Abstract

An optical system that comprises two devices for remote measurements, a broadband optical interferometer and a scanning Hartmann sensor, is described. The results of simultaneous measurements with both devices and the results of numerical modeling of sample surface heating are presented.

© 2006 Optical Society of America

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  1. J. Degallaix, C. Zhao, J. Li, and D. Blair, "Thermal lensing compensation for AIGO high optical power test facilities," Class. Quantum Grav. 21, 903-908 (2004).
    [CrossRef]
  2. A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, "LIGO--the Laser-Interferometer-Gravitational-Wave Observatory," Science 256, 325-333 (1992).
    [CrossRef] [PubMed]
  3. M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.
  4. J. Hecht, "Laser weapons go solid-state," Laser Focus World 40, 61 (2004).
  5. G. S. Gorelik, "On application of the modulation method to optical interferometry," Dokl. Akad. Nauk USSR 83, 549-552 (1952).
  6. O. Sasaki and H. Okazaki, "Sinusoidal phase modulating interferometry for surface profile measurements," Appl. Opt. 25, 3137-3140 (1986).
    [CrossRef] [PubMed]
  7. M. Adachi, H. Miki, Y. Nakai, and I. Kawaguchi, "Optical precision using the differential method," Opt. Lett. 12, 792-796 (1987).
    [CrossRef] [PubMed]
  8. Y. Y. Cheng and J. C. Wyant, "Phase shifter callibration in phase-shifting interferometry," Appl. Opt. 24, 3049-3052 (1985).
    [CrossRef] [PubMed]
  9. S. W. Kim, M. G. Kang, and G. S. Han, "Accelerated phase-measuring algorithm of least squares for phase-shifting interferometry," Opt. Eng. 36, 3101-3106 (1997).
    [CrossRef]
  10. A. G. Olszak, E. Novak, K. Stumpe, and J. Semrad, "High-performance interferometer for site flatness inspection," in Interferometry '99: Applications, P. Krzysztof and P. J. Werner, eds., Proc. SPIE 3745, 408-415 (1999).
    [CrossRef]
  11. E. Novak, A. G. Olszak, K. Stumpe, R. E. Knowlden, L. Malevanchik, and G. Z. Angeli, "Laser Fizeau interferometer for silicon wafer site flatness testing," in Surface Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE 3619, 101-109 (1999).
    [CrossRef]
  12. I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "Absolute testing of the profiles of large-size flat optical surfaces," Radiophys. Quantum Electron. 44, 575-581 (2001).
    [CrossRef]
  13. G. E. Sommarggren, "Diffraction methods raise interferometer accuracy," Laser Focus World 32, 61 (1996).
  14. I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "A new remote method for estimating the parameters of optical elements," in International Quantum Electronics Conference (IQEC) (2002), p. 147.
  15. I. E. Kozhevatov and E. H. Kulikova, "High-order broadband optical interferometry," Radiophys. Quantum Electron. 46, 65-72 (2003).
    [CrossRef]
  16. R. J. Bell, Introduction to Fourier Spectroscopy (Mir, 1975).
  17. J. Hartman, "Bemerkungen uber den Bau und die Justirung von Spektrographen," Z. Instrumentenkd. 20, 47 (1900).
  18. R. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1998).
  19. WaveFrontSciences, "CLAS-2D data sheet" (WaveFront Sciences, Albuquerque, N.M., 2002).
  20. A. K. Potemkin, A. I. Makarov, and A. N. Mal'shakov, "Measurement of small wavefront distortions of laser radiation," Opt. Spectrosc. 86, 148-152 (1999).
  21. E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
    [CrossRef]
  22. A. K. Potemkin, A. N. Mal'shakov, N. F. Andreev, and D. H. Reitze, "Use of self-focusing for measurements of ultrasmall (less than lambda/3000) wave-front distortions," J. Opt. Soc. Am. B 19, 650-655 (2002).
    [CrossRef]
  23. C. Magnan and J. C. Pecker, "Asymmetry in solar spectral lines," Highlights Astron. 3, 171-203 (1973).
  24. N. M. Belyaev and A. A. Ryadno, Methods of Thermal Conductivity Theory, Part 2 (Higher School, Moscow, 1982).
  25. L. D. Landau and E. M. Lifshitz, Theoretical Physics. Fluid Mechanics. (Science, Moscow, 1987).
  26. A. A. Samarsky and P. N. Vabishevich, Numerical Methods for Solving Inverse Problems of Mathematical Physics (USSR, Moscow, 2004).
  27. L. D. Landau and E. M. Lifshitz, Theoretical Physics. Theory of Elasticity (Science, Moscow, 1987).
  28. W. Koechner, Solid-State Laser Engineering (Springer-Verlag, 1999).

