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  1. A. Ames, K. N. Ogle, and G. H. Gliddon, “Corresponding retinal points, the horopter, etc.,” J. Opt. Soc. Am. 22, 538–631 (1932).
    [Crossref]
  2. A. Ames, “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).
    [Crossref]
  4. A. Ames, “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).
    [Crossref]
  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.
    [Crossref]
  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).
    [Crossref]
  9. K. N. Ogle, “An optical unit for obtaining variable magnification for ophthalmic use,” J. Opt. Soc. Am. 32, 143–146 (March, 1942).
    [Crossref]
  10. Since any given aniseikonic correction can be resolved into an over-all magnification, 0percent, combined with a meridional magnification, f percent, at some axis ϕ°, the components in the horizontal and vertical meridians will be given by h= 0+f sin2ϕ, and v= 0+f cos2ϕ, respectively. The correction for the declination error between the images of the two eyes due to the oblique magnification will be δ= 0.29 f sin 2 ϕ. Thus, if the quantities h, v, and δ can be measured, 0,f, 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 Sehen mit 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 (July1945).
  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).
    [Crossref]
  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).
    [Crossref]
  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).
    [Crossref]
  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 δ0and 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=−12(δbc+δbv)and τ=12(δbc−δbv), where δbc and δbv 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.

1945 (3)

A. Ames, “The space-eikonometer test for aniseikonia,” Am. J. Ophthal. 28, 248–262 (March, 1945).

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).
[Crossref]

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 (July1945).

1944 (1)

1943 (1)

For a brief description see K. N. Ogle, “Association between aniseikonia and binocular spatial localization,” Arch. f. Ophth. 30, 54–64 (July, 1943).
[Crossref]

1942 (1)

1938 (2)

K. N. Ogle, “The induced size effect,” Arch. f. Ophth. 20, 604–623 (Oct., 1938).
[Crossref]

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).
[Crossref]

1935 (1)

A. Ames, “Aniseikonia—A factor in the functioning of vision,” Am. J. Ophthal. 18, 1014–1020 (Nov., 1935).

1932 (2)

1900 (1)

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).
[Crossref]

Ames, A.

A. Ames, “The space-eikonometer test for aniseikonia,” Am. J. Ophthal. 28, 248–262 (March, 1945).

A. Ames, “Aniseikonia—A factor in the functioning of vision,” Am. J. Ophthal. 18, 1014–1020 (Nov., 1935).

A. Ames, K. N. Ogle, and G. H. Gliddon, “Corresponding retinal points, the horopter, etc.,” J. Opt. Soc. Am. 22, 538–631 (1932).
[Crossref]

Bielschowsky, A.

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).
[Crossref]

Burian, H. M.

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 (July1945).

Ellerbrock, V. J.

K. N. Ogle and V. J. Ellerbrock, “Cyclofusional movements,” Arch. f. Ophthal., at publishers.

K. N. Ogle and V. J. Ellerbrock, “Stereoscopic sensitivity in the space-eikonometer,” Arch. f. Ophthal. at publishers.

Gliddon, G. H.

Hofmann, F. B.

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).
[Crossref]

Madigan, L. F.

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).
[Crossref]

Ogle, K. N.

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 (July1945).

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).
[Crossref]

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.
[Crossref]

For a brief description see K. N. Ogle, “Association between aniseikonia and binocular spatial localization,” Arch. f. Ophth. 30, 54–64 (July, 1943).
[Crossref]

K. N. Ogle, “An optical unit for obtaining variable magnification for ophthalmic use,” J. Opt. Soc. Am. 32, 143–146 (March, 1942).
[Crossref]

K. N. Ogle, “The induced size effect,” Arch. f. Ophth. 20, 604–623 (Oct., 1938).
[Crossref]

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).
[Crossref]

A. Ames, K. N. Ogle, and G. H. Gliddon, “Corresponding retinal points, the horopter, etc.,” J. Opt. Soc. Am. 22, 538–631 (1932).
[Crossref]

K. N. Ogle and V. J. Ellerbrock, “Cyclofusional movements,” Arch. f. Ophthal., at publishers.

K. N. Ogle and V. J. Ellerbrock, “Stereoscopic sensitivity in the space-eikonometer,” Arch. f. Ophthal. at publishers.

Panum, A.

A. Panum, Physiol. Untersuchungen über das Sehen mit zwei Augen (Kiel, 1858), see p. 81. A. Nagel, Das Sehen mit zwei Augen (Leipzig, 1861).

Werner, H.

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).
[Crossref]

Am. J. Ophthal. (3)

A. Ames, “The space-eikonometer test for aniseikonia,” Am. J. Ophthal. 28, 248–262 (March, 1945).

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 (July1945).

A. Ames, “Aniseikonia—A factor in the functioning of vision,” Am. J. Ophthal. 18, 1014–1020 (Nov., 1935).

Am. J. Psych. (1)

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).
[Crossref]

Arch. f. Ophth. (3)

For a brief description see K. N. Ogle, “Association between aniseikonia and binocular spatial localization,” Arch. f. Ophth. 30, 54–64 (July, 1943).
[Crossref]

K. N. Ogle, “The induced size effect,” Arch. f. Ophth. 20, 604–623 (Oct., 1938).
[Crossref]

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).
[Crossref]

J. Opt. Soc. Am. (4)

Pflügers Arch. (1)

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).
[Crossref]

Other (10)

K. N. Ogle and V. J. Ellerbrock, “Cyclofusional movements,” Arch. f. Ophthal., at publishers.

For the effect of magnifying the image of the left eye, it is only necessary to substitute 1/M for M in subsequent formulas.

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.

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.

