Abstract

The apparent distortion of stereoscopic space perception, caused by unequaļ magnifications of the images of the two eyes, as described by Ames, is studied from a mathematical point of view. It is shown that, at least qualitatively, the spatial distortions can be predicted on a geometric basis.

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  1. K. N. Ogle, "The correction of aniseikonia with ophthalmic lenses," J. Opt. Soc. Am. 26, 323 (1936).
  2. O. F. Wadsworth, "On the effect of a cylindrical lens, with vertical axis placed before one eye," Tr. Am. Ophth. Soc. 342 (1876).
  3. H. Culbertson, " Binocular astigmatism," J. Am. Med. Assn. 11, 622 (1888); Am. J. Ophth. 5, 117 (1888).
  4. J. A. Lippincott, "On the binocular metamorphopsia produced by correcting glasses," Arch. Ophth. 18, 18 (1889).
  5. J. Green, "On certain stereoscopical illusions evoked by prismatic and cylindrical glasses," Tr. Am. Ophth. Soc. 449 (1889).
  6. Harry Friedenwald, " Binocular metamorphopsia produced by correcting glasses," Arch. Ophth. 21, 204 (1892).
  7. C. Koller, "Ueber eine eigenthümliche Sorte dioptrischer Bilder: Ein Beitrag zur Theorie der Cylinderlinsen," Arch. f. Ophth. 32, 169 (1886), Part 3; " The form of retinal images in the astigmatic eye," Tr. Am. Ophth. Soc. 6, 425 (1892).
  8. J. A. Lippincott, "On the binocular metamorphopsia produced by optical means," Arch. Ophth. 46, 397 (1917); also J. A. Lippincott, "New tests for binocular vision," Tr. Am. Ophth. Soc. 560 (1890).
  9. M. von Rohr, "Die Brille als optische Instrument," (Verlag Julius Springer, Berlin, 1921), third edition, pp. 195.
  10. Franz Hillebrand, " Die Stabilität der Raumwerte auf der Netzhaut," Zeits. Psychol. 5, 1 (1893).
  11. Adelbert Ames, Jr., "Binocular vision as affected by relations between uniocular stimulus-patterns in commonplace environments," Am. J. Psychol. 59, 333 (1946).
  12. Adelbert Ames, Jr. and K. N. Ogle, "Size and shape of ocular images: III. Visual sensitivity to differences in the relative sizes of the ocular images of the two eyes," Arch. Ophth. 7, 904 (1932).
  13. Adelbert Ames, Jr., "Aniseikonia—a factor in the functioning of vision," Am. J. Ophth. 18, 1014 (1935).
  14. K. N. Ogle, "Association between aniseikonia and anomalous binocular space perception," Arch. Ophth. 30, 54 (1943).
  15. K. N. Ogle and V. J. Ellerbrock, "Stereoscopic sensitivity in the space eikonometer," Arch. Ophth. 34, 303 (1945).
  16. K. N. Ogle, "Induced size effect: III. A study of the phenomenon as influenced by horizontal disparity of the fusion contours," Arch. Ophth. 22, 613 (1939).
  17. K. N. Ogle, " Induced size effect: I. A new phenomenon in binocular space perception associated with the relative sizes of the images of the two eyes," Arch. Ophth. 20, 604 (1938); "II. An experimental study of the phenomenon with restricted fusion stimuli," 21, 604 (1939); "II. A study of the phenomenon as influenced by horizontal disparity of the fusion contours," 22, 613 (1939); K. N. Ogle, "Induced size effect," J. Opt. Soc. Am. 30, 145 (1940); K. N. Ogle, "Induced size effect with eyes in asymmetric convergence," Arch. Ophth. 23, 1023 (1940); A. S. Householder, "A theory of the induced size effect," Bull. Math. Biophys. 5, 155 (1943). *** For a consideration of the spatial distortions in cases of astigmatic spectacle corrections with oblique axes see: K. N. Ogle and L. F. Madigan, "Astigmatism at oblique axes and binocular stereoscopic spatial localization," Arch. Opth. 33, 116 (1945).
  18. K. N. Ogle and L. F. Madigan, "Astigmatism at oblique axes and binocular stereoscopic spatial localization," Arch. Ophth. 33, 116 (1945).
  19. K. N. Ogle, " Meridional magnifying lens systems in the measurement and correction of aniseikonia," J. Opt. Soc. Am. 34, 302 (1944).
  20. A. Ames, Jr., K. N. Ogle, and G. H. Glidden, " Corresponding retinal points, the horopter and size and shape of ocular images," J. Opt. Soc. Am. 22, 576 (1932).
  21. H. von Helmholtz, Physiological Optics (English translation) (The Optical Society of America, 1925), Vol. 3, p. 349.