2004 (3)

J. Degallaix, C. Zhao, J. Li, and D. Blair, "Thermal lensing compensation for AIGO high optical power test facilities," Class. Quantum Grav. 21, 903-908 (2004).
[CrossRef]

J. Hecht, "Laser weapons go solid-state," Laser Focus World 40, 61 (2004).

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

2003 (1)

I. E. Kozhevatov and E. H. Kulikova, "High-order broadband optical interferometry," Radiophys. Quantum Electron. 46, 65-72 (2003).
[CrossRef]

2002 (1)

2001 (1)

I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "Absolute testing of the profiles of large-size flat optical surfaces," Radiophys. Quantum Electron. 44, 575-581 (2001).
[CrossRef]

1999 (3)

A. G. Olszak, E. Novak, K. Stumpe, and J. Semrad, "High-performance interferometer for site flatness inspection," in Interferometry '99: Applications, P. Krzysztof and P. J. Werner, eds., Proc. SPIE 3745, 408-415 (1999).
[CrossRef]

E. Novak, A. G. Olszak, K. Stumpe, R. E. Knowlden, L. Malevanchik, and G. Z. Angeli, "Laser Fizeau interferometer for silicon wafer site flatness testing," in Surface Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE 3619, 101-109 (1999).
[CrossRef]

A. K. Potemkin, A. I. Makarov, and A. N. Mal'shakov, "Measurement of small wavefront distortions of laser radiation," Opt. Spectrosc. 86, 148-152 (1999).

1997 (1)

S. W. Kim, M. G. Kang, and G. S. Han, "Accelerated phase-measuring algorithm of least squares for phase-shifting interferometry," Opt. Eng. 36, 3101-3106 (1997).
[CrossRef]

1996 (1)

G. E. Sommarggren, "Diffraction methods raise interferometer accuracy," Laser Focus World 32, 61 (1996).

1992 (1)

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

1987 (1)

1986 (1)

1985 (1)

1973 (1)

C. Magnan and J. C. Pecker, "Asymmetry in solar spectral lines," Highlights Astron. 3, 171-203 (1973).

1952 (1)

G. S. Gorelik, "On application of the modulation method to optical interferometry," Dokl. Akad. Nauk USSR 83, 549-552 (1952).

1900 (1)

J. Hartman, "Bemerkungen uber den Bau und die Justirung von Spektrographen," Z. Instrumentenkd. 20, 47 (1900).

Abramovici, A.

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

Adachi, M.

Althouse, W. E.

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

Amin, R. S.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

Andreev, N. F.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

A. K. Potemkin, A. N. Mal'shakov, N. F. Andreev, and D. H. Reitze, "Use of self-focusing for measurements of ultrasmall (less than lambda/3000) wave-front distortions," J. Opt. Soc. Am. B 19, 650-655 (2002).
[CrossRef]

Angeli, G. Z.

E. Novak, A. G. Olszak, K. Stumpe, R. E. Knowlden, L. Malevanchik, and G. Z. Angeli, "Laser Fizeau interferometer for silicon wafer site flatness testing," in Surface Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE 3619, 101-109 (1999).
[CrossRef]

Bell, R. J.

R. J. Bell, Introduction to Fourier Spectroscopy (Mir, 1975).

Belyaev, N. M.

N. M. Belyaev and A. A. Ryadno, Methods of Thermal Conductivity Theory, Part 2 (Higher School, Moscow, 1982).

Blair, D.

J. Degallaix, C. Zhao, J. Li, and D. Blair, "Thermal lensing compensation for AIGO high optical power test facilities," Class. Quantum Grav. 21, 903-908 (2004).
[CrossRef]

Cheng, Y. Y.

Cheragin, N. P.

I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "Absolute testing of the profiles of large-size flat optical surfaces," Radiophys. Quantum Electron. 44, 575-581 (2001).
[CrossRef]

I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "A new remote method for estimating the parameters of optical elements," in International Quantum Electronics Conference (IQEC) (2002), p. 147.

