Abstract

Results of the use of self-focusing in Kerr liquids for the measurement of small wave-front distortions transmitted through a transparent optical sample are presented. Using controlled self-focusing to decrease the spot size of the deflected beam, we have been able to improve the measurement resolution by an order of magnitude compared with that achieved with a conventional Hartmann detector. We examine a variety of materials to determine the optimal nonlinear medium and demonstrate measurements of absolute wave-front deviations at the level of λ/3000. A prototype of a new device, the scanning nonlinear Hartmann sensor, is described.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  2. M. J. Lavan, W. K. Cadwallender, and T. F. Van Damme, “Optical heterodyne interferometer with radio frequency phase reference,” Appl. Opt. 15, 2627–2631 (1976).
    [CrossRef] [PubMed]
  3. A. D. Valuev, B. L. Vasin, N. N. Ilichev, and S. I. Fedorov, “The PIR-1 device for measurements of laser beam divergence,” Kvantovaya Elektron. (Moscow) 5, 951–951 (1978).
  4. M. Abitbol and N. Ben-Yosef, “Use of the Hartmann sensor to measure the unisoplanatic wavefront tilt,” Appl. Opt. 30, 1512–1516 (1991).
    [CrossRef] [PubMed]
  5. D. R. Neal, W. J. Alford, J. K. Gruetzner, and N. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Micromachining and Microfabrication Process Technology II, S. Chang and S. W. Pang, eds., Proc. SPIE 2879, 72–82 (1994).
  6. A. I. Makarov, A. N. Malshakov, and A. K. Potemkin, “Measurement of small distortions of the wavefront of laser radiation,” Opt. Spectrosc. 86, 148–152 (1999).
  7. S. L. Shapiro, Ultrashort Light Pulses (Springer-Verlag, Berlin, 1977).
  8. Y. R. Shen, Self-Focusing: Experimental, Prog. Quantum Electron. 4, 3–34 (1975).
    [CrossRef]
  9. A. N. Malshakov, G. A. Pasmanik, and A. K. Potemkin, “Comparative characteristics of magneto-optical materials,” Appl. Opt. 36, 6403–6410 (1997).
    [CrossRef]
  10. A. Angot, Mathematics for Radio Engineers (Nauka, Moscow, 1965), pp. 615–621.
  11. 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]

1999 (1)

A. I. Makarov, A. N. Malshakov, and A. K. Potemkin, “Measurement of small distortions of the wavefront of laser radiation,” Opt. Spectrosc. 86, 148–152 (1999).

1997 (1)

1994 (1)

D. R. Neal, W. J. Alford, J. K. Gruetzner, and N. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Micromachining and Microfabrication Process Technology II, S. Chang and S. W. Pang, eds., Proc. SPIE 2879, 72–82 (1994).

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]

1991 (1)

1978 (1)

A. D. Valuev, B. L. Vasin, N. N. Ilichev, and S. I. Fedorov, “The PIR-1 device for measurements of laser beam divergence,” Kvantovaya Elektron. (Moscow) 5, 951–951 (1978).

1976 (1)

1975 (1)

Y. R. Shen, Self-Focusing: Experimental, Prog. Quantum Electron. 4, 3–34 (1975).
[CrossRef]

Abitbol, M.

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]

Alford, W. J.

D. R. Neal, W. J. Alford, J. K. Gruetzner, and N. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Micromachining and Microfabrication Process Technology II, S. Chang and S. W. Pang, eds., Proc. SPIE 2879, 72–82 (1994).

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]

Ben-Yosef, N.

Cadwallender, W. K.

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]

Fedorov, S. I.

A. D. Valuev, B. L. Vasin, N. N. Ilichev, and S. I. Fedorov, “The PIR-1 device for measurements of laser beam divergence,” Kvantovaya Elektron. (Moscow) 5, 951–951 (1978).

Gruetzner, J. K.

D. R. Neal, W. J. Alford, J. K. Gruetzner, and N. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Micromachining and Microfabrication Process Technology II, S. Chang and S. W. Pang, eds., Proc. SPIE 2879, 72–82 (1994).

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]

Ilichev, N. N.

A. D. Valuev, B. L. Vasin, N. N. Ilichev, and S. I. Fedorov, “The PIR-1 device for measurements of laser beam divergence,” Kvantovaya Elektron. (Moscow) 5, 951–951 (1978).

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]

Lavan, M. J.

Makarov, A. I.

A. I. Makarov, A. N. Malshakov, and A. K. Potemkin, “Measurement of small distortions of the wavefront of laser radiation,” Opt. Spectrosc. 86, 148–152 (1999).

Malshakov, A. N.

A. I. Makarov, A. N. Malshakov, and A. K. Potemkin, “Measurement of small distortions of the wavefront of laser radiation,” Opt. Spectrosc. 86, 148–152 (1999).

A. N. Malshakov, G. A. Pasmanik, and A. K. Potemkin, “Comparative characteristics of magneto-optical materials,” Appl. Opt. 36, 6403–6410 (1997).
[CrossRef]

Neal, D. R.

