Abstract

Gravitational waves are a prediction of Einstein's general theory of relativity. These waves are created by massive objects, like neutron stars or black holes, oscillating at speeds appreciable to the speed of light. The detectable effect on the Earth of these waves is extremely small, however, creating strains of the order of 1021. There are a number of basic physics experiments around the world designed to detect these waves by using interferometers with very long arms, up to 4  km in length. The next-generation interferometers are currently being designed, and the thermal noise in the mirrors will set the sensitivity over much of the usable bandwidth. Thermal noise arising from mechanical loss in the optical coatings put on the mirrors will be a significant source of noise. Achieving higher sensitivity through lower mechanical loss coatings, while preserving the crucial optical and thermal properties, is an area of active research right now.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. K. S. Thorne and C. Cutler, 'An overview of gravitational wave sources,' in Proceedings of 16th International Conference on General Relativity and Gravitation, N.T.Bishop and S.D.Maharaj, eds. (World Scientific, 2002), pp. 72-112.
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    [CrossRef]
  7. Yu. Levin, 'Internal thermal noise in the LIGO test masses: a direct approach,' Phys. Rev. D 57, 659-663 (1998).
    [CrossRef]
  8. C. Zener, 'Internal friction in solids. I. Theory of internal friction in reeds,' Phys. Rev. 52, 230-235 (1937).
    [CrossRef]
  9. M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. K. Numata, A. Kemery, and J. Camp, 'Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,' Phys. Rev. Lett. 93, 250602 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
    [CrossRef]
  18. K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, 'Wide-band direct measurement of thermal fluctuations in an interferometer,' Phys. Rev. Lett. 91, 260602 (2003).
    [CrossRef]
  19. E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
    [CrossRef]
  20. V. B. Braginsky and S. P. Vyatchanin, 'Corner reflectors and quantum-non-demolition measurements in gravitational wave antennae,' Phys. Lett. A 324, 345-360 (2004).
    [CrossRef]
  21. F. Ya. Khalili, 'Reducing the mirrors coating noise in laser gravitational-wave antennae by means of double mirrors,' Phys. Lett. A 334, 67-72 (2005).
    [CrossRef]

2005 (1)

F. Ya. Khalili, 'Reducing the mirrors coating noise in laser gravitational-wave antennae by means of double mirrors,' Phys. Lett. A 334, 67-72 (2005).
[CrossRef]

2004 (7)

R. Lawrence, D. Ottaway, P. Fritschel, and M. Zucker, 'Active correction of beam heating induced phase distortions in optics via external radiative thermal acutation,' Opt. Lett. 29, 2635-2637 (2004).
[CrossRef] [PubMed]

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

V. B. Braginsky and S. P. Vyatchanin, 'Corner reflectors and quantum-non-demolition measurements in gravitational wave antennae,' Phys. Lett. A 324, 345-360 (2004).
[CrossRef]

K. Numata, A. Kemery, and J. Camp, 'Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,' Phys. Rev. Lett. 93, 250602 (2004).
[CrossRef]

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

B. Abbott and The LIGO Science Collaboration, 'Detector description and performance for the first coincidence observations between LIGO and GEO,' Nucl. Instrum. Methods Phys. Res. A 517, 154-179 (2004).
[CrossRef]

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

2003 (3)

V. B. Braginsky and S. P. Vyatchanin, 'Thermodynamical fluctuations in optical mirror coatings,' Phys. Lett. A 312, 224-255 (2003).
[CrossRef]

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, 'Wide-band direct measurement of thermal fluctuations in an interferometer,' Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

S. D. Penn, P. H. Sneddon, H. Armandula, Betzweiser, G. Cagnoli, J. Camp, D. R. M. Crooks, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, S. E. Kittelberger, M. J. Mortonson, R. Route, S. Rowan, and C. C. Vassiliou, 'Mechanical loss in tantala/silica dielectric mirror coatings,' Class. Quantum Grav. 20, 2917-2928 (2003).
[CrossRef]

2002 (4)

