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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 6 — Jun. 1, 2003
  • pp: 1120–1131

Looking into the water with oblique head tilting: revision of the aerial binocular imaging of underwater objects

Gábor Horváth, Krisztián Buchta, and Dezsö Varjú  »View Author Affiliations

JOSA A, Vol. 20, Issue 6, pp. 1120-1131 (2003)

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It is a well-known phenomenon that when we look into the water with two aerial eyes, both the apparent position and the apparent shape of underwater objects are different from the real ones because of refraction at the water surface. Earlier studies of the refraction-distorted structure of the underwater binocular visual field of aerial observers were restricted to either vertically or horizontally oriented eyes. We investigate a generalized version of this problem: We calculate the position of the binocular image point of an underwater object point viewed by two arbitrarily positioned aerial eyes, including oblique orientations of the eyes relative to the flat water surface. Assuming that binocular image fusion is performed by appropriate vergent eye movements to bring the object’s image onto the foveas, the structure of the underwater binocular visual field is computed and visualized in different ways as a function of the relative positions of the eyes. We show that a revision of certain earlier treatments of the aerial imaging of underwater objects is necessary. We analyze and correct some widespread erroneous or incomplete representations of this classical geometric optical problem that occur in different textbooks. Improving the theory of aerial binocular imaging of underwater objects, we demonstrate that the structure of the underwater binocular visual field of aerial 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

Original Manuscript: September 13, 2002
Revised Manuscript: January 23, 2003
Manuscript Accepted: January 23, 2003
Published: June 1, 2003

Gábor Horváth, Krisztián Buchta, and Dezsö 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)

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