R. Day, on behalf of the Virgo Collaboration, “Central heating radius of curvature correction for use in large scale gravitational wave interferometers,” Classical Quantum Gravity 30, 055017 (2013).

[CrossRef]

B. Canuel, R. Day, E. Genin, P. La Penna, and J. Marque, “Wavefront aberration compensation with a thermally deformable mirror,” Classical Quantum Gravity 29, 085012 (2012).

[CrossRef]

LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7, 962–965 (2011).

[CrossRef]

M. Arain, W. Korth, L. Williams, R. Martin, G. Mueller, D. Tanner, and D. Reitze, “Adaptive control of modal properties of optical beams using photothermal effects,” Opt. Express 18, 2767–2781 (2010).

[CrossRef]

S. Verpoort, and U. Wittrock, “Actuator patterns for unimorph and bimorph deformable mirrors,” Appl. Opt. 49, G37–G46 (2010).

[CrossRef]

J.-Y. Vinet, “On special optical modes and thermal issues in advanced gravitational wave interferometric detectors,” Living Rev. Relativity 12, 2009-5 (2009).

[CrossRef]

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

T. Corbitt, N. Mavalvala, and S. Whitcomb, “Optical cavities as amplitude filters for squeezed fields,” Phys. Rev. D 70, 022002 (2004).

[CrossRef]

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Classical Quantum Gravity 21, S903–S908 (2004).

[CrossRef]

H. Luck, A. Freise, S. Gobler, S. Hild, K. Kawabe, and K. Danzmann, “Thermal correction of the radii of curvature of mirrors for GEO 600,” Classical Quantum Gravity 21, S985–S989 (2004).

[CrossRef]

R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active correction of thermal lensing through external radiative thermal actuation,” Opt. Lett. 29, 2635–2637 (2004).

[CrossRef]

E. Calloni, J. T. Baker, F. Barone, R. DeRosa, L. Di Fiore, L. Milano, and S. R. Restaino, “Adaptive optics approach for prefiltering of geometrical fluctuations of the input laser beam of an interferometric gravitational waves detector,” Rev. Sci. Instrum. 74, 2570–2574 (2003).

[CrossRef]

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Classical Quantum Gravity 19, 1793–1801 (2002).

[CrossRef]

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, “Adaptive thermal compensation of test masses in advanced LIGO,” Classical Quantum Gravity 19, 1803–1812 (2002).

P. Hello, “Compensation for thermal effects in mirrors of gravitational wave interferometers,” Eur. Phys. J. D 15, 373–383 (2001).

[CrossRef]

H. Luck, K. O. Muller, P. Aufmuth, and K. Danzmann, “Correction of wavefront distortions by means of thermally adaptive optics,” Opt. Commun. 175, 275–287 (2000).

[CrossRef]

G. Mueller, Q. Shu, R. Adhikari, D. B. Tanner, D. Reitze, D. Sigg, N. Mavalvala, and J. Camp, “Determination and optimization of mode matching into optical cavities by heterodyne detection,” Opt. Lett. 25, 266–268 (2000).

[CrossRef]

T. F. Coleman and Y. Li, “A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6, 1040–1058 (1996).

[CrossRef]

W. Winkler, K. Danzmann, A. Rudiger, and R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022 (1991).

[CrossRef]

P. Hello and J. Y. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. France 51, 1267–1282 (1990).

[CrossRef]

P. Hello and J. Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. France 51, 2243–2261 (1990).

[CrossRef]

G. Mueller, Q. Shu, R. Adhikari, D. B. Tanner, D. Reitze, D. Sigg, N. Mavalvala, and J. Camp, “Determination and optimization of mode matching into optical cavities by heterodyne detection,” Opt. Lett. 25, 266–268 (2000).

[CrossRef]

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Classical Quantum Gravity 19, 1793–1801 (2002).

[CrossRef]

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

H. Luck, K. O. Muller, P. Aufmuth, and K. Danzmann, “Correction of wavefront distortions by means of thermally adaptive optics,” Opt. Commun. 175, 275–287 (2000).

[CrossRef]

S. Avino, “Adaptive optics techniques for gravitational wave interferometers,” Ph.D. thesis (Universita Degli Studi di Napoli Federico II, 2006).