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

F. Acernese and the VIRGO Collaboration, ' Status of VIRGO,' Class. Quantum Grav. 19, 1421-1428 (2002).
[CrossRef]

M. Ando and the TAMA Collaboration, 'Current status of TAMA,' Class. Quantum Grav. 19, 1409-1419 (2002).
[CrossRef]

1999 (1)

V. B. Braginsky, M. L. Gorodetsky, and S. B. Vyatchanin, 'Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,' Phys. Lett. A 264, 1-10 (1999).
[CrossRef]

1998 (1)

Yu. Levin, 'Internal thermal noise in the LIGO test masses: a direct approach,' Phys. Rev. D 57, 659-663 (1998).
[CrossRef]

1988 (1)

B. J. Meers, 'Recycling in a laser-interferometric gravitational-wave detector,' Phys. Rev. D 38, 2317-2326 (1988).
[CrossRef]

1952 (1)

H. B. Callen and R. F. Greene, 'On a theorem of irreversible thermodynamics,' Phys. Rev. 86, 702-710 (1952).
[CrossRef]

1937 (1)

C. Zener, 'Internal friction in solids. I. Theory of internal friction in reeds,' Phys. Rev. 52, 230-235 (1937).
[CrossRef]

Abbott, B.

B. Abbott and The LIGO Science Collaboration, 'Detector description and performance for the first coincidence observations between LIGO and GEO,' Nucl. Instrum. Methods Phys. Res. A 517, 154-179 (2004).
[CrossRef]

Acernese, F.

F. Acernese and the VIRGO Collaboration, ' Status of VIRGO,' Class. Quantum Grav. 19, 1421-1428 (2002).
[CrossRef]

Ando, M.

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, 'Wide-band direct measurement of thermal fluctuations in an interferometer,' Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

M. Ando and the TAMA Collaboration, 'Current status of TAMA,' Class. Quantum Grav. 19, 1409-1419 (2002).
[CrossRef]

Armandula, H.

S. D. Penn, P. H. Sneddon, H. Armandula, Betzweiser, G. Cagnoli, J. Camp, D. R. M. Crooks, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, S. E. Kittelberger, M. J. Mortonson, R. Route, S. Rowan, and C. C. Vassiliou, 'Mechanical loss in tantala/silica dielectric mirror coatings,' Class. Quantum Grav. 20, 2917-2928 (2003).
[CrossRef]

Barbary, K.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Black, E. D.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Braginsky, V. B.

V. B. Braginsky and S. P. Vyatchanin, 'Corner reflectors and quantum-non-demolition measurements in gravitational wave antennae,' Phys. Lett. A 324, 345-360 (2004).
[CrossRef]

V. B. Braginsky and S. P. Vyatchanin, 'Thermodynamical fluctuations in optical mirror coatings,' Phys. Lett. A 312, 224-255 (2003).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and S. B. Vyatchanin, 'Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,' Phys. Lett. A 264, 1-10 (1999).
[CrossRef]

Bushmaker, A.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Cagnoli, G.

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

Callen, H. B.

H. B. Callen and R. F. Greene, 'On a theorem of irreversible thermodynamics,' Phys. Rev. 86, 702-710 (1952).
[CrossRef]

Camp, J.

K. Numata, A. Kemery, and J. Camp, 'Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,' Phys. Rev. Lett. 93, 250602 (2004).
[CrossRef]

Coyne, D.

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

Crooks, D. R. M.

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

Cutler, C.

K. S. Thorne and C. Cutler, 'An overview of gravitational wave sources,' in Proceedings of 16th International Conference on General Relativity and Gravitation, N.T.Bishop and S.D.Maharaj, eds. (World Scientific, 2002), pp. 72-112.

Fejer, M. M.

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

Fritschel, P.

Gorodetsky, M. L.

V. B. Braginsky, M. L. Gorodetsky, and S. B. Vyatchanin, 'Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,' Phys. Lett. A 264, 1-10 (1999).
[CrossRef]

Greene, R. F.

H. B. Callen and R. F. Greene, 'On a theorem of irreversible thermodynamics,' Phys. Rev. 86, 702-710 (1952).
[CrossRef]

Gretarsson, A.

