Page 177 - Modern Optical Engineering The Design of Optical Systems

160 Chapter Eight

There are about 7 million cones in the retina, about 125 million rods,
and only about 1 million nerve fibers. The cones of the fovea are 1 to
1.5 m in diameter and are about 2 to 2.5 m apart. The rods are
about 2 m in diameter. In the outer portions of the retina, the sensi-
tive cells are more widely spaced and are multiply connected to nerve
fibers (several hundred to a fiber), accounting for the less distinct
vision in this area of the retina. In the fovea, however, for some cones
there is one cone cell per fiber; but there are 7 million cones and only
one million nerve fibers.
The field of vision of an eye approximates an ellipse about 130° high
by about 160° wide. The binocular field of vision, seen by both eyes
simultaneously, is approximately circular and about 120° in diameter.

8.3 Characteristics of the Eye
Visual acuity
The characteristic of the eye which is probably of greatest interest to the
optical engineer is its ability to recognize small, fine details. Visual acuity
(VA) is defined and measured in terms of the angular size of the small-
est character that can be recognized. The characters most frequently
used to test VA are uppercase letters or a heavy ring with a break in the
outline. Many uppercase letters can be considered as made up of five
elements; e.g., the letter E has three bars and two spaces. Visual acuity
is the reciprocal of the angular size (in minutes of arc) of one of the ele-
ments of the letter. “Normal” VA is considered to be 1.0, i.e., when the
smallest recognizable letter subtends an angular height of 5 minutes
from the eye and each element of the letter subtends 1 minute. Acuity
is frequently expressed as the ratio between the distance to the target
(usually 20 ft) and the distance at which the target element would sub-
tend 1 minute. Thus, a VA of one-half, or 20/40, indicates that the
minimum recognizable letter subtends 10 minutes and its elements
2 minutes. In the Landolt broken ring test, the width of the ring and the
width of the break correspond to the letter element size, and recognition
consists of determining the orientation of the break. Visual acuity may
reach 2 (or 3 in unusual individuals) under ideal conditions.
As indicated above, the “normal” visual acuity is 1 minute, and this
is also the value for the angular resolution of the eye which is conven-
tionally assumed in connection with the design of optical instruments.
Note however that a resolution of one line pair (or one cycle) per minute
of arc actually corresponds to a VA of 2, or 20/10. However, this is the
value of VA under what might be termed “normal conditions,” and it is
the value only for that part of the field of view which corresponds to the
fovea of the retina. Outside the fovea, the acuity drops rapidly, as indi-
cated in Fig. 8.2, which is a logarithmic plot of visual acuity (relative to