1946 (1)

Adelbert Ames, Jr., "Binocular vision as affected by relations between uniocular stimulus-patterns in commonplace environments," Am. J. Psychol. 59, 333 (1946).

1945 (2)

K. N. Ogle and V. J. Ellerbrock, "Stereoscopic sensitivity in the space eikonometer," Arch. Ophth. 34, 303 (1945).

K. N. Ogle and L. F. Madigan, "Astigmatism at oblique axes and binocular stereoscopic spatial localization," Arch. Ophth. 33, 116 (1945).

1944 (1)

1943 (1)

K. N. Ogle, "Association between aniseikonia and anomalous binocular space perception," Arch. Ophth. 30, 54 (1943).

1939 (1)

K. N. Ogle, "Induced size effect: III. A study of the phenomenon as influenced by horizontal disparity of the fusion contours," Arch. Ophth. 22, 613 (1939).

1938 (1)

K. N. Ogle, " Induced size effect: I. A new phenomenon in binocular space perception associated with the relative sizes of the images of the two eyes," Arch. Ophth. 20, 604 (1938); "II. An experimental study of the phenomenon with restricted fusion stimuli," 21, 604 (1939); "II. A study of the phenomenon as influenced by horizontal disparity of the fusion contours," 22, 613 (1939); K. N. Ogle, "Induced size effect," J. Opt. Soc. Am. 30, 145 (1940); K. N. Ogle, "Induced size effect with eyes in asymmetric convergence," Arch. Ophth. 23, 1023 (1940); A. S. Householder, "A theory of the induced size effect," Bull. Math. Biophys. 5, 155 (1943). *** For a consideration of the spatial distortions in cases of astigmatic spectacle corrections with oblique axes see: K. N. Ogle and L. F. Madigan, "Astigmatism at oblique axes and binocular stereoscopic spatial localization," Arch. Opth. 33, 116 (1945).

1936 (1)

1935 (1)

Adelbert Ames, Jr., "Aniseikonia—a factor in the functioning of vision," Am. J. Ophth. 18, 1014 (1935).

1932 (2)

A. Ames, Jr., K. N. Ogle, and G. H. Glidden, " Corresponding retinal points, the horopter and size and shape of ocular images," J. Opt. Soc. Am. 22, 576 (1932).

Adelbert Ames, Jr. and K. N. Ogle, "Size and shape of ocular images: III. Visual sensitivity to differences in the relative sizes of the ocular images of the two eyes," Arch. Ophth. 7, 904 (1932).

1917 (1)

J. A. Lippincott, "On the binocular metamorphopsia produced by optical means," Arch. Ophth. 46, 397 (1917); also J. A. Lippincott, "New tests for binocular vision," Tr. Am. Ophth. Soc. 560 (1890).

1893 (1)

Franz Hillebrand, " Die Stabilität der Raumwerte auf der Netzhaut," Zeits. Psychol. 5, 1 (1893).

1892 (1)

Harry Friedenwald, " Binocular metamorphopsia produced by correcting glasses," Arch. Ophth. 21, 204 (1892).

1889 (1)

J. A. Lippincott, "On the binocular metamorphopsia produced by correcting glasses," Arch. Ophth. 18, 18 (1889).

1886 (1)

C. Koller, "Ueber eine eigenthümliche Sorte dioptrischer Bilder: Ein Beitrag zur Theorie der Cylinderlinsen," Arch. f. Ophth. 32, 169 (1886), Part 3; " The form of retinal images in the astigmatic eye," Tr. Am. Ophth. Soc. 6, 425 (1892).

Ames, Jr., A.

A. Ames, Jr., K. N. Ogle, and G. H. Glidden, " Corresponding retinal points, the horopter and size and shape of ocular images," J. Opt. Soc. Am. 22, 576 (1932).

Ames, Jr., Adelbert

Adelbert Ames, Jr., "Binocular vision as affected by relations between uniocular stimulus-patterns in commonplace environments," Am. J. Psychol. 59, 333 (1946).

Adelbert Ames, Jr., "Aniseikonia—a factor in the functioning of vision," Am. J. Ophth. 18, 1014 (1935).

Adelbert Ames, Jr. and K. N. Ogle, "Size and shape of ocular images: III. Visual sensitivity to differences in the relative sizes of the ocular images of the two eyes," Arch. Ophth. 7, 904 (1932).

Culbertson, H.

H. Culbertson, " Binocular astigmatism," J. Am. Med. Assn. 11, 622 (1888); Am. J. Ophth. 5, 117 (1888).

Ellerbrock, V. J.