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

Gretarsson, A. M.

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

Gustafson, E.

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

Harry, G. M.

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

Heefner, J.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Hough, J.

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

Kawamura, S.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Kawazoe, F.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Kemery, A.

K. Numata, A. Kemery, and J. Camp, 'Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,' Phys. Rev. Lett. 93, 250602 (2004).
[CrossRef]

Khalili, F. Ya.

F. Ya. Khalili, 'Reducing the mirrors coating noise in laser gravitational-wave antennae by means of double mirrors,' Phys. Lett. A 334, 67-72 (2005).
[CrossRef]

Kittelberger, S. E.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

Lawrence, R.

Levin, Yu.

Yu. Levin, 'Internal thermal noise in the LIGO test masses: a direct approach,' Phys. Rev. D 57, 659-663 (1998).
[CrossRef]

Libbrecht, K. G.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Matone, L.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Meers, B. J.

B. J. Meers, 'Recycling in a laser-interferometric gravitational-wave detector,' Phys. Rev. D 38, 2317-2326 (1988).
[CrossRef]

Meidt, S.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Nakagawa, N.

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

Numata, K.

K. Numata, A. Kemery, and J. Camp, 'Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,' Phys. Rev. Lett. 93, 250602 (2004).
[CrossRef]

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, 'Wide-band direct measurement of thermal fluctuations in an interferometer,' Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

Otsuka, S.

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, 'Wide-band direct measurement of thermal fluctuations in an interferometer,' Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

Ottaway, D.

Penn, S.

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

Penn, S. D.

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

S. D. Penn, P. H. Sneddon, H. Armandula, Betzweiser, G. Cagnoli, J. Camp, D. R. M. Crooks, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, S. E. Kittelberger, M. J. Mortonson, R. Route, S. Rowan, and C. C. Vassiliou, 'Mechanical loss in tantala/silica dielectric mirror coatings,' Class. Quantum Grav. 20, 2917-2928 (2003).
[CrossRef]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

Rao, S. R.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Route, R.

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

Rowan, S.

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

Saulson, P. R.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

Schulz, K.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Sneddon, P.

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

Sneddon, P. H.

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

S. D. Penn, P. H. Sneddon, H. Armandula, Betzweiser, G. Cagnoli, J. Camp, D. R. M. Crooks, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, S. E. Kittelberger, M. J. Mortonson, R. Route, S. Rowan, and C. C. Vassiliou, 'Mechanical loss in tantala/silica dielectric mirror coatings,' Class. Quantum Grav. 20, 2917-2928 (2003).
[CrossRef]

Startin, W. J.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

Thorne, K. S.

K. S. Thorne and C. Cutler, 'An overview of gravitational wave sources,' in Proceedings of 16th International Conference on General Relativity and Gravitation, N.T.Bishop and S.D.Maharaj, eds. (World Scientific, 2002), pp. 72-112.

Tsubono, K.

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, 'Wide-band direct measurement of thermal fluctuations in an interferometer,' Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

Villar, A.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Vyatchanin, S. B.

V. B. Braginsky, M. L. Gorodetsky, and S. B. Vyatchanin, 'Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,' Phys. Lett. A 264, 1-10 (1999).
[CrossRef]

Vyatchanin, S. P.

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

V. B. Braginsky and S. P. Vyatchanin, 'Corner reflectors and quantum-non-demolition measurements in gravitational wave antennae,' Phys. Lett. A 324, 345-360 (2004).
[CrossRef]

V. B. Braginsky and S. P. Vyatchanin, 'Thermodynamical fluctuations in optical mirror coatings,' Phys. Lett. A 312, 224-255 (2003).
[CrossRef]

Yamamoto, K.

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, 'Wide-band direct measurement of thermal fluctuations in an interferometer,' Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

Zener, C.

C. Zener, 'Internal friction in solids. I. Theory of internal friction in reeds,' Phys. Rev. 52, 230-235 (1937).
[CrossRef]

Zhang, M.

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

Zucker, M.

