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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 12 — Dec. 1, 2003
  • pp: 2370–2377

Underwater binocular imaging of aerial objects versus the position of eyes relative to the flat water surface

András Barta and Gábor Horváth  »View Author Affiliations

JOSA A, Vol. 20, Issue 12, pp. 2370-2377 (2003)

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The apparent position, size, and shape of aerial objects viewed binocularly from water change as a result of the refraction of light at the water surface. Earlier studies of the refraction-distorted structure of the aerial binocular visual field of underwater observers were restricted to either vertically or horizontally oriented eyes. Here we calculate the position of the binocular image point of an aerial object point viewed by two arbitrarily positioned underwater eyes when the water surface is flat. Assuming that binocular image fusion is performed by appropriate vergent eye movements to bring the object’s image onto the foveae, the structure of the aerial binocular visual field is computed and visualized as a function of the relative positions of the eyes. We also analyze two erroneous representations of the underwater imaging of aerial objects that have occurred in the literature. It is demonstrated that the structure of the aerial binocular visual field of underwater observers distorted by refraction is more complex than has been thought previously.

© 2003 Optical Society of America

OCIS Codes
(000.2690) General : General physics
(080.1510) Geometric optics : Propagation methods
(080.2720) Geometric optics : Mathematical methods (general)
(170.1420) Medical optics and biotechnology : Biology
(330.1400) Vision, color, and visual optics : Vision - binocular and stereopsis
(330.7310) Vision, color, and visual optics : Vision

András Barta and Gábor Horváth, "Underwater binocular imaging of aerial objects versus the position of eyes relative to the flat water surface," J. Opt. Soc. Am. A 20, 2370-2377 (2003)

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  1. G. Horváth and D. Varjú, “On the structure of the aerial visual field of aquatic animals distorted by refraction,” Bull. Math. Biol. 53, 425–441 (1991).
  2. D. Regan, ed., Binocular Vision, Vol. 9 of Vision and Visual Dysfunction, J. R. Cronly-Dillon, gen. ed. (MacMillan, New York, 1991).
  3. I. P. Howard and B. J. Rogers, Binocular Vision and Stereopsis (Oxford U. Press, Oxford, UK, 1995).
  4. G. Horváth and D. Varjú, “Geometric optical investigation of the underwater visual field of aerial animals,” Math. Biosci. 102, 1–19 (1990).
  5. G. Horváth, K. Buchta, and D. Varjú, “Looking into the water with oblique head tilting: revision of the aerial binocular imaging of underwater objects,” J. Opt. Soc. Am. A 20, 1120–1131 (2003).
  6. D. L. Shealy and D. G. Burkhard, “Flux density for ray propagation in discrete index media expressed in terms of the intrinsic geometry of the deflecting surface,” Opt. Acta 20, 287–301 (1973).
  7. D. L. Shealy and D. G. Burkhard, “Analytical illuminance calculation in a multi-interface optical system,” Opt. Acta 22, 485–501 (1975).
  8. G. Silva-Ortigoza, J. Castro-Ramos, and A. Cordero-Dávila, “Exact calculation of the circle of least confusion of a rotationally symmetric mirror. II,” Appl. Opt. 40, 1021–1028 (2001).
  9. G. Silva-Ortigoza, M. Marciano-Melchor, O. Carvente-Munoz, and R. Silva-Ortigoza, “Exact computation of the caustic associated with the evolution of an aberrated wavefront,” J. Opt. A Pure Appl. Opt. 4, 358–365 (2002).
  10. E. Schwartz, “Können ‘blinde’ Fische sehen? Fische haben einen sechsten Sinn,” Aquarien Magazin July 1969, 272–275.
  11. J. Walker, “What is a fish’s view of a fisherman and the fly he has cast on the water?” Sci. Am. 250 (3), 108–113 (1984).
  12. K. H. Lüling, “The archer fish,” Sci. Am. 209 (1), 100–108 (1963).
  13. M. Bekoff and R. Dorr, “Predation by ‘shooting’ in archerfish, Toxotes jaculatrix: accuracy and sequences,” Bull. Psychon. Soc. 7, 167–168 (1976).
  14. L. M. Dill, “Refraction and the spitting behaviour of the archerfish (Toxotes chatareus),” Behav. Ecol. Sociobiol. 2, 169–184 (1977).
  15. S. Rossel, J. Corlija, and S. Schuster, “Predicting three-dimensional target motion: how archer fish determine where to catch their dislodged prey,” J. Exp. Biol. 205, 3321–3326 (2002).
  16. R. Harmon and J. Cline, “At the edge of the window,” Rod Reel, July 1980, pp. 41–45.

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