K. N. Ogle and V. J. Ellerbrock, "Stereoscopic sensitivity in the space eikonometer," Arch. Ophth. 34, 303 (1945).

Friedenwald, Harry

Harry Friedenwald, " Binocular metamorphopsia produced by correcting glasses," Arch. Ophth. 21, 204 (1892).

Glidden, G. H.

A. Ames, Jr., K. N. Ogle, and G. H. Glidden, " Corresponding retinal points, the horopter and size and shape of ocular images," J. Opt. Soc. Am. 22, 576 (1932).

Green, J.

J. Green, "On certain stereoscopical illusions evoked by prismatic and cylindrical glasses," Tr. Am. Ophth. Soc. 449 (1889).

Hillebrand, Franz

Franz Hillebrand, " Die Stabilität der Raumwerte auf der Netzhaut," Zeits. Psychol. 5, 1 (1893).

Koller, C.

C. Koller, "Ueber eine eigenthümliche Sorte dioptrischer Bilder: Ein Beitrag zur Theorie der Cylinderlinsen," Arch. f. Ophth. 32, 169 (1886), Part 3; " The form of retinal images in the astigmatic eye," Tr. Am. Ophth. Soc. 6, 425 (1892).

Lippincott, J. A.

J. A. Lippincott, "On the binocular metamorphopsia produced by optical means," Arch. Ophth. 46, 397 (1917); also J. A. Lippincott, "New tests for binocular vision," Tr. Am. Ophth. Soc. 560 (1890).

J. A. Lippincott, "On the binocular metamorphopsia produced by correcting glasses," Arch. Ophth. 18, 18 (1889).

Madigan, L. F.

K. N. Ogle and L. F. Madigan, "Astigmatism at oblique axes and binocular stereoscopic spatial localization," Arch. Ophth. 33, 116 (1945).

Ogle, K. N.

K. N. Ogle and V. J. Ellerbrock, "Stereoscopic sensitivity in the space eikonometer," Arch. Ophth. 34, 303 (1945).

K. N. Ogle and L. F. Madigan, "Astigmatism at oblique axes and binocular stereoscopic spatial localization," Arch. Ophth. 33, 116 (1945).

K. N. Ogle, " Meridional magnifying lens systems in the measurement and correction of aniseikonia," J. Opt. Soc. Am. 34, 302 (1944).

K. N. Ogle, "Association between aniseikonia and anomalous binocular space perception," Arch. Ophth. 30, 54 (1943).

K. N. Ogle, "Induced size effect: III. A study of the phenomenon as influenced by horizontal disparity of the fusion contours," Arch. Ophth. 22, 613 (1939).

K. N. Ogle, " Induced size effect: I. A new phenomenon in binocular space perception associated with the relative sizes of the images of the two eyes," Arch. Ophth. 20, 604 (1938); "II. An experimental study of the phenomenon with restricted fusion stimuli," 21, 604 (1939); "II. A study of the phenomenon as influenced by horizontal disparity of the fusion contours," 22, 613 (1939); K. N. Ogle, "Induced size effect," J. Opt. Soc. Am. 30, 145 (1940); K. N. Ogle, "Induced size effect with eyes in asymmetric convergence," Arch. Ophth. 23, 1023 (1940); A. S. Householder, "A theory of the induced size effect," Bull. Math. Biophys. 5, 155 (1943). *** For a consideration of the spatial distortions in cases of astigmatic spectacle corrections with oblique axes see: K. N. Ogle and L. F. Madigan, "Astigmatism at oblique axes and binocular stereoscopic spatial localization," Arch. Opth. 33, 116 (1945).

K. N. Ogle, "The correction of aniseikonia with ophthalmic lenses," J. Opt. Soc. Am. 26, 323 (1936).

Adelbert Ames, Jr. and K. N. Ogle, "Size and shape of ocular images: III. Visual sensitivity to differences in the relative sizes of the ocular images of the two eyes," Arch. Ophth. 7, 904 (1932).

A. Ames, Jr., K. N. Ogle, and G. H. Glidden, " Corresponding retinal points, the horopter and size and shape of ocular images," J. Opt. Soc. Am. 22, 576 (1932).

von Helmholtz, H.

H. von Helmholtz, Physiological Optics (English translation) (The Optical Society of America, 1925), Vol. 3, p. 349.

von Rohr, M.

M. von Rohr, "Die Brille als optische Instrument," (Verlag Julius Springer, Berlin, 1921), third edition, pp. 195.

Wadsworth, O. F.

O. F. Wadsworth, "On the effect of a cylindrical lens, with vertical axis placed before one eye," Tr. Am. Ophth. Soc. 342 (1876).