Degallaix, J.

J. Degallaix, C. Zhao, J. Li, and D. Blair, "Thermal lensing compensation for AIGO high optical power test facilities," Class. Quantum Grav. 21, 903-908 (2004).
[CrossRef]

Drever, R. W. P.

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

Eguchi, T.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Gorelik, G. S.

G. S. Gorelik, "On application of the modulation method to optical interferometry," Dokl. Akad. Nauk USSR 83, 549-552 (1952).

Gursel, Y.

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

Han, G. S.

S. W. Kim, M. G. Kang, and G. S. Han, "Accelerated phase-measuring algorithm of least squares for phase-shifting interferometry," Opt. Eng. 36, 3101-3106 (1997).
[CrossRef]

Hartman, J.

J. Hartman, "Bemerkungen uber den Bau und die Justirung von Spektrographen," Z. Instrumentenkd. 20, 47 (1900).

Hecht, J.

J. Hecht, "Laser weapons go solid-state," Laser Focus World 40, 61 (2004).

Ivanov, I.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

Izawa, Y.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Kan, H.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Kanabe, T.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Kandasamy, R.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Kang, M. G.

S. W. Kim, M. G. Kang, and G. S. Han, "Accelerated phase-measuring algorithm of least squares for phase-shifting interferometry," Opt. Eng. 36, 3101-3106 (1997).
[CrossRef]

Kanzaki, T.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Kawada, Y.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Kawaguchi, I.

Kawamura, S.

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

Kawashima, T.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Khazanov, E. A.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

Kim, S. W.

S. W. Kim, M. G. Kang, and G. S. Han, "Accelerated phase-measuring algorithm of least squares for phase-shifting interferometry," Opt. Eng. 36, 3101-3106 (1997).
[CrossRef]

Knowlden, R. E.

E. Novak, A. G. Olszak, K. Stumpe, R. E. Knowlden, L. Malevanchik, and G. Z. Angeli, "Laser Fizeau interferometer for silicon wafer site flatness testing," in Surface Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE 3619, 101-109 (1999).
[CrossRef]

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, 1999).

Kozhevatov, I. E.

I. E. Kozhevatov and E. H. Kulikova, "High-order broadband optical interferometry," Radiophys. Quantum Electron. 46, 65-72 (2003).
[CrossRef]

I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "Absolute testing of the profiles of large-size flat optical surfaces," Radiophys. Quantum Electron. 44, 575-581 (2001).
[CrossRef]

I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "A new remote method for estimating the parameters of optical elements," in International Quantum Electronics Conference (IQEC) (2002), p. 147.

Kulikova, E. H.

I. E. Kozhevatov and E. H. Kulikova, "High-order broadband optical interferometry," Radiophys. Quantum Electron. 46, 65-72 (2003).
[CrossRef]

I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "Absolute testing of the profiles of large-size flat optical surfaces," Radiophys. Quantum Electron. 44, 575-581 (2001).
[CrossRef]

I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "A new remote method for estimating the parameters of optical elements," in International Quantum Electronics Conference (IQEC) (2002), p. 147.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Theoretical Physics. Theory of Elasticity (Science, Moscow, 1987).

L. D. Landau and E. M. Lifshitz, Theoretical Physics. Fluid Mechanics. (Science, Moscow, 1987).

Li, J.

J. Degallaix, C. Zhao, J. Li, and D. Blair, "Thermal lensing compensation for AIGO high optical power test facilities," Class. Quantum Grav. 21, 903-908 (2004).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Theoretical Physics. Fluid Mechanics. (Science, Moscow, 1987).

L. D. Landau and E. M. Lifshitz, Theoretical Physics. Theory of Elasticity (Science, Moscow, 1987).

Magnan, C.

C. Magnan and J. C. Pecker, "Asymmetry in solar spectral lines," Highlights Astron. 3, 171-203 (1973).

Makarov, A. I.

A. K. Potemkin, A. I. Makarov, and A. N. Mal'shakov, "Measurement of small wavefront distortions of laser radiation," Opt. Spectrosc. 86, 148-152 (1999).

Malevanchik, L.

