forward. With feed- forward, displacement noise at low frequencies and L + noise increase compared with the case without feed-forward.

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

Y = 1 1 + G H ( H x + H N x + N s ) + α H 1 + G H ( x aux + n x g y aux ) ,
y aux = h 1 + g h ( x aux + n x ) n s 1 + g h .
x n = N x + N s H + α ( n x 1 + g h + g h 1 + g h n s h ) ̲ .
y = D x + n ,
x cal = D 1 y = x + D 1 n .
x ˜ 2 cal = y 2 / H 2 = x 2 + j 2 A 2 j x j + n 2 / H 2 ,
y = DG y + D x + n ,
y = ( I + DG ) 1 ( D x + n ) .
y 2 = j x 2 + A 2 j 1 n j / H j G 22 ,
x loop = j 2 A 2 j 1 n j / H j .
A = ( 1 0 0 0 0 0 1 0 a 0 0 0 1 b 1 + ϵ 0 0 b 1 b 0 0 1 ϵ b 1 ) .
A 1 ( 1 0 0 0 0 0 1 a b / ϵ a a b / ϵ 0 0 1 / ϵ 2 b / ϵ 1 / ϵ 2 0 0 b / ϵ 1 b / ϵ 0 0 1 / ϵ 2 b 1 / ϵ 2 ) ,
x sens = x shot + x loop = n 2 H 2 + a b ϵ ( n 3 H 3 ) a ( n 4 H 4 ) a b ϵ ( n 5 H 5 ) .
y G 1 D 1 n + G 1 x .
D ˜ i k l m = ( D k 3 1 D k 4 1 D k 5 1 D l 3 1 D l 4 1 D l 5 1 D m 3 1 D m 4 1 D m 5 1 ) ,
G 23 G 33 | D ˜ i 245 | | D ˜ i 345 | G 33 D 23 1 D 33 1 ,
G 24 G 44 | D ˜ i 235 | | D ˜ i 345 | G 44 D 24 1 D 44 1 ,
G 25 G 55 | D ˜ i 234 | | D ˜ i 345 | G 55 D 25 1 D 55 1 .
G 23 G 33 | D ˜ i 245 | F 2 | D ˜ i 124 | | D ˜ i 345 | F 1 | D ˜ i 145 | F 2 | D ˜ i 134 | ,
G 24 G 44 | D ˜ i 235 | + F 1 | D ˜ i 125 | F 2 | D ˜ i 123 | B 1 | D ˜ i 245 | B 2 | D ˜ i 234 | ( F 1 B 2 F 2 B 1 ) | D ˜ i 124 | | D ˜ i 345 | F 1 | D ˜ i 145 | F 2 | D ˜ i 134 | ,
G 25 G 55 | D ˜ i 234 | + F 1 | D ˜ i 124 | | D ˜ i 345 | F 1 | D ˜ i 145 | F 2 | D ˜ i 134 | .

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