Class. Quantum Grav. (6)

F. Acernese and the VIRGO Collaboration, ' Status of VIRGO,' Class. Quantum Grav. 19, 1421-1428 (2002).
[CrossRef]

M. Ando and the TAMA Collaboration, 'Current status of TAMA,' Class. Quantum Grav. 19, 1409-1419 (2002).
[CrossRef]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, 'Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,' Class. Quantum Grav. 19, 897-917 (2002).
[CrossRef]

D. R. M. Crooks, P. Sneddon, G. Cagnoli, J. Hough, S. Rowan, M. M. Fejer, E. Gustafson, R. Route, N. Nakagawa, D. Coyne, G. M. Harry, and A. M. Gretarsson, 'Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors,' Class. Quantum Grav. 19-5, 883-896 (2002).
[CrossRef]

S. D. Penn, P. H. Sneddon, H. Armandula, Betzweiser, G. Cagnoli, J. Camp, D. R. M. Crooks, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, S. E. Kittelberger, M. J. Mortonson, R. Route, S. Rowan, and C. C. Vassiliou, 'Mechanical loss in tantala/silica dielectric mirror coatings,' Class. Quantum Grav. 20, 2917-2928 (2003).
[CrossRef]

D. R. M. Crooks, G. Cagnoli, M. M. Fejer, A. M. Gretarsson, G. M. Harry, J. Hough, N. Nakagawa, S. Penn, R. Route, S. Rowan, and P. H. Sneddon, 'Experimental measurements of coating mechanical loss factors,' Class. Quantum Grav. 21, S1059-S1065 (2004).
[CrossRef]

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

B. Abbott and The LIGO Science Collaboration, 'Detector description and performance for the first coincidence observations between LIGO and GEO,' Nucl. Instrum. Methods Phys. Res. A 517, 154-179 (2004).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (5)

V. B. Braginsky and S. P. Vyatchanin, 'Thermodynamical fluctuations in optical mirror coatings,' Phys. Lett. A 312, 224-255 (2003).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and S. B. Vyatchanin, 'Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,' Phys. Lett. A 264, 1-10 (1999).
[CrossRef]

E. D. Black, A. Villar, K. Barbary, A. Bushmaker, J. Heefner, S. Kawamura, F. Kawazoe, L. Matone, S. Meidt, S. R. Rao, K. Schulz, M. Zhang, and K. G. Libbrecht, 'Direct observation of broadband coating thermal noise in a suspended interferometer,' Phys. Lett. A 328, 1-5 (2004).
[CrossRef]

V. B. Braginsky and S. P. Vyatchanin, 'Corner reflectors and quantum-non-demolition measurements in gravitational wave antennae,' Phys. Lett. A 324, 345-360 (2004).
[CrossRef]

F. Ya. Khalili, 'Reducing the mirrors coating noise in laser gravitational-wave antennae by means of double mirrors,' Phys. Lett. A 334, 67-72 (2005).
[CrossRef]

Phys. Rev. (2)

H. B. Callen and R. F. Greene, 'On a theorem of irreversible thermodynamics,' Phys. Rev. 86, 702-710 (1952).
[CrossRef]

C. Zener, 'Internal friction in solids. I. Theory of internal friction in reeds,' Phys. Rev. 52, 230-235 (1937).
[CrossRef]

Phys. Rev. D (3)

M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, 'Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,' Phys. Rev. D 70, 082003 (2004).
[CrossRef]

Yu. Levin, 'Internal thermal noise in the LIGO test masses: a direct approach,' Phys. Rev. D 57, 659-663 (1998).
[CrossRef]

B. J. Meers, 'Recycling in a laser-interferometric gravitational-wave detector,' Phys. Rev. D 38, 2317-2326 (1988).
[CrossRef]

Phys. Rev. Lett. (2)

K. Numata, A. Kemery, and J. Camp, 'Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,' Phys. Rev. Lett. 93, 250602 (2004).
[CrossRef]

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, 'Wide-band direct measurement of thermal fluctuations in an interferometer,' Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

Other (1)

K. S. Thorne and C. Cutler, 'An overview of gravitational wave sources,' in Proceedings of 16th International Conference on General Relativity and Gravitation, N.T.Bishop and S.D.Maharaj, eds. (World Scientific, 2002), pp. 72-112.