Am. J. Ophth. (1)

Adelbert Ames, Jr., "Aniseikonia—a factor in the functioning of vision," Am. J. Ophth. 18, 1014 (1935).

Am. J. Psychol. (1)

Adelbert Ames, Jr., "Binocular vision as affected by relations between uniocular stimulus-patterns in commonplace environments," Am. J. Psychol. 59, 333 (1946).

Arch. f. Ophth. (1)

C. Koller, "Ueber eine eigenthümliche Sorte dioptrischer Bilder: Ein Beitrag zur Theorie der Cylinderlinsen," Arch. f. Ophth. 32, 169 (1886), Part 3; " The form of retinal images in the astigmatic eye," Tr. Am. Ophth. Soc. 6, 425 (1892).

Arch. Ophth. (9)

J. A. Lippincott, "On the binocular metamorphopsia produced by optical means," Arch. Ophth. 46, 397 (1917); also J. A. Lippincott, "New tests for binocular vision," Tr. Am. Ophth. Soc. 560 (1890).

Harry Friedenwald, " Binocular metamorphopsia produced by correcting glasses," Arch. Ophth. 21, 204 (1892).

J. A. Lippincott, "On the binocular metamorphopsia produced by correcting glasses," Arch. Ophth. 18, 18 (1889).

K. N. Ogle, "Association between aniseikonia and anomalous binocular space perception," Arch. Ophth. 30, 54 (1943).

K. N. Ogle and V. J. Ellerbrock, "Stereoscopic sensitivity in the space eikonometer," Arch. Ophth. 34, 303 (1945).

K. N. Ogle, "Induced size effect: III. A study of the phenomenon as influenced by horizontal disparity of the fusion contours," Arch. Ophth. 22, 613 (1939).

K. N. Ogle, " Induced size effect: I. A new phenomenon in binocular space perception associated with the relative sizes of the images of the two eyes," Arch. Ophth. 20, 604 (1938); "II. An experimental study of the phenomenon with restricted fusion stimuli," 21, 604 (1939); "II. A study of the phenomenon as influenced by horizontal disparity of the fusion contours," 22, 613 (1939); K. N. Ogle, "Induced size effect," J. Opt. Soc. Am. 30, 145 (1940); K. N. Ogle, "Induced size effect with eyes in asymmetric convergence," Arch. Ophth. 23, 1023 (1940); A. S. Householder, "A theory of the induced size effect," Bull. Math. Biophys. 5, 155 (1943). *** For a consideration of the spatial distortions in cases of astigmatic spectacle corrections with oblique axes see: K. N. Ogle and L. F. Madigan, "Astigmatism at oblique axes and binocular stereoscopic spatial localization," Arch. Opth. 33, 116 (1945).

K. N. Ogle and L. F. Madigan, "Astigmatism at oblique axes and binocular stereoscopic spatial localization," Arch. Ophth. 33, 116 (1945).

Adelbert Ames, Jr. and K. N. Ogle, "Size and shape of ocular images: III. Visual sensitivity to differences in the relative sizes of the ocular images of the two eyes," Arch. Ophth. 7, 904 (1932).

J. Opt. Soc. Am. (3)

K. N. Ogle, " Meridional magnifying lens systems in the measurement and correction of aniseikonia," J. Opt. Soc. Am. 34, 302 (1944).

A. Ames, Jr., K. N. Ogle, and G. H. Glidden, " Corresponding retinal points, the horopter and size and shape of ocular images," J. Opt. Soc. Am. 22, 576 (1932).

K. N. Ogle, "The correction of aniseikonia with ophthalmic lenses," J. Opt. Soc. Am. 26, 323 (1936).

Zeits. Psychol. (1)

Franz Hillebrand, " Die Stabilität der Raumwerte auf der Netzhaut," Zeits. Psychol. 5, 1 (1893).

Other (5)

M. von Rohr, "Die Brille als optische Instrument," (Verlag Julius Springer, Berlin, 1921), third edition, pp. 195.

O. F. Wadsworth, "On the effect of a cylindrical lens, with vertical axis placed before one eye," Tr. Am. Ophth. Soc. 342 (1876).

H. Culbertson, " Binocular astigmatism," J. Am. Med. Assn. 11, 622 (1888); Am. J. Ophth. 5, 117 (1888).

J. Green, "On certain stereoscopical illusions evoked by prismatic and cylindrical glasses," Tr. Am. Ophth. Soc. 449 (1889).

H. von Helmholtz, Physiological Optics (English translation) (The Optical Society of America, 1925), Vol. 3, p. 349.

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