Abstract

An observer’s just discriminable difference in depth is a function of his interocular distance, his threshold difference in binocular parallax, and the observation distance. Magnification devices consisting of lenses and/or prisms will change the threshold of depth resolution because the latter now depends on the optical properties of the device as well as on the observer’s characteristics. An equation has been derived expressing this change in linear threshold of depth resolution as a function of the lens and prism power of the device, the separation of the components of the device from the eye, the observer’s interocular distance, and the object distance. Free choice of the optical properties of such magnifiers is, however, restricted since these properties must permit a clear retinal image of the object to be formed simultaneously on the foveas of both of the observer’s eyes. In general, plus lenses and base-in prisms will enhance the depth resolution and this points to the use of such devices in tasks demanding high depth resolution at close observation distances, as, for example, in surgery or inspection of surface defects.

An experimental determination of the change in linear depth resolution produced by a binocular magnifier showed close agreement with the theoretical prediction.

© 1956 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. S. Duke-Elder, Textbook of Ophthalmology (C. V. Mosby Company, St. Louis, 1938), Vol. I, p. 1077.
  2. G. Westheimer, Am. J. Optom. 31, 578 (1954).
    [CrossRef]
  3. K. N. Ogle and V. J. Ellerbrock, Arch. Ophthalmol. 34, 301 (1945).
    [CrossRef]

1954 (1)

G. Westheimer, Am. J. Optom. 31, 578 (1954).
[CrossRef]

1945 (1)

K. N. Ogle and V. J. Ellerbrock, Arch. Ophthalmol. 34, 301 (1945).
[CrossRef]

Duke-Elder, W. S.

W. S. Duke-Elder, Textbook of Ophthalmology (C. V. Mosby Company, St. Louis, 1938), Vol. I, p. 1077.

Ellerbrock, V. J.

K. N. Ogle and V. J. Ellerbrock, Arch. Ophthalmol. 34, 301 (1945).
[CrossRef]

Ogle, K. N.

K. N. Ogle and V. J. Ellerbrock, Arch. Ophthalmol. 34, 301 (1945).
[CrossRef]

Westheimer, G.

G. Westheimer, Am. J. Optom. 31, 578 (1954).
[CrossRef]

Am. J. Optom. (1)

G. Westheimer, Am. J. Optom. 31, 578 (1954).
[CrossRef]

Arch. Ophthalmol. (1)

K. N. Ogle and V. J. Ellerbrock, Arch. Ophthalmol. 34, 301 (1945).
[CrossRef]

Other (1)

W. S. Duke-Elder, Textbook of Ophthalmology (C. V. Mosby Company, St. Louis, 1938), Vol. I, p. 1077.

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 (3)

Fig. 1
Fig. 1

Relationship between g (smallest discernible antero-posterior displacement of one object behind another one lying at a distance x in the median plane) and η0 (angular measure of stereoscopic acuity). O is the center of the entrance pupil, C is the center of rotation, and γ/2 is half the angle of convergence.

Fig. 2
Fig. 2

Right eye of an observer viewing a point in the median plane through a device consisting of a lens of power F diopters placed at a distance h in front of the center of the entrance pupil and centered in the median plane, and a prism of power Δ placed at a distance t in front of the center of rotation. The linear threshold of depth resolution is now du which is the image of du′. O is the center of the entrance pupil, C the center of rotation, and O′ and C′ the positions of these points to which the prism effectively displaces them.

Fig. 3
Fig. 3

Apparatus used to measure depth resolution. (a) Top view, (b) front view. Glass plate A mounted on turntable B can be rotated around a vertical axis by means of micrometer screw C. A milk glass panel D in front of a show case lamp E provides a homogeneous background against which the target, consisting of two black vertical lines photographically reproduced on plate A, can be seen.

Tables (1)

Tables Icon

Table I Depth resolution with and without magnifying device.

Equations (6)

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

g = x · ( x + s ) · η 0 / 2 a ,
d u = - ( h - u ) · ( h + s - u ) · η 0 / 2 a .
d u = - [ h ( u F + 1 ) - u ] · [ ( h + s ) ( u F + 1 ) - u ] · η 0 / 2 ( a + Δ t ) .
g * = [ x ( 1 - h F ) + h 2 F ] · [ ( x + s ) - ( h + s ) ( x - h ) F ] · η 0 / 2 ( a + Δ t ) .
g * g = [ a a + Δ t ] · [ x ( 1 - h F ) + h 2 F x ] · [ ( x + s ) - ( h + s ) ( x - h ) · F x + s ] .
g * / g = a / ( a + Δ t )