Abstract

This study reports data on the question as to how precise is stereoscopic depth localization with double images and what is the relationship between that subjective depth and objective depth. Instrumentation was used which permitted a test object to be adjusted relative to a reference object, when both of these were observed in increasing disparity between the images of the two eyes and in increasing peripheral angle. The data show that the precision of the stereoscopic depth seems to decrease exponentially with disparity, becoming very small near the limiting values of disparity for stereopsis. When the test object is adjusted for half the depth of the reference object, and adjusted to be as far in front of the fixation point as the reference is behind, the data show a remarkable validity for a wide range of disparity, until the limiting disparities are approached. Then the stereoscopic depth levels off to a constant value. These results are discussed in relation to the visual processes and spatial localization.

© 1953 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Skubich, Z. psychol. physiol. d. Sinnesorg. 96, 353 (1925).
  2. K. N. Ogle, Arch. Ophth. 48, 50 (1952).
    [Crossref]
  3. K. N. Ogle, J. Exptl. Psych. 44, 253 (1952).
    [Crossref]
  4. A. Tschermak, P. Hoefer, and Pflügers, Arch. ges. Physiol. 98, 299 (1903).
    [Crossref]
  5. H. Burian, Arch. Ophthalmol. 136, 172 (1936).
  6. Walther Poppelreuter, Z. Psychol. u. Physiol. d. Sinnesorg. 58, 200 (1911).
  7. R. A. Pfeiffer, Psychol. Studien. 2, 129 (1907).
  8. Anathon Aall, Z. Psychol. u. Physiol. d. Sinnesorg. 49, 108, 161 (1908).
  9. L. N. Gassovsky and N. A. Nikolskaya, Compt. rend. Acad. d. sc. URSS. 38, 15 (1943).
  10. Karl-Friedrich Vilmar, Klin. Monatsbl. Augenheilk. 117, 242 (1950).
  11. K. N. Ogle, Researches in Binocular Vision (W. B. Saunders Company, Philadelphia, 1950), p. 345.
  12. Armin von Tschermak-Seysenegg, Introduction to Physiological Optics, translated by P. Boeder (Charles C. Thomas, Springfield, Illinois, 1952), p. 299.
  13. S. A. Talbot and W. H. Marshall, Am. J. Ophthalmol. 24, 1255 (1941).
  14. W. H. Marshall and S. A. Talbot, “Recent evidence for neural mechanisms in vision leading to a general theory of sensory acuity.” In Heinrich Klüver: Visual Mechanisms (The Jacques Cattell Press, Lancaster, Pennsylvania, 1942), Biological Symposia, Vol. 7, pp. 117–164.
  15. R. Lorente de Nó, J. Psychol. u. Neurol. 46, 113 (1934).
  16. J. von Kries, in Helmholtz’s Treatise on Physiological Optics, translated by J. P. C. Southall (Optical Society of America, New York, 1925), Vol. 3, p. 736.
  17. Quoted by R. A. Pfeiffer, reference 7.
  18. Ewald Hering, Spatial Sense and Movements of the Eye, translated by C. A. Radde (The American Academy of Optometry, Baltimore, Maryland, 1942), p. 78.
  19. L. Heine, Arch. Ophthalmol. 51, 563 (1900).

1952 (2)

K. N. Ogle, Arch. Ophth. 48, 50 (1952).
[Crossref]

K. N. Ogle, J. Exptl. Psych. 44, 253 (1952).
[Crossref]

1950 (1)

Karl-Friedrich Vilmar, Klin. Monatsbl. Augenheilk. 117, 242 (1950).

1943 (1)

L. N. Gassovsky and N. A. Nikolskaya, Compt. rend. Acad. d. sc. URSS. 38, 15 (1943).

1941 (1)

S. A. Talbot and W. H. Marshall, Am. J. Ophthalmol. 24, 1255 (1941).

1936 (1)

H. Burian, Arch. Ophthalmol. 136, 172 (1936).

1934 (1)

R. Lorente de Nó, J. Psychol. u. Neurol. 46, 113 (1934).

1925 (1)

G. Skubich, Z. psychol. physiol. d. Sinnesorg. 96, 353 (1925).

1911 (1)

Walther Poppelreuter, Z. Psychol. u. Physiol. d. Sinnesorg. 58, 200 (1911).

1908 (1)

Anathon Aall, Z. Psychol. u. Physiol. d. Sinnesorg. 49, 108, 161 (1908).

