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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 31, Iss. 9 — Mar. 20, 1992
  • pp: 1267–1273

Simulation of mirages

W. H. Lehn and W. Friesen  »View Author Affiliations


Applied Optics, Vol. 31, Issue 9, pp. 1267-1273 (1992)
http://dx.doi.org/10.1364/AO.31.001267


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Abstract

A mirage is seen when atmospheric refraction distorts or displaces an image. We describe a mirage simulator that uses digital imaging equipment to generate mirage images from normal photographs. The simulation program relocates horizonal image lies into positions that they appear to occupy, according to rays traced from observer to object. Image-brightness adjustments are not required; we show that, while the atmosphere can change the size or shape of an object, it does not change its apparent brightness. The realistic quality of the computed images makes this simulator a useful tool in mirage analysis.

© 1992 Optical Society of America

History
Original Manuscript: March 13, 1991
Published: March 20, 1992

Citation
W. H. Lehn and W. Friesen, "Simulation of mirages," Appl. Opt. 31, 1267-1273 (1992)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-31-9-1267


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References

  1. R. G. Fleagle, J. A. Businger, An Introduction to Atmospheric Physics, 2nd ed. (Academic, New York, 1980).
  2. W. H. Lehn, R. E. Wallace, “Continuous-tone mirage images computed from digitized source photographs,” in Digest of Topical Meeting on Meteorological Optics (Optical Society of America, Washington, D.C., 1986), of paper ThB4, pp. 36–38.
  3. M. Berger, T. Trout, N. Levit, “Ray tracing mirages,” IEEE Comput. Graphics Appl. 10, 36–41 (1990). [CrossRef]
  4. A. B. Fraser, W. H. Mach, “Mirages,” Sci. Am. 234, 102–111 (1976). [CrossRef]
  5. W. H. Lehn, M. B. El-Arini, “Computer-graphics analysis of atmospheric refraction,” Appl. Opt. 17, 3146–3151 (1978). The TC concept introduced in this reference plots zobj versus ray angle ϕ at the eye. For image calculations it is more convenient to interchange the axes and replace ϕ by zapp. The latter form previously appeared in J. K. Sparkman, “A remote sensing technique using terrestrial refraction, for the study of low-level lapse rate,” Ph.D. dissertation (University of Wisconsin, Madison, Wisconsin, 1971). [CrossRef] [PubMed]
  6. J. S. Morrish, “Inferior mirages and their corresponding temperature structures,” M.Sc. thesis (University of Manitoba, Winnipeg, Canada, 1985).
  7. A. B. Fraser, “Solutions of the refraction and extinction integrals for use in inversions and image formation,” Appl. Opt. 16, 160–165 (1977). [CrossRef] [PubMed]
  8. W. H. Lehn, “A simple parabolic model for the optics of the atmospheric surface layer,” Appl. Math. Model. 9, 447–453 (1985). [CrossRef]
  9. W. H. Lehn, “Atmospheric refraction and lake monsters,” Science, 205, 183–185 (1979). [CrossRef] [PubMed]
  10. W. H. Lehn, I. Schroeder, “The Norse merman as an optical phenomenon,” Nature (London) 289, 362–366 (1981). [CrossRef]
  11. J. B. Sweeney, A Pictorial History of Sea Monsters (Crown, New York, 1972).
  12. F. Bruemmer, Encounters with Arctic Animals (McGraw-Hill, Toronto, 1972), p. 73.
  13. L. M. Larson (translator), The King’s Mirror (Twayne, New York, 1917), pp. 135–136.
  14. W. J. Humphreys, Physics of the Air, 3rd ed. (Dover, New York, 1964).
  15. J. M. Pernter, F. Exner, Meteorologische Optik, 2nd ed. (Braumüller, Vienna, 1922).
  16. In the case of a flat earth, the ray invariant is n sin θ = k. Equation (A10) then becomes dα = dθ, but Eq. (A11) remains unchanged.
  17. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1986).
  18. An unnamed reviewer suggested an alternative approach to this result, based on the discussions of image brightness in Ref. 17: if the atmosphere is regarded as part of the (lossless) image-forming lens, and if the refractive indices of the medium are the same at object and image, the photometric brightness of the image will equal that of the object.

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