E. Calloni, J. T. Baker, F. Barone, R. DeRosa, L. Di Fiore, L. Milano, and S. R. Restaino, “Adaptive optics approach for prefiltering of geometrical fluctuations of the input laser beam of an interferometric gravitational waves detector,” Rev. Sci. Instrum. 74, 2570–2574 (2003).

[CrossRef]

E. Calloni, J. T. Baker, F. Barone, R. DeRosa, L. Di Fiore, L. Milano, and S. R. Restaino, “Adaptive optics approach for prefiltering of geometrical fluctuations of the input laser beam of an interferometric gravitational waves detector,” Rev. Sci. Instrum. 74, 2570–2574 (2003).

[CrossRef]

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Classical Quantum Gravity 21, S903–S908 (2004).

[CrossRef]

M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).

E. Calloni, J. T. Baker, F. Barone, R. DeRosa, L. Di Fiore, L. Milano, and S. R. Restaino, “Adaptive optics approach for prefiltering of geometrical fluctuations of the input laser beam of an interferometric gravitational waves detector,” Rev. Sci. Instrum. 74, 2570–2574 (2003).

[CrossRef]

G. Mueller, Q. Shu, R. Adhikari, D. B. Tanner, D. Reitze, D. Sigg, N. Mavalvala, and J. Camp, “Determination and optimization of mode matching into optical cavities by heterodyne detection,” Opt. Lett. 25, 266–268 (2000).

[CrossRef]

B. Canuel, R. Day, E. Genin, P. La Penna, and J. Marque, “Wavefront aberration compensation with a thermally deformable mirror,” Classical Quantum Gravity 29, 085012 (2012).

[CrossRef]

T. F. Coleman and Y. Li, “A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6, 1040–1058 (1996).

[CrossRef]

T. Corbitt, N. Mavalvala, and S. Whitcomb, “Optical cavities as amplitude filters for squeezed fields,” Phys. Rev. D 70, 022002 (2004).

[CrossRef]

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

H. Luck, A. Freise, S. Gobler, S. Hild, K. Kawabe, and K. Danzmann, “Thermal correction of the radii of curvature of mirrors for GEO 600,” Classical Quantum Gravity 21, S985–S989 (2004).

[CrossRef]

H. Luck, K. O. Muller, P. Aufmuth, and K. Danzmann, “Correction of wavefront distortions by means of thermally adaptive optics,” Opt. Commun. 175, 275–287 (2000).

[CrossRef]

W. Winkler, K. Danzmann, A. Rudiger, and R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022 (1991).

[CrossRef]

R. Day, on behalf of the Virgo Collaboration, “Central heating radius of curvature correction for use in large scale gravitational wave interferometers,” Classical Quantum Gravity 30, 055017 (2013).

[CrossRef]

B. Canuel, R. Day, E. Genin, P. La Penna, and J. Marque, “Wavefront aberration compensation with a thermally deformable mirror,” Classical Quantum Gravity 29, 085012 (2012).

[CrossRef]

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Classical Quantum Gravity 21, S903–S908 (2004).

[CrossRef]

E. Calloni, J. T. Baker, F. Barone, R. DeRosa, L. Di Fiore, L. Milano, and S. R. Restaino, “Adaptive optics approach for prefiltering of geometrical fluctuations of the input laser beam of an interferometric gravitational waves detector,” Rev. Sci. Instrum. 74, 2570–2574 (2003).

[CrossRef]

E. Calloni, J. T. Baker, F. Barone, R. DeRosa, L. Di Fiore, L. Milano, and S. R. Restaino, “Adaptive optics approach for prefiltering of geometrical fluctuations of the input laser beam of an interferometric gravitational waves detector,” Rev. Sci. Instrum. 74, 2570–2574 (2003).

[CrossRef]

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

H. Luck, A. Freise, S. Gobler, S. Hild, K. Kawabe, and K. Danzmann, “Thermal correction of the radii of curvature of mirrors for GEO 600,” Classical Quantum Gravity 21, S985–S989 (2004).

[CrossRef]

R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active correction of thermal lensing through external radiative thermal actuation,” Opt. Lett. 29, 2635–2637 (2004).

[CrossRef]

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, “Adaptive thermal compensation of test masses in advanced LIGO,” Classical Quantum Gravity 19, 1803–1812 (2002).

B. Canuel, R. Day, E. Genin, P. La Penna, and J. Marque, “Wavefront aberration compensation with a thermally deformable mirror,” Classical Quantum Gravity 29, 085012 (2012).