1907 (1)

R. A. Pfeiffer, Psychol. Studien. 2, 129 (1907).

1903 (1)

A. Tschermak, P. Hoefer, and Pflügers, Arch. ges. Physiol. 98, 299 (1903).
[Crossref]

1900 (1)

L. Heine, Arch. Ophthalmol. 51, 563 (1900).

Aall, Anathon

Anathon Aall, Z. Psychol. u. Physiol. d. Sinnesorg. 49, 108, 161 (1908).

Burian, H.

H. Burian, Arch. Ophthalmol. 136, 172 (1936).

Gassovsky, L. N.

L. N. Gassovsky and N. A. Nikolskaya, Compt. rend. Acad. d. sc. URSS. 38, 15 (1943).

Heine, L.

L. Heine, Arch. Ophthalmol. 51, 563 (1900).

Helmholtz,

J. von Kries, in Helmholtz’s Treatise on Physiological Optics, translated by J. P. C. Southall (Optical Society of America, New York, 1925), Vol. 3, p. 736.

Hering, Ewald

Ewald Hering, Spatial Sense and Movements of the Eye, translated by C. A. Radde (The American Academy of Optometry, Baltimore, Maryland, 1942), p. 78.

Hoefer, P.

A. Tschermak, P. Hoefer, and Pflügers, Arch. ges. Physiol. 98, 299 (1903).
[Crossref]

Klüver, Heinrich

W. H. Marshall and S. A. Talbot, “Recent evidence for neural mechanisms in vision leading to a general theory of sensory acuity.” In Heinrich Klüver: Visual Mechanisms (The Jacques Cattell Press, Lancaster, Pennsylvania, 1942), Biological Symposia, Vol. 7, pp. 117–164.

Lorente de Nó, R.

R. Lorente de Nó, J. Psychol. u. Neurol. 46, 113 (1934).

Marshall, W. H.

S. A. Talbot and W. H. Marshall, Am. J. Ophthalmol. 24, 1255 (1941).

W. H. Marshall and S. A. Talbot, “Recent evidence for neural mechanisms in vision leading to a general theory of sensory acuity.” In Heinrich Klüver: Visual Mechanisms (The Jacques Cattell Press, Lancaster, Pennsylvania, 1942), Biological Symposia, Vol. 7, pp. 117–164.

Nikolskaya, N. A.

L. N. Gassovsky and N. A. Nikolskaya, Compt. rend. Acad. d. sc. URSS. 38, 15 (1943).

Ogle, K. N.

K. N. Ogle, Arch. Ophth. 48, 50 (1952).
[Crossref]

K. N. Ogle, J. Exptl. Psych. 44, 253 (1952).
[Crossref]

K. N. Ogle, Researches in Binocular Vision (W. B. Saunders Company, Philadelphia, 1950), p. 345.

Pfeiffer, R. A.

R. A. Pfeiffer, Psychol. Studien. 2, 129 (1907).

Quoted by R. A. Pfeiffer, reference 7.

Pflügers,

A. Tschermak, P. Hoefer, and Pflügers, Arch. ges. Physiol. 98, 299 (1903).
[Crossref]

Poppelreuter, Walther

Walther Poppelreuter, Z. Psychol. u. Physiol. d. Sinnesorg. 58, 200 (1911).

Skubich, G.

G. Skubich, Z. psychol. physiol. d. Sinnesorg. 96, 353 (1925).

Talbot, S. A.

S. A. Talbot and W. H. Marshall, Am. J. Ophthalmol. 24, 1255 (1941).

W. H. Marshall and S. A. Talbot, “Recent evidence for neural mechanisms in vision leading to a general theory of sensory acuity.” In Heinrich Klüver: Visual Mechanisms (The Jacques Cattell Press, Lancaster, Pennsylvania, 1942), Biological Symposia, Vol. 7, pp. 117–164.

Tschermak, A.

A. Tschermak, P. Hoefer, and Pflügers, Arch. ges. Physiol. 98, 299 (1903).
[Crossref]

Vilmar, Karl-Friedrich

Karl-Friedrich Vilmar, Klin. Monatsbl. Augenheilk. 117, 242 (1950).

von Kries, J.

J. von Kries, in Helmholtz’s Treatise on Physiological Optics, translated by J. P. C. Southall (Optical Society of America, New York, 1925), Vol. 3, p. 736.

von Tschermak-Seysenegg, Armin

Armin von Tschermak-Seysenegg, Introduction to Physiological Optics, translated by P. Boeder (Charles C. Thomas, Springfield, Illinois, 1952), p. 299.