E. Novak, A. G. Olszak, K. Stumpe, R. E. Knowlden, L. Malevanchik, and G. Z. Angeli, "Laser Fizeau interferometer for silicon wafer site flatness testing," in Surface Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE 3619, 101-109 (1999).
[CrossRef]

Mal'shakov, A. N.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

A. K. Potemkin, A. N. Mal'shakov, N. F. Andreev, and D. H. Reitze, "Use of self-focusing for measurements of ultrasmall (less than lambda/3000) wave-front distortions," J. Opt. Soc. Am. B 19, 650-655 (2002).
[CrossRef]

A. K. Potemkin, A. I. Makarov, and A. N. Mal'shakov, "Measurement of small wavefront distortions of laser radiation," Opt. Spectrosc. 86, 148-152 (1999).

Matsui, H.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Miki, H.

Miyajima, H.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Miyamoto, M.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Mueller, G.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

Nakai, S.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Nakai, Y.

Nakatsuka, M.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Novak, E.

E. Novak, A. G. Olszak, K. Stumpe, R. E. Knowlden, L. Malevanchik, and G. Z. Angeli, "Laser Fizeau interferometer for silicon wafer site flatness testing," in Surface Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE 3619, 101-109 (1999).
[CrossRef]

A. G. Olszak, E. Novak, K. Stumpe, and J. Semrad, "High-performance interferometer for site flatness inspection," in Interferometry '99: Applications, P. Krzysztof and P. J. Werner, eds., Proc. SPIE 3745, 408-415 (1999).
[CrossRef]

Okada, Y.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Okazaki, H.

Olszak, A. G.

A. G. Olszak, E. Novak, K. Stumpe, and J. Semrad, "High-performance interferometer for site flatness inspection," in Interferometry '99: Applications, P. Krzysztof and P. J. Werner, eds., Proc. SPIE 3745, 408-415 (1999).
[CrossRef]

E. Novak, A. G. Olszak, K. Stumpe, R. E. Knowlden, L. Malevanchik, and G. Z. Angeli, "Laser Fizeau interferometer for silicon wafer site flatness testing," in Surface Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE 3619, 101-109 (1999).
[CrossRef]

Palashov, O. V.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

Pecker, J. C.

C. Magnan and J. C. Pecker, "Asymmetry in solar spectral lines," Highlights Astron. 3, 171-203 (1973).

Potemkin, A. K.

A. K. Potemkin, A. N. Mal'shakov, N. F. Andreev, and D. H. Reitze, "Use of self-focusing for measurements of ultrasmall (less than lambda/3000) wave-front distortions," J. Opt. Soc. Am. B 19, 650-655 (2002).
[CrossRef]

A. K. Potemkin, A. I. Makarov, and A. N. Mal'shakov, "Measurement of small wavefront distortions of laser radiation," Opt. Spectrosc. 86, 148-152 (1999).

Poteomkin, A. K.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

Raab, F. J.

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

Reitze, D. H.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

A. K. Potemkin, A. N. Mal'shakov, N. F. Andreev, and D. H. Reitze, "Use of self-focusing for measurements of ultrasmall (less than lambda/3000) wave-front distortions," J. Opt. Soc. Am. B 19, 650-655 (2002).
[CrossRef]

Rudenchik, E. A.

I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "Absolute testing of the profiles of large-size flat optical surfaces," Radiophys. Quantum Electron. 44, 575-581 (2001).
[CrossRef]

I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "A new remote method for estimating the parameters of optical elements," in International Quantum Electronics Conference (IQEC) (2002), p. 147.

Ryadno, A. A.

N. M. Belyaev and A. A. Ryadno, Methods of Thermal Conductivity Theory, Part 2 (Higher School, Moscow, 1982).

Samarsky, A. A.

A. A. Samarsky and P. N. Vabishevich, Numerical Methods for Solving Inverse Problems of Mathematical Physics (USSR, Moscow, 2004).

Sasaki, O.

Semrad, J.

A. G. Olszak, E. Novak, K. Stumpe, and J. Semrad, "High-performance interferometer for site flatness inspection," in Interferometry '99: Applications, P. Krzysztof and P. J. Werner, eds., Proc. SPIE 3745, 408-415 (1999).
[CrossRef]

Sergeev, A. M.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

Shaykin, A. A.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

Shoemaker, D.

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

Sievers, L.

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

Sommarggren, G. E.