D. R. Neal, W. J. Alford, J. K. Gruetzner, and N. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Micromachining and Microfabrication Process Technology II, S. Chang and S. W. Pang, eds., Proc. SPIE 2879, 72–82 (1994).

Pasmanik, G. A.

Potemkin, A. K.

A. I. Makarov, A. N. Malshakov, and A. K. Potemkin, “Measurement of small distortions of the wavefront of laser radiation,” Opt. Spectrosc. 86, 148–152 (1999).

A. N. Malshakov, G. A. Pasmanik, and A. K. Potemkin, “Comparative characteristics of magneto-optical materials,” Appl. Opt. 36, 6403–6410 (1997).
[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]

Shen, Y. R.

Y. R. Shen, Self-Focusing: Experimental, Prog. Quantum Electron. 4, 3–34 (1975).
[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]

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]

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]

Valuev, A. D.

A. D. Valuev, B. L. Vasin, N. N. Ilichev, and S. I. Fedorov, “The PIR-1 device for measurements of laser beam divergence,” Kvantovaya Elektron. (Moscow) 5, 951–951 (1978).

Van Damme, T. F.

Vasin, B. L.

A. D. Valuev, B. L. Vasin, N. N. Ilichev, and S. I. Fedorov, “The PIR-1 device for measurements of laser beam divergence,” Kvantovaya Elektron. (Moscow) 5, 951–951 (1978).

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]

Warren, N. E.

D. R. Neal, W. J. Alford, J. K. Gruetzner, and N. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Micromachining and Microfabrication Process Technology II, S. Chang and S. W. Pang, eds., Proc. SPIE 2879, 72–82 (1994).

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]

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. (3)

Kvantovaya Elektron. (Moscow) (1)

A. D. Valuev, B. L. Vasin, N. N. Ilichev, and S. I. Fedorov, “The PIR-1 device for measurements of laser beam divergence,” Kvantovaya Elektron. (Moscow) 5, 951–951 (1978).

Opt. Spectrosc. (1)

A. I. Makarov, A. N. Malshakov, and A. K. Potemkin, “Measurement of small distortions of the wavefront of laser radiation,” Opt. Spectrosc. 86, 148–152 (1999).

Proc. SPIE (1)

D. R. Neal, W. J. Alford, J. K. Gruetzner, and N. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” in Micromachining and Microfabrication Process Technology II, S. Chang and S. W. Pang, eds., Proc. SPIE 2879, 72–82 (1994).

Prog. Quantum Electron. (1)

Y. R. Shen, Self-Focusing: Experimental, Prog. Quantum Electron. 4, 3–34 (1975).
[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]

Other (3)

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

A. Angot, Mathematics for Radio Engineers (Nauka, Moscow, 1965), pp. 615–621.

S. L. Shapiro, Ultrashort Light Pulses (Springer-Verlag, Berlin, 1977).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Conceptual diagrams of a traditional linear Hartmann sensor and a nonlinear Hartmann sensor. The self-focusing effect of the nonlinear medium permits the beam centroid to be located with as much as 20 times better precision than with a conventional Hartmann detector.

Fig. 2
Fig. 2

Schematic optical diagram of the experimental setup. The sample under test is first removed from the beam to establish the optimal self-focusing. It is then placed in the beam near the input lens and the deflection is recorded.

Fig. 3
Fig. 3

Cross section of laser radiation intensity at the output window of the cell filled with benzene. b, The linear case, i.e., power in the pulse is much less than the threshold self-focusing power, PPthr. c, Pthr<P<2Pthr at beam self-focusing. a, Gaussian fit of b, I(r)=I0 exp[-(r/a)2], where a=280 µm. The sizes of the CCD camera pixels were too large to permit us to resolve the self-focusing point at one magnification and to see the whole diffraction spot in the absence of self-focusing.

Fig. 4
Fig. 4

Fragment of the cross section of the self-focusing point. Circles, experimental data obtained by computer processing of a CCD camera frame; solid curve, Gaussian fit, I(r)=I0 exp[-(r/amin)2], where amin=5 µm.

Fig. 5
Fig. 5

Accuracy of determination of the angle of deviation of a probe beam by a sample versus diffraction limit of the laser beam as a function of reliability, i.e., the probability that the measured quantity is within ±Δϑ/ϑd. Top curve, vertical beam axis; bottom curve, horizontal axis.

Fig. 6
Fig. 6

Accuracy of determination of wave-front distortions Δz=λ/M in terms of wavelengths as a function of reliability Φ(Δz). Top curve, the horizontal direction; bottom curve, the vertical direction.

Tables (1)

Tables Icon

Table 1 Transverse Size of Self-Focusing Points for Several Nonlinear Media, Pulse Durations, and Cell Lengths

Equations (1)

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

Φ(a)=2π1σ0aexp-x22σ2dx.

Metrics