Am. J. Ophthalmol. (1)

S. A. Talbot and W. H. Marshall, Am. J. Ophthalmol. 24, 1255 (1941).

Arch. ges. Physiol. (1)

A. Tschermak, P. Hoefer, and Pflügers, Arch. ges. Physiol. 98, 299 (1903).
[Crossref]

Arch. Ophth. (1)

K. N. Ogle, Arch. Ophth. 48, 50 (1952).
[Crossref]

Arch. Ophthalmol. (2)

H. Burian, Arch. Ophthalmol. 136, 172 (1936).

L. Heine, Arch. Ophthalmol. 51, 563 (1900).

Compt. rend. Acad. d. sc. URSS. (1)

L. N. Gassovsky and N. A. Nikolskaya, Compt. rend. Acad. d. sc. URSS. 38, 15 (1943).

J. Exptl. Psych. (1)

K. N. Ogle, J. Exptl. Psych. 44, 253 (1952).
[Crossref]

J. Psychol. u. Neurol. (1)

R. Lorente de Nó, J. Psychol. u. Neurol. 46, 113 (1934).

Klin. Monatsbl. Augenheilk. (1)

Karl-Friedrich Vilmar, Klin. Monatsbl. Augenheilk. 117, 242 (1950).

Psychol. Studien. (1)

R. A. Pfeiffer, Psychol. Studien. 2, 129 (1907).

Z. psychol. physiol. d. Sinnesorg. (1)

G. Skubich, Z. psychol. physiol. d. Sinnesorg. 96, 353 (1925).

Z. Psychol. u. Physiol. d. Sinnesorg. (2)

Anathon Aall, Z. Psychol. u. Physiol. d. Sinnesorg. 49, 108, 161 (1908).

Walther Poppelreuter, Z. Psychol. u. Physiol. d. Sinnesorg. 58, 200 (1911).

Other (6)

K. N. Ogle, Researches in Binocular Vision (W. B. Saunders Company, Philadelphia, 1950), p. 345.

Armin von Tschermak-Seysenegg, Introduction to Physiological Optics, translated by P. Boeder (Charles C. Thomas, Springfield, Illinois, 1952), p. 299.

W. H. Marshall and S. A. Talbot, “Recent evidence for neural mechanisms in vision leading to a general theory of sensory acuity.” In Heinrich Klüver: Visual Mechanisms (The Jacques Cattell Press, Lancaster, Pennsylvania, 1942), Biological Symposia, Vol. 7, pp. 117–164.

J. von Kries, in Helmholtz’s Treatise on Physiological Optics, translated by J. P. C. Southall (Optical Society of America, New York, 1925), Vol. 3, p. 736.

Quoted by R. A. Pfeiffer, reference 7.

Ewald Hering, Spatial Sense and Movements of the Eye, translated by C. A. Radde (The American Academy of Optometry, Baltimore, Maryland, 1942), p. 78.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic illustration of the apparatus used to determine precision and validity of stereoscopic depth with double images.

Fig. 2
Fig. 2

Scheme showing how disparity introduced was kept symmetrical about a given peripheral angle.

Fig. 3
Fig. 3

Typical data for peripheral angles of 1 degree and 8 degrees showing increase in standard deviations (decrease in stereoscopic sensitivity) of stereoscopic depth settings with double images, with increase in the disparity between the images. Circles and triangles are for uncrossed and crossed disparities, respectively.

Fig. 4
Fig. 4

Data for 2 subjects showing validity of stereoscopic depth with double images for a peripheral angle of 1 degree, plotted in terms of actual positions of the reference and test images from the objective frontoparallel plane.

Fig. 5
Fig. 5

Data as in Fig. 4 plotted according to disparities between the images in the two eyes. The heavy dashed lines indicate theoretical curves for strict stereoscopic validity.

Fig. 6
Fig. 6

Data similar to those of Fig. 4, except for a peripheral angle of 6 degrees.

Fig. 7
Fig. 7

Same data as in Fig. 6 plotted in terms of the disparities between the images of the two eyes.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

1 / tan η - A / d = B ,
1 / tan η - A cos 2 α 0 / ( d + d 0 ) = B
2 tan η 1 2 / ( 1 - B tan η 1 2 ) - tan η / ( 1 - B tan η ) = d 0 / A ,
tan η N / ( 1 - B tan η N ) + tan η F / ( 1 - B tan η F ) = 2 d 0 / A ,