G. E. Sommarggren, "Diffraction methods raise interferometer accuracy," Laser Focus World 32, 61 (1996).

Spero, R. E.

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

Stumpe, K.

E. Novak, A. G. Olszak, K. Stumpe, R. E. Knowlden, L. Malevanchik, and G. Z. Angeli, "Laser Fizeau interferometer for silicon wafer site flatness testing," in Surface Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE 3619, 101-109 (1999).
[CrossRef]

A. G. Olszak, E. Novak, K. Stumpe, and J. Semrad, "High-performance interferometer for site flatness inspection," in Interferometry '99: Applications, P. Krzysztof and P. J. Werner, eds., Proc. SPIE 3745, 408-415 (1999).
[CrossRef]

Tanner, D. B.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

Thorne, K. S.

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

Tyson, R.

R. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1998).

Vabishevich, P. N.

A. A. Samarsky and P. N. Vabishevich, Numerical Methods for Solving Inverse Problems of Mathematical Physics (USSR, Moscow, 2004).

Vogt, R. E.

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

Weiss, R.

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

Whitcomb, S. E.

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

Wyant, J. C.

Yamanaka, M.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

Zelenogorsky, V. V.

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

Zhao, C.

J. Degallaix, C. Zhao, J. Li, and D. Blair, "Thermal lensing compensation for AIGO high optical power test facilities," Class. Quantum Grav. 21, 903-908 (2004).
[CrossRef]

Zucker, M. E.

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

Appl. Opt. (2)

Class. Quantum Grav. (1)

J. Degallaix, C. Zhao, J. Li, and D. Blair, "Thermal lensing compensation for AIGO high optical power test facilities," Class. Quantum Grav. 21, 903-908 (2004).
[CrossRef]

Dokl. Akad. Nauk USSR (1)

G. S. Gorelik, "On application of the modulation method to optical interferometry," Dokl. Akad. Nauk USSR 83, 549-552 (1952).

IEEE J. Quantum Electron. (1)

E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

Laser Focus World (2)

J. Hecht, "Laser weapons go solid-state," Laser Focus World 40, 61 (2004).

G. E. Sommarggren, "Diffraction methods raise interferometer accuracy," Laser Focus World 32, 61 (1996).

Opt. Eng. (1)

S. W. Kim, M. G. Kang, and G. S. Han, "Accelerated phase-measuring algorithm of least squares for phase-shifting interferometry," Opt. Eng. 36, 3101-3106 (1997).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (1)

A. K. Potemkin, A. I. Makarov, and A. N. Mal'shakov, "Measurement of small wavefront distortions of laser radiation," Opt. Spectrosc. 86, 148-152 (1999).

Proc. SPIE (2)

A. G. Olszak, E. Novak, K. Stumpe, and J. Semrad, "High-performance interferometer for site flatness inspection," in Interferometry '99: Applications, P. Krzysztof and P. J. Werner, eds., Proc. SPIE 3745, 408-415 (1999).
[CrossRef]

E. Novak, A. G. Olszak, K. Stumpe, R. E. Knowlden, L. Malevanchik, and G. Z. Angeli, "Laser Fizeau interferometer for silicon wafer site flatness testing," in Surface Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE 3619, 101-109 (1999).
[CrossRef]

Radiophys. Quantum Electron. (2)

I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "Absolute testing of the profiles of large-size flat optical surfaces," Radiophys. Quantum Electron. 44, 575-581 (2001).
[CrossRef]

I. E. Kozhevatov and E. H. Kulikova, "High-order broadband optical interferometry," Radiophys. Quantum Electron. 46, 65-72 (2003).
[CrossRef]

Science (1)

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

Z. Instrumentenkd. (1)

J. Hartman, "Bemerkungen uber den Bau und die Justirung von Spektrographen," Z. Instrumentenkd. 20, 47 (1900).

Other (11)

R. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1998).

WaveFrontSciences, "CLAS-2D data sheet" (WaveFront Sciences, Albuquerque, N.M., 2002).

R. J. Bell, Introduction to Fourier Spectroscopy (Mir, 1975).

I. E. Kozhevatov, E. A. Rudenchik, N. P. Cheragin, and E. H. Kulikova, "A new remote method for estimating the parameters of optical elements," in International Quantum Electronics Conference (IQEC) (2002), p. 147.

