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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 36, Iss. 1 — Jan. 1, 1946
  • pp: 20–32

Theory of the Space-Eikonometer

KENNETH N. OGLE  »View Author Affiliations

JOSA, Vol. 36, Issue 1, pp. 20-32 (1946)

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KENNETH N. OGLE, "Theory of the Space-Eikonometer," J. Opt. Soc. Am. 36, 20-32 (1946)

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  1. A. Ames, Jr., K. N. Ogle, and G. H. Gliddon, "Corresponding retinal points, the horopter, etc.," J. Opt. Soc. Am. 22, 538–631 (1932).
  2. A. Ames, Jr., "Aniseikonia—A factor in the functioning of vision," Am. J. Ophthal. 18, 1014–1020 (Nov., 1935).
  3. For a brief description see K. N. Ogle, "Association between aniseikonia and binocular spatial localization," Arch. f. Ophth. 30, 54–64 (July, 1943).
  4. A. Ames, Jr., "The space-eikonometer test for aniseikonia," Am. J. Ophthal. 28, 248–262 (March, 1945).
  5. K. N. Ogle, "The induced size effect," Arch. f. Ophth. 20, 604–623 (Oct., 1938).
  6. K. N. Ogle, "Meridional magnifying lens systems in the measurement and correction of aniseikonia," J. Opt. Soc. Am. 34, 302–312 (June, 1944). For a description of the different types of aniseikonic errors see Ames, reference 4.
  7. As will be shown later, a fourth measurement may be necessary, to eliminate the effect of a cyclotorsion between the eyes.
  8. K. N. Ogle and L. F. Madigan, "Astigmatism at oblique axes and binocular stereoscopic spatial localization," Arch. f. Ophth. 33, 116–127 (Feb., 1945); also H. M. Burian and K. N. Ogle, "Meridional aniseikonia at oblique axes," Arch. f. Ophth. 33, 293–309 (April, 1945).
  9. K. N. Ogle, "An optical unit for obtaining variable magnification for ophthalmic use," J. Opt. Soc. Am. 32, 143–146 (March, 1942).
  10. Since any given aniseikonic correction can be resolved into an over-all magnification, o percent, combined with a meridional magnification, ƒ percent, at some axis ϕ°, the components in the horizontal and vertical meridians will be given by h = o+ƒ sin2 ϕ, and υ = o+ƒ cos2 ϕ, respectively. The correction for the declination error between the images of the two eyes due to the oblique magnification will be δ = 0.29 ƒ sin 2ϕ. Thus, if the quantities h, υ, and δ can be measured, o, ƒ, and ϕ can be found. Tables have been prepared from which these quantities can be found directly, see reference 6.
  11. A. Panum, Physiol. Untersuchungen über das Sehen mit zwei Augen (Kiel, 1858), see p. 81. A. Nagel, Das Sehenmit zwei Augen (Leipzig, 1861).
  12. In normal surroundings the stereoscopic space sense (as distinguished from a simple depth differentiation) for any group of point objects may, of course, be inhibited if many uni-ocular factors or empirical motives for space perception are present. Cf. H. M. Burian and K. N. Ogle, "Aniseikonia and spatial orientation," Am. J. Ophthal. 28, 735–743 (July 1945).
  13. 13 K. N. Ogle, "An analytical treatment of the longitudinal horopter, etc." J. Opt. Soc. Am. 22, 665–728 (1932); see also Pflügers Arch. f. d. g. Physiol. [6], 239, 748–766 (1938).
  14. For the effect of magnifying the image of the left eye, it is only necessary to substitute 1/M for M in subsequent formulas.
  15. In order for the formulas to be strictly correct the elevation angles of the lines should be such that tan σ = cos ∊. For the visual distances ordinarily used, the error in taking σ = ±45° is negligible.
  16. A cyclotorsion pertains to any rotary movement of the eyes about their axes of fixation, and is designated as parallel if in the same direction in the two eyes and contra (or disjunctive) if in opposite directions. A cyclotropia defines an anomalous contra cyclotorsional position of the eyes with binocular vision. A cyclophoria defines the tendency for contra-cyclotorsions, which, when the eyes are dissociated, results in an actual cyclotropia.
  17. It is well known that under normal circumstances the cyclotorsional movements occur equally in the two eyes. F. B. Hofmann and A. Bielschowsky, "Über die der Willkür entzogenen Fusionsbewegungen der Augen," Pflügers Arch. 80, 1–40 (1900).
  18. K. N. Ogle and V. J. Ellerbrock, "Cyclofusional movements," Arch. f. Ophthal., at publishers.
  19. A similar phenomenon to the apparent orientation of vertical lines and the cross described here has been described by H. Werner, "Binocular depth contrast and conditions of the binocular field," Am. J. Psych. 51, 489–497 (July, 1938).
  20. The thread supporting the two beads should not be visible. This is usually a difficult thing to obtain. One solution is to mount the separated beads so that they may be seen by means of a half-silvered mirror set at 45° to the principal direction of the instrument before the test lens unit. Each bead is separately illuminated and seen against a black background. See reference 18.
  21. This technique with the beads makes it possible to find both δ0 and τ without the need for the declination (geared lens) unit at all. The beads are adjusted first to appear inclined the same as the cross appears inclined (to appear to lie in the plane of the cross), and second to appear vertical. One finds, then, δ0 = -½(δbcbυ) and τ = ½(δbcbυ), where δbc and δbυ are the declinations associated with the first and second adjustments. The difficulty lies in the fact that, when the cross appears inclined, the subject experiences difficulty in judging the orientation of the cross about a vertical axis which is needed to correct the vertical component of the image size difference.
  22. K. N. Ogle and V. J. Ellerbrock, "Stereoscopic sensitivity in the space-eikonometer," Arch. f. Ophthal. at publishers.

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