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## High-precision methods and devices for **
***in situ*
measurements of thermally induced aberrations in optical elements

*in situ*

Victor V. Zelenogorsky, Alexander A. Solovyov, Ilya E. Kozhevatov, Eugene E. Kamenetsky, Eugene A. Rudenchik, Oleg V. Palashov, Dmitry E. Silin, and Efim A. Khazanov »View Author Affiliations

^{1}Alexander A. Solovyov,

^{1}Ilya E. Kozhevatov,

^{1}Eugene E. Kamenetsky,

^{1}Eugene A. Rudenchik,

^{1}Oleg V. Palashov,

^{1}Dmitry E. Silin,

^{1}and Efim A. Khazanov

^{1}

^{1}The authors are with the Institute of Applied Physics of the Russian Academy of Science, Uljanov Street 46, Nizhny Novgorod, 603950, Russia. V. Zelenogorsky's e-mail address is vvmailv@mail.ru.

Applied Optics, Vol. 45, Issue 17, pp. 4092-4101 (2006)

http://dx.doi.org/10.1364/AO.45.004092

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### 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

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(120.6810) Instrumentation, measurement, and metrology : Thermal effects

**History**

Original Manuscript: October 20, 2005

Manuscript Accepted: December 17, 2005

**Citation**

Victor V. Zelenogorsky, Alexander A. Solovyov, Ilya E. Kozhevatov, Eugene E. Kamenetsky, Eugene A. Rudenchik, Oleg V. Palashov, Dmitry E. Silin, and Efim A. Khazanov, "High-precision methods and devices for in situ measurements of thermally induced aberrations in optical elements," Appl. Opt. **45**, 4092-4101 (2006)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-17-4092

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### References

- 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]
- 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]
- 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.
- J. Hecht, "Laser weapons go solid-state," Laser Focus World 40, 61 (2004).
- G. S. Gorelik, "On application of the modulation method to optical interferometry," Dokl. Akad. Nauk USSR 83, 549-552 (1952).
- O. Sasaki and H. Okazaki, "Sinusoidal phase modulating interferometry for surface profile measurements," Appl. Opt. 25, 3137-3140 (1986). [CrossRef] [PubMed]
- M. Adachi, H. Miki, Y. Nakai, and I. Kawaguchi, "Optical precision using the differential method," Opt. Lett. 12, 792-796 (1987). [CrossRef] [PubMed]
- Y. Y. Cheng and J. C. Wyant, "Phase shifter callibration in phase-shifting interferometry," Appl. Opt. 24, 3049-3052 (1985). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- G. E. Sommarggren, "Diffraction methods raise interferometer accuracy," Laser Focus World 32, 61 (1996).
- 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.
- I. E. Kozhevatov and E. H. Kulikova, "High-order broadband optical interferometry," Radiophys. Quantum Electron. 46, 65-72 (2003). [CrossRef]
- R. J. Bell, Introduction to Fourier Spectroscopy (Mir, 1975).
- J. Hartman, "Bemerkungen uber den Bau und die Justirung von Spektrographen," Z. Instrumentenkd. 20, 47 (1900).
- R. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1998).
- WaveFrontSciences, "CLAS-2D data sheet" (WaveFront Sciences, Albuquerque, N.M., 2002).
- 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).
- 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]
- 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).

**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.**

**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.**

**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.**

**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.**

**Kanabe, T.**

**Kandasamy, R.**

**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.**

**Kawada, Y.**

**Kawaguchi, I.**

**Kawamura, S.**

**Kawashima, T.**

**Khazanov, E. A.**

**Kim, S. W.**

**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]

**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.**

**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.**

**Mal'shakov, A. N.**

- 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.**

**Miki, H.**

**Miyajima, H.**

**Miyamoto, M.**

**Mueller, G.**

**Nakai, S.**

**Nakai, Y.**

**Nakatsuka, M.**

**Novak, E.**

- 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.**

**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]

**Palashov, O. V.**

**Pecker, J. C.**

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

**Potemkin, A. K.**

**Poteomkin, A. K.**

**Raab, F. J.**

**Reitze, D. H.**

**Rudenchik, E. A.**

**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.**

**Sergeev, A. M.**

**Shaykin, A. A.**

**Shoemaker, D.**

**Sievers, L.**

**Sommarggren, G. E.**

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

**Spero, R. E.**

**Stumpe, K.**

**Tanner, D. B.**

**Thorne, K. S.**

**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.**

**Weiss, R.**

**Whitcomb, S. E.**

**Wyant, J. C.**

**Yamanaka, M.**

**Zelenogorsky, V. V.**

**Zhao, C.**

**Zucker, M. E.**

### Appl. Opt.

- Y. Y. Cheng and J. C. Wyant, "Phase shifter callibration in phase-shifting interferometry," Appl. Opt. 24, 3049-3052 (1985). [CrossRef] [PubMed]
- O. Sasaki and H. Okazaki, "Sinusoidal phase modulating interferometry for surface profile measurements," Appl. Opt. 25, 3137-3140 (1986). [CrossRef] [PubMed]

### Class. Quantum Grav.

### Dokl. Akad. Nauk USSR

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

### IEEE J. Quantum Electron.

### J. Opt. Soc. Am. B

### Laser Focus World

- 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.

### Opt. Lett.

- M. Adachi, H. Miki, Y. Nakai, and I. Kawaguchi, "Optical precision using the differential method," Opt. Lett. 12, 792-796 (1987). [CrossRef] [PubMed]

### Opt. Spectrosc.

### Proc. SPIE

### Radiophys. Quantum Electron.

### Science

### Z. Instrumentenkd.

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

### Other

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

**2004, Degallaix, Class. Quantum Grav.**

**2004, Hecht, Laser Focus World**

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

**2004, Khazanov, IEEE J. Quantum Electron.**

**2003, Kozhevatov, Radiophys. Quantum Electron.**

**2002, Potemkin, J. Opt. Soc. Am. B**

**2001, Kozhevatov, Radiophys. Quantum Electron.**

**1999, Olszak, Proc. SPIE**

**1999, Novak, Proc. SPIE**

**1999, Potemkin, Opt. Spectrosc.**

**1997, Kim, Opt. Eng.**

**1996, Sommarggren, Laser Focus World**

**1992, Abramovici, Science**

**1987, Adachi, Opt. Lett.**

**1986, Sasaki, Appl. Opt.**

**1985, Cheng, Appl. Opt.**

**1973, Magnan,**

**1952, Gorelik, Dokl. Akad. Nauk USSR**

**1900, Hartman, Z. Instrumentenkd.**

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