Abstract

The locus of perceived equidistance in the eye-level plane was determined at distances of 1.2, 2.2, 3.2, and 4.2 m from the observer. The stimuli were small, point-like light sources viewed in complete darkness. The observer’s head was held fixed; his eyes were allowed to move freely. There were five lights, one in the median plane which remained fixed on every trial, and two variable lights on each side of this at angles of 12° and 24° with respect to the median plane. The locus of perceived equidistance was found to be concave toward the observer at all distances, usually slightly asymmetric with respect to the median plane, and with a variable curvature generally intermediate between that of the physically equidistant circle and that of the corresponding Vieth–Müller circle. The results are inconsistent with an assumption made by Luneburg in his theory of space perception. The pattern of disparities provided by the locus of perceived equidistance was found to vary with viewing distance. This indicates that the perception does not depend on the spatial distribution of retinal stimulation alone and poses a problem as to the nature of the cues that determine perceived equidistance in this situation.

© 1966 Optical Society of America

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References

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  1. R. K. Luneburg, Mathematical Analysis of Binocular Vision (Princeton University Press, Princeton, N. J., 1947).
  2. A. A. Blank, J. Opt. Soc. Am. 48, 911 (1958).
    [CrossRef] [PubMed]
  3. The other assumption concerns the relation between perceived direction and physical direction. It is treated in J. M. Foley, Proc. Am. Psychol. Assoc. 1, 49 (1965).
  4. Luneburg proposed the more general hypothesis that the locus of points perceived as equidistant from an observer is a Vieth–Müller torus (a surface formed by rotating a VMC about the line joining the two rotation centers). However, since the present investigation is limited to the horizontal eye-level plane, the hypothesis is stated in the more restricted form.
  5. E. Hering and C. A. Radde (translator), Spatial Sense and Movements of the Eye (The American Academy of Optometry, Baltimore, 1942), (a) p. 51, (b) p. 52.
  6. T. Shipley, Doc. Opthalmol. 13, 487 (1959).
    [CrossRef]
  7. A. Linksz, Trans. Am. Opthalmol. Soc. 52, 877, 916–944 (1954).
  8. K. N. Ogle, Researches in Binocular Vision (W. B. Saunders Company, Philadelphia, 1950), Chap. 16.
  9. L. Hardy, G. Rand, C. Rittler, A. Blank, and P. Boeder, The Geometry of Binocular Space Perception (Knapp Memorial Laboratories, Institute of Opthalmology, Columbia University College of Physicians and Surgeons, New York, 1953), pp. 37–38.
  10. A. Zajaczkowska, unpublished dissertation, University College, London, 1956.
  11. T. Shipley, Doc. Opthalmol. 15, 321 (1959), (a) p. 340, Fig. 11, observer M. Cy., (b) p. 339, Fig. 10.
    [CrossRef]
  12. G. Kienle, “Experiments Concerning the Non-Euclidian Structure of the Visual Space” in Bioastronautics, K. E. Schaefer, Ed. (The Macmillan Co., New York, 1964), pp. 386–400.

1965 (1)

The other assumption concerns the relation between perceived direction and physical direction. It is treated in J. M. Foley, Proc. Am. Psychol. Assoc. 1, 49 (1965).

1959 (2)

T. Shipley, Doc. Opthalmol. 13, 487 (1959).
[CrossRef]

T. Shipley, Doc. Opthalmol. 15, 321 (1959), (a) p. 340, Fig. 11, observer M. Cy., (b) p. 339, Fig. 10.
[CrossRef]

1958 (1)

1954 (1)

A. Linksz, Trans. Am. Opthalmol. Soc. 52, 877, 916–944 (1954).

Blank, A.

L. Hardy, G. Rand, C. Rittler, A. Blank, and P. Boeder, The Geometry of Binocular Space Perception (Knapp Memorial Laboratories, Institute of Opthalmology, Columbia University College of Physicians and Surgeons, New York, 1953), pp. 37–38.

Blank, A. A.

Boeder, P.

L. Hardy, G. Rand, C. Rittler, A. Blank, and P. Boeder, The Geometry of Binocular Space Perception (Knapp Memorial Laboratories, Institute of Opthalmology, Columbia University College of Physicians and Surgeons, New York, 1953), pp. 37–38.

Foley, J. M.

The other assumption concerns the relation between perceived direction and physical direction. It is treated in J. M. Foley, Proc. Am. Psychol. Assoc. 1, 49 (1965).

Hardy, L.

L. Hardy, G. Rand, C. Rittler, A. Blank, and P. Boeder, The Geometry of Binocular Space Perception (Knapp Memorial Laboratories, Institute of Opthalmology, Columbia University College of Physicians and Surgeons, New York, 1953), pp. 37–38.

Kienle, G.