[CrossRef]

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

H. Luck, A. Freise, S. Gobler, S. Hild, K. Kawabe, and K. Danzmann, “Thermal correction of the radii of curvature of mirrors for GEO 600,” Classical Quantum Gravity 21, S985–S989 (2004).

[CrossRef]

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Classical Quantum Gravity 19, 1793–1801 (2002).

[CrossRef]

P. Hello, “Compensation for thermal effects in mirrors of gravitational wave interferometers,” Eur. Phys. J. D 15, 373–383 (2001).

[CrossRef]

P. Hello and J. Y. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. France 51, 1267–1282 (1990).

[CrossRef]

P. Hello and J. Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. France 51, 2243–2261 (1990).

[CrossRef]

H. Luck, A. Freise, S. Gobler, S. Hild, K. Kawabe, and K. Danzmann, “Thermal correction of the radii of curvature of mirrors for GEO 600,” Classical Quantum Gravity 21, S985–S989 (2004).

[CrossRef]

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Classical Quantum Gravity 21, S903–S908 (2004).

[CrossRef]

H. Luck, A. Freise, S. Gobler, S. Hild, K. Kawabe, and K. Danzmann, “Thermal correction of the radii of curvature of mirrors for GEO 600,” Classical Quantum Gravity 21, S985–S989 (2004).

[CrossRef]

B. Canuel, R. Day, E. Genin, P. La Penna, and J. Marque, “Wavefront aberration compensation with a thermally deformable mirror,” Classical Quantum Gravity 29, 085012 (2012).

[CrossRef]

R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active correction of thermal lensing through external radiative thermal actuation,” Opt. Lett. 29, 2635–2637 (2004).

[CrossRef]

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, “Adaptive thermal compensation of test masses in advanced LIGO,” Classical Quantum Gravity 19, 1803–1812 (2002).

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

T. F. Coleman and Y. Li, “A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6, 1040–1058 (1996).

[CrossRef]

H. Luck, A. Freise, S. Gobler, S. Hild, K. Kawabe, and K. Danzmann, “Thermal correction of the radii of curvature of mirrors for GEO 600,” Classical Quantum Gravity 21, S985–S989 (2004).

[CrossRef]

H. Luck, K. O. Muller, P. Aufmuth, and K. Danzmann, “Correction of wavefront distortions by means of thermally adaptive optics,” Opt. Commun. 175, 275–287 (2000).

[CrossRef]

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Classical Quantum Gravity 19, 1793–1801 (2002).

[CrossRef]

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, “Adaptive thermal compensation of test masses in advanced LIGO,” Classical Quantum Gravity 19, 1803–1812 (2002).

B. Canuel, R. Day, E. Genin, P. La Penna, and J. Marque, “Wavefront aberration compensation with a thermally deformable mirror,” Classical Quantum Gravity 29, 085012 (2012).

[CrossRef]

T. Corbitt, N. Mavalvala, and S. Whitcomb, “Optical cavities as amplitude filters for squeezed fields,” Phys. Rev. D 70, 022002 (2004).

[CrossRef]

G. Mueller, Q. Shu, R. Adhikari, D. B. Tanner, D. Reitze, D. Sigg, N. Mavalvala, and J. Camp, “Determination and optimization of mode matching into optical cavities by heterodyne detection,” Opt. Lett. 25, 266–268 (2000).

[CrossRef]

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Classical Quantum Gravity 19, 1793–1801 (2002).

[CrossRef]

E. Calloni, J. T. Baker, F. Barone, R. DeRosa, L. Di Fiore, L. Milano, and S. R. Restaino, “Adaptive optics approach for prefiltering of geometrical fluctuations of the input laser beam of an interferometric gravitational waves detector,” Rev. Sci. Instrum. 74, 2570–2574 (2003).

[CrossRef]

M. Arain, W. Korth, L. Williams, R. Martin, G. Mueller, D. Tanner, and D. Reitze, “Adaptive control of modal properties of optical beams using photothermal effects,” Opt. Express 18, 2767–2781 (2010).

[CrossRef]

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Classical Quantum Gravity 19, 1793–1801 (2002).

[CrossRef]

G. Mueller, Q. Shu, R. Adhikari, D. B. Tanner, D. Reitze, D. Sigg, N. Mavalvala, and J. Camp, “Determination and optimization of mode matching into optical cavities by heterodyne detection,” Opt. Lett. 25, 266–268 (2000).