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Figures (5)

Fig. 1
Fig. 1

Schematic drawing of a gravitational wave interferometer. The laser on the left puts light into the system, which then passes the power recycling mirror and is then divided by the beam splitter into two beams going to each arm. The arms are Fabry–Perot cavities formed by an input test mirror and an end test mirror. The light power in each cavity is shown.

Fig. 2
Fig. 2

Photographs of the LIGO sites: left, Livingston, Louisiana; right, Hanford, Washington. Each arm reaches 4 km from the building at the corner.

Fig. 3
Fig. 3

Noise for the 4 km long LIGO interferometer in Hanford (left). The solid curve is the design noise; the curves above that show the measured noise from September 2002 to August 2004. The design sensitivity of the proposed Advanced LIGO interferometer is shown on the right. Note the difference in the y-axis offset between the two graphs; the Advanced LIGO will have lower noise (about a factor of 15) than the initial LIGO in most bands.

Fig. 4
Fig. 4

Schematic of the thin-disk experimental setup is presented on the left, showing the welded silica suspension and birefringence readout. A schematic of the thick-disk experimental setup is presented on the right, showing the interferometer readout and related electronics.

Fig. 5
Fig. 5

Direct measurement of coating thermal noise by LIGO's thermal noise interferometer (TNI). Direct measurements allow a check on the inferred coating loss angles from ringdown measurements. The noise between 500 Hz and 6 kHz is due to thermal noise from the coating.

Tables (3)

Tables Icon

Table 1 Requirements for the Advanced LIGO Coating a

Tables Icon

Table 2 Results of the First Round of the Mechanical Loss Experiments a

Tables Icon

Table 3 Mechanical Loss of SiO2∕TiO2-Doped Ta2O5 Coatings from LMA∕Virgo a

Equations (14)

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

G m v 2 / ( r c 4 ) 10 21 ( m M ) ( v c ) 2 ( 100   Mpc r ) ,
S x ( f ) = 2 k B T ϕ eff ( 1 σ ) / ( π 3 / 2 f w Y )
ϕ eff = ϕ + d / ( π w Y ) ( { Y / ( 1 σ ) 2 σ     2 Y Y / [ Y ( 1 σ 2 ) ( 1 σ ) ] } ϕ + Y σ ( 1 2 σ ) / [ ( 1 σ ) ( 1 σ ) ] ( ϕ ϕ ) + Y Y ( 1 + σ ) ×   ( 1 2 σ ) 2 / [ Y ( 1 σ     2 ) ( 1 σ ) ] ϕ ) ,
ϕ eff ϕ + d / ( π w ) ( Y / Y ϕ + Y / Y ϕ ) .
Y = ( d 1 + d 2 ) / ( d 1 / Y 1 + d 2 / Y 2 ) ,
Y = ( Y 1 d 1 + Y 2 d 2 ) / ( d 1 + d 2 ) ,
σ = ( σ 1 Y 1 d 1 + σ 2 Y 2 d 2 ) / ( Y 1 d 1 + Y 2 d 2 ) ,
ϕ = Y ( ϕ 1 d 1 / Y 1 + ϕ 2 d 2 / Y 2 ) ,
ϕ = ( Y 1 ϕ 1 d 1 + Y 2 ϕ 2 d 2 ) / ( Y ( d 1 + d 2 ) ) ,
1 / Q coated = 1 / Q uncoated + ϕ E coating / E total ,
ϕ SiO 2 = 0.5 ± 0.3 × 10 4 ,
ϕ Ta 2 O 5 = 4.4 ± 0.2 × 10 4 .
ϕ SiO 2 = ( 0.4 ± 0.3 ) × 10 4 + f ( 2.7 ± 0.9 ) × 10 9 ,
ϕ Ta 2 O 5 = ( 4.2 ± 0.4 ) × 10 4 + f ( 0.4 ± 0.9 ) × 10 9 ,

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