As will be shown later, a fourth measurement may be necessary, to eliminate the effect of a cyclotorsion between the eyes.

Since any given aniseikonic correction can be resolved into an over-all magnification, 0percent, combined with a meridional magnification, f percent, at some axis ϕ°, the components in the horizontal and vertical meridians will be given by h= 0+f sin2ϕ, and v= 0+f cos2ϕ, respectively. The correction for the declination error between the images of the two eyes due to the oblique magnification will be δ= 0.29 f sin 2 ϕ. Thus, if the quantities h, v, and δ can be measured, 0,f, and ϕ can be found. Tables have been prepared from which these quantities can be found directly, see reference 6.

A. Panum, Physiol. Untersuchungen über das Sehen mit zwei Augen (Kiel, 1858), see p. 81. A. Nagel, Das Sehen mit zwei Augen (Leipzig, 1861).

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.

This technique with the beads makes it possible to find both δ0and 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=−12(δbc+δbv)and τ=12(δbc−δbv), where δbc and δbv 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.

K. N. Ogle and V. J. Ellerbrock, “Stereoscopic sensitivity in the space-eikonometer,” Arch. f. Ophthal. at publishers.

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Figures (10)

Fig. 1
Fig. 1

Perspective drawing of the space-eikonometer.

Fig. 2
Fig. 2

Geometrical scheme in determining the apparent change in distance of the vertical lines of the space-eikonometer, when the size of the image of the right eye is magnified.

Fig. 3
Fig. 3

Perspective of coordinate system used in study of the apparent orientation of the cross of the space-eikonometer.

Fig. 4
Fig. 4

Diagram showing rotary deviation of meridians when a meridional magnification is introduced.

Fig. 5
Fig. 5

Scheme for designating the symmetrical and asymmetrical elevation angles to the lines of the cross.

Fig. 6
Fig. 6

Theoretical apparent inclination of the cross when the symmetrical elevation angles are varied, both for a meridional magnification of the image in one eye and for a torsion difference between the images of the two eyes.

Fig. 7
Fig. 7

Typical data showing transverse rotation and angle of inclination of a cross consisting of two lines at right angles, but variously orientated, when a meridional magnification is introduced in the image of one eye. Data of K.N.O.

Fig. 8
Fig. 8

An equal incyclotorsion of the two eyes and the apparent orientation of the retinal images of the cross of the space-eikonometer.

Fig. 9
Fig. 9

Photograph of the geared meridional size lens device used on the space-eikonometer for measuring the declination error between the two eyes.

Fig. 10
Fig. 10

Schematic drawing of the manner in which the geared size lens unit introduces changes in the vertical declinations between the two eyes.

Equations (33)

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( x a ) / y = M ( x a ) / b
( x + a ) / y = ( x + a ) / b ,
y p = 2 a b / [ ( M + 1 ) a ( M 1 ) x ] .
y q = 2 a b / [ ( M + 1 ) a + ( M 1 ) x ] .
D = 4 a s b ( M 1 ) / [ ( M + 1 ) 2 a 2 ( M 1 ) 2 s 2 ] .
D = ( 0.01 ) m b s / a ,
x y ( a / b ) / z cot ρ L = 0
x + y ( a / b ) z cot ρ R = 0 ,
x cos y sin z cot ρ L = 0 , x cos + y sin z cot ρ R = 0 ,
x / p sin = y / q cos = z / sin 2 ,
p = cot ρ R + cot ρ L and q = cot ρ R cot ρ L .
A x + B y + C z = 0 ,
A = ( q 1 q 2 ) cos B = ( p 2 p 1 ) sin C = 1 2 ( p 1 q 2 p 2 q 1 ) .
tan ψ = A / B = ( q 1 q 2 ) cot / ( p 1 p 2 ) , and tan ι = C / B = 1 2 ( p 1 q 2 p 2 q 1 ) csc / ( p 1 p 2 ) ,
tan ρ = [ F G ] [ G + tan ρ 1 + F tan ρ ] ,
F = K sin 2 θ / ( 1 + K cos 2 θ ) ,
G = K sin 2 θ / ( 1 K cos 2 θ ) , K = ( M 1 ) / ( M + 1 ) .
cot ρ R 1 = G F F + r 1 1 + G r 1 , cot ρ R 2 = G F F + r 2 1 + G r 2 ,
cot ρ L 1 = r 1 , and cot ρ L 2 = r 2 .
tan ψ = K cos 2 θ cot / ( 1 k ) ,
tan ι = K 2 sin 4 θ 2 ( 1 K cos 2 θ ) ( 1 k ) csc ,
tan ι v = y / z = g / h .
tan ι v = 1 2 ( tan δ d tan δ s ) csc = 1 2 tan δ csc ,
tan δ = K sin 2 θ 1 K cos 2 θ ,
tan ι v = 1 2 K sin 2 θ 1 K cos 2 θ csc .
cot ρ R 1 = cot ( ρ 1 τ 2 ) , cot ρ R 2 = cot ( ρ 2 τ 2 ) , cot ρ L 1 = cot ( ρ 1 + τ 2 ) , cot ρ L 2 = cot ( ρ 2 + τ 2 ) .
tan ι c = 2 tan τ 2 csc / ( 1 tan 2 τ ) ,
tan ι c = tan τ csc ,
tan δ = 2 K sin 2 α / ( 1 K cos 2 α ) ,
tan ι c = tan τ csc = 1 2 ( tan τ + tan δ 0 + tan δ g ) csc ,
τ δ 0 = δ g .
1 2 ( tan τ + tan δ 0 + tan δ g + tan δ b ) csc = 0 ,
τ = 1 2 δ b and δ 0 = ( δ g + 1 2 δ b )