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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 67, Iss. 11 — Nov. 1, 1977
  • pp: 1569–1575

Theoretical aspects of thermal blooming compensation

James Wallace and Joseph Pasciak  »View Author Affiliations


JOSA, Vol. 67, Issue 11, pp. 1569-1575 (1977)
http://dx.doi.org/10.1364/JOSA.67.001569


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Abstract

In this paper we present the theoretical background required for evaluating phase compensation as a technique for reducing the effects of thermal blooming. By using a time-dependent approach for thermal blooming, we can define and evaluate the instantaneous Green’s function for the heated atmosphere. The phase at the mirror is determined by propagating a point source from the focal point to the laser. The effectiveness of this technique is determined by propagating point sources within a diffraction-limited spot to the laser and comparing the resulting phase to the phase of a point source at the focal point. The phase difference will be small and the increase in irradiance large if the heating occurs where geometric optics is valid. The phase difference is large and the increase in irradiance small if atmospheric heating occurs where significant diffractive spreading is also occurring. The resulting gradients lie in the geometric shadow of the aperture and are not accessible to correction by contouring the mirror. Numerical results illustrating the analysis are presented for both cw and pulsed lasers.

© 1977 Optical Society of America

Citation
James Wallace and Joseph Pasciak , "Theoretical aspects of thermal blooming compensation," J. Opt. Soc. Am. 67, 1569-1575 (1977)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-67-11-1569


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References

  1. L. C. Bradley and J. Herrmann, "Phase compensation for thermal blooming," Appl. Opt. 13, 331 (1974).
  2. J. Wallace and J. Pasciak, "Compensating for thermal blooming of repetitively pulsed lasers," J. Opt. Soc. Am. 65, 1257 (1975).
  3. J. R. Dunphy and D. C. Smith, "Multiple-pulse thermal blooming and phase compensation," J. Opt. Soc. Am. 67, 295 (1977).
  4. W. P. Brown, Jr., "Computer simulation of adaptive optical systems," Hughes Research Laboratory Report N60921-74-C-0249 (September 1975).
  5. F. G. Gebhardt, "Experimental demonstration of the use of phase correction to reduce thermal blooming" (private communication).
  6. G. S. Avila and J. B. Keller, "High-frequency asymptolic field of a point source in an inhomogeneous medium," Commun. Pure Appl. Math. 16, 363 (1963).
  7. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965).
  8. R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. II (Interscience, New York, 1962).
  9. J. Hermann, "Properties of phase conjugate adaptive optical systems," J. Opt. Soc. Am. 67, 290 (1977).
  10. P. T. Berger, P. B. Ulrich, J. J. Ulrich, and F. G. Gebhardt, "Transient thermal blooming of a slewed laser beam containing a region of stagnant absorber," Appl. Opt. 16, 345 (1977).
  11. P. B. Ulrich, Naval Research Laboratory, Washington D. C. (private communication).
  12. C. B. Hogge, "Propagation of high-energy laser beams in the atmosphere," Air Force Weapons Lab TR-74-74 (1974).

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