M. Yamanaka, H. Matsui, Y. Kawada, R. Kandasamy, T. Eguchi, T. Kanabe, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kawashima, Y. Okada, T. Kanzaki, H. Miyajima, M. Miyamoto, and H. Kan, "Laser-diode pumped 10J × 10Hz Nd: glass slab laser for inertial fusion energy," paper TuO2cl 199 presented at the First International Conference on Inertial Fusion Sciences and Applications, Bordeaux, France, 12-17 September 1999.

C. Magnan and J. C. Pecker, "Asymmetry in solar spectral lines," Highlights Astron. 3, 171-203 (1973).

N. M. Belyaev and A. A. Ryadno, Methods of Thermal Conductivity Theory, Part 2 (Higher School, Moscow, 1982).

L. D. Landau and E. M. Lifshitz, Theoretical Physics. Fluid Mechanics. (Science, Moscow, 1987).

A. A. Samarsky and P. N. Vabishevich, Numerical Methods for Solving Inverse Problems of Mathematical Physics (USSR, Moscow, 2004).

L. D. Landau and E. M. Lifshitz, Theoretical Physics. Theory of Elasticity (Science, Moscow, 1987).

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, 1999).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the Michelson interferometer: S, point source; L1, collimator; BS, beam splitter; M, reference mirror; D, diaphragm; L2, output objective.

Fig. 2
Fig. 2

Schematic of the Fizeau interferometer: L, objective.

Fig. 3
Fig. 3

Optical layout of the broadband optical interferometer: S1, point light source, light-emitting diode; objective O1, collimator; M1–M4, half-transparent flat mirrors; O2, objective; D, diaphragm; PSS, CO2 laser power stabilization system.

Fig. 4
Fig. 4

Shack–Hartmann sensor.

Fig. 5
Fig. 5

Scanning Hartmann sensor: GR, galvanometer-based rotator.

Fig. 6
Fig. 6

Optical layout of the experimental setup: S1, point light source; O1, O2, objectives; M1–M4, flat semitransparent mirrors; D, diaphragm; O3, O4, lenses; M6, rotating mirror; M5, salt plate; A, controllable mechanical attenuator; SM, stepper motor moving the attenuator; PM, powermeter.

Fig. 7
Fig. 7

Transverse intensity distribution of CO2 laser beams (points) and Gaussian function (solid curve).

Fig. 8
Fig. 8

Interferograms of stationary states of the sample (a) not heated and (b) heated by the CO2 laser and (c) profile of the heating-induced change in the optical thickness of the sample.

Fig. 9
Fig. 9

Experimental results (thicker curves) and numerical modeling (thinner curves) of changes of optical thickness measured by the optical interferometer (solid curves) and changes of phase front measured by the scanning Hartmann sensor (dashed curves) at surface heating of a fused-silica sample by CO2 laser radiation with powers (a) 85 and (b) 30 mW along horizontal axis x.

Equations (17)

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

I ( Δ ) = A ( Δ ) cos Ψ ( Δ ) ,
Ψ ( Δ ) = 2 π Δ / λ ,
δ = λ 0 ( λ 0 / Δ λ ) ,
Δ = λ 0 ( λ 0 / δ λ ) .
α i = ( x 2 , i x 1 , i ) / F 3 ,
w i = 0 ,
w i = j = 1 N ( α j 1 + α j ) h x 2 , i > 1 ,
C p ρ T ( r ) t = κ 2 T ( r ) + q ( r , t ) ,
κ T ( r ) n 0 = σ ε [ T ( r ) ] [ T ( r ) ] 4 + q s , r S , t > 0 ,
μ Δ U + ( λ + μ ) ( U ) = α T ( λ + 2 3 μ ) T ,
U i k = 1 2 ( U i r k + U k r i ) .
σ i k n k = 0
σ i j = 2 μ U i j + [ λ U k k ( λ + 2 3 μ ) α T ] δ i j .
Δ L i = 0 l [ 1 2 n 3 π i i k l σ k l β T n 0     3 + ( n 1 ) U z z ] d z ,
ϕ = ( n 1 ) L , h = n l ,
Δϕ = [ P + ( n 0 1 ) α T ] L Δ T , Δ h = ( P + n 0 α T ) L Δ T ,
P = β α T n 0     3 4 1 + ν 1 ν ( p 11 + p 12 )

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