[CrossRef]

H. Luck, K. O. Muller, P. Aufmuth, and K. Danzmann, “Correction of wavefront distortions by means of thermally adaptive optics,” Opt. Commun. 175, 275–287 (2000).

[CrossRef]

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

M. Arain, W. Korth, L. Williams, R. Martin, G. Mueller, D. Tanner, and D. Reitze, “Adaptive control of modal properties of optical beams using photothermal effects,” Opt. Express 18, 2767–2781 (2010).

[CrossRef]

G. Mueller, Q. Shu, R. Adhikari, D. B. Tanner, D. Reitze, D. Sigg, N. Mavalvala, and J. Camp, “Determination and optimization of mode matching into optical cavities by heterodyne detection,” Opt. Lett. 25, 266–268 (2000).

[CrossRef]

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Classical Quantum Gravity 19, 1793–1801 (2002).

[CrossRef]

E. Calloni, J. T. Baker, F. Barone, R. DeRosa, L. Di Fiore, L. Milano, and S. R. Restaino, “Adaptive optics approach for prefiltering of geometrical fluctuations of the input laser beam of an interferometric gravitational waves detector,” Rev. Sci. Instrum. 74, 2570–2574 (2003).

[CrossRef]

W. Winkler, K. Danzmann, A. Rudiger, and R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022 (1991).

[CrossRef]

W. Winkler, K. Danzmann, A. Rudiger, and R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022 (1991).

[CrossRef]

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, “Adaptive thermal compensation of test masses in advanced LIGO,” Classical Quantum Gravity 19, 1803–1812 (2002).

G. Mueller, Q. Shu, R. Adhikari, D. B. Tanner, D. Reitze, D. Sigg, N. Mavalvala, and J. Camp, “Determination and optimization of mode matching into optical cavities by heterodyne detection,” Opt. Lett. 25, 266–268 (2000).

[CrossRef]

G. Mueller, Q. Shu, R. Adhikari, D. B. Tanner, D. Reitze, D. Sigg, N. Mavalvala, and J. Camp, “Determination and optimization of mode matching into optical cavities by heterodyne detection,” Opt. Lett. 25, 266–268 (2000).

[CrossRef]

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Classical Quantum Gravity 19, 1793–1801 (2002).

[CrossRef]

G. Mueller, Q. Shu, R. Adhikari, D. B. Tanner, D. Reitze, D. Sigg, N. Mavalvala, and J. Camp, “Determination and optimization of mode matching into optical cavities by heterodyne detection,” Opt. Lett. 25, 266–268 (2000).

[CrossRef]

P. Hello and J. Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. France 51, 2243–2261 (1990).

[CrossRef]

P. Hello and J. Y. Vinet, “Analytical models of thermal aberrations in massive mirrors heated by high power laser beams,” J. Phys. France 51, 1267–1282 (1990).

[CrossRef]

J.-Y. Vinet, “On special optical modes and thermal issues in advanced gravitational wave interferometric detectors,” Living Rev. Relativity 12, 2009-5 (2009).

[CrossRef]

T. Corbitt, N. Mavalvala, and S. Whitcomb, “Optical cavities as amplitude filters for squeezed fields,” Phys. Rev. D 70, 022002 (2004).

[CrossRef]

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

W. Winkler, K. Danzmann, A. Rudiger, and R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022 (1991).

[CrossRef]

M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).

V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Yoshiki Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, “Adaptive control of laser modal properties,” Opt. Lett. 31, 217–219 (2006).

[CrossRef]

J. Degallaix, C. Zhao, L. Ju, and D. Blair, “Thermal lensing compensation for AIGO high optical power test facility,” Classical Quantum Gravity 21, S903–S908 (2004).

[CrossRef]

R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, “Active correction of thermal lensing through external radiative thermal actuation,” Opt. Lett. 29, 2635–2637 (2004).

[CrossRef]

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, “Adaptive thermal compensation of test masses in advanced LIGO,” Classical Quantum Gravity 19, 1803–1812 (2002).

J. Alda and G. D. Boreman, “Zernike-based matrix model of deformable mirrors: optimization of the aperture size,” Appl. Opt. 32, 2431–2438 (1993).

[CrossRef]

M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46, 2153–2165 (2007).

[CrossRef]

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