G. Kienle, “Experiments Concerning the Non-Euclidian Structure of the Visual Space” in Bioastronautics, K. E. Schaefer, Ed. (The Macmillan Co., New York, 1964), pp. 386–400.

Linksz, A.

A. Linksz, Trans. Am. Opthalmol. Soc. 52, 877, 916–944 (1954).

Luneburg, R. K.

R. K. Luneburg, Mathematical Analysis of Binocular Vision (Princeton University Press, Princeton, N. J., 1947).

Ogle, K. N.

K. N. Ogle, Researches in Binocular Vision (W. B. Saunders Company, Philadelphia, 1950), Chap. 16.

Rand, G.

L. Hardy, G. Rand, C. Rittler, A. Blank, and P. Boeder, The Geometry of Binocular Space Perception (Knapp Memorial Laboratories, Institute of Opthalmology, Columbia University College of Physicians and Surgeons, New York, 1953), pp. 37–38.

Rittler, C.

L. Hardy, G. Rand, C. Rittler, A. Blank, and P. Boeder, The Geometry of Binocular Space Perception (Knapp Memorial Laboratories, Institute of Opthalmology, Columbia University College of Physicians and Surgeons, New York, 1953), pp. 37–38.

Shipley, T.

T. Shipley, Doc. Opthalmol. 13, 487 (1959).
[CrossRef]

T. Shipley, Doc. Opthalmol. 15, 321 (1959), (a) p. 340, Fig. 11, observer M. Cy., (b) p. 339, Fig. 10.
[CrossRef]

Zajaczkowska, A.

A. Zajaczkowska, unpublished dissertation, University College, London, 1956.

Doc. Opthalmol. (2)

T. Shipley, Doc. Opthalmol. 13, 487 (1959).
[CrossRef]

T. Shipley, Doc. Opthalmol. 15, 321 (1959), (a) p. 340, Fig. 11, observer M. Cy., (b) p. 339, Fig. 10.
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. Am. Psychol. Assoc. (1)

The other assumption concerns the relation between perceived direction and physical direction. It is treated in J. M. Foley, Proc. Am. Psychol. Assoc. 1, 49 (1965).

Trans. Am. Opthalmol. Soc. (1)

A. Linksz, Trans. Am. Opthalmol. Soc. 52, 877, 916–944 (1954).

Other (7)

K. N. Ogle, Researches in Binocular Vision (W. B. Saunders Company, Philadelphia, 1950), Chap. 16.

L. Hardy, G. Rand, C. Rittler, A. Blank, and P. Boeder, The Geometry of Binocular Space Perception (Knapp Memorial Laboratories, Institute of Opthalmology, Columbia University College of Physicians and Surgeons, New York, 1953), pp. 37–38.

A. Zajaczkowska, unpublished dissertation, University College, London, 1956.

Luneburg proposed the more general hypothesis that the locus of points perceived as equidistant from an observer is a Vieth–Müller torus (a surface formed by rotating a VMC about the line joining the two rotation centers). However, since the present investigation is limited to the horizontal eye-level plane, the hypothesis is stated in the more restricted form.

E. Hering and C. A. Radde (translator), Spatial Sense and Movements of the Eye (The American Academy of Optometry, Baltimore, 1942), (a) p. 51, (b) p. 52.

G. Kienle, “Experiments Concerning the Non-Euclidian Structure of the Visual Space” in Bioastronautics, K. E. Schaefer, Ed. (The Macmillan Co., New York, 1964), pp. 386–400.

R. K. Luneburg, Mathematical Analysis of Binocular Vision (Princeton University Press, Princeton, N. J., 1947).

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Figures (3)

F. 1
F. 1

Mean settings for Observer 1. N = 25. Circumhoropter is relatively flat and symmetric.

F. 2
F. 2

Mean settings for Observer 10. N = 25. These curves are those with the greatest curvature and most skewing.

F. 3
F. 3

Curvature (mm−1) as a function of viewing distance at outside light (24°) and inside light (12°). Data from all 10 observers and from left and right sides combined. N = 500. Dashed lines represent theoretical curves, Vieth–Müller circle (VMC) and physically equidistant circle (EDC).

Tables (2)

Tables Icon

Table I Means and standard deviations of lights perceived as equidistant with a fixed light in the median plane (All values are in cm).

Tables Icon

Table II Disparity of mean setting with respect to the fixed lighta (all values are in minutes of arc).

Equations (2)

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

a s = ϕ + arctan ( i d 0 ) arcsin [ i cos ϕ ( d 2 + i 2 2 d i sin ϕ ) 1 2 ] a 0 = arcsin [ 1 d 2 cos 2 ϕ d 2 + i 2 + 2 d i sin ϕ ] 1 2 arctan ( i d 0 ) ,
η = a s a 0 .