An analysis of retinal receptor orientation
IV. Center of the entrance pupil and the center
of convergence of orientation and
directional sensitivity
Jay M. Enoch and G. M. Hope
In the previous study, we related the peaks of photopic directional sensitivity (Stiles-Crawford)
functions determined, across the retina to the center of the dilated entrance pupil. It was
found that the peaks of directionality were oriented toward a point in close proximity to the
center of the dilated exit pupil of the eye. Here we consider whether this center of convergence
of orientation and directional sensitivity (projected to the plane of the entrance pupil) bears
an improved relationship to the center of the constricted entrance pupil, on the chance that
the dilated and constricted entrance pupils in the same observer have different centers. In the
three normal observers tested, the small variations in pupil centration recorded with change in
pupil size did not further clarify the result. The constricted pupil when compared to the dilated
pupil shifted slightly nasal and/'or upward.
Key words: vision, retina, directional sensitivity of the eye, Stiles-Crawford effect,
retinal receptor orientation, mydriasis, miosis, center of the entrance and
the exit pupils of the eye, corneal reflex, center of convergence
of orientation and directional sensitivity.
I
n a previous paper1 evidence was presented to suggest that the retinal receptors
across the human retina have a carefully
ordered distribution of orientation. They
are aligned transretinally (across the ret-
ina) such that their long axes converge at
a point in close proximity to the center of
the exit pupil of the eye. This point of convergence of the receptor axes in the exit
pupil may be considered as the center
of the aperture of the retina. Alignment
was evaluated by relating the peak of the
Stiles-Crawford function, determined at
each of several retinal test points, to the
center of the dilated entrance pupil. These
peaks fell in a small area within the entrance pupil. Their collective mean position, projected to the plane of the exit pupil, was taken as the estimate of the center
of convergence of orientation and directional sensitivity. Note: Since the exit pupil is
imaged in the entrance pupil of the eye, it
From the Department of Ophthalmology and the
Oscar Johnson Institute, Washington University
School of Medicine, 660 S. Euclid Ave., St.
Louis, Mo. 63110.
This research has been supported in part by National Eye Institute Grant EY-00204 and Career
Development Award No. K3-15138 (to J. M.
E.), and in part by ARPA, Department of the
Army Grant No. DA-ARO-D-31-124-G759.
Manuscript submitted June 26, 1972; revised
manuscript accepted Aug. 30, 1972.
1017
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Investigative Ophthalmology
December 1972
1018 Enoch and Hope
is possible to relate factors in the exit pupil
to each other when studying relationships
present in the entrance pupil.
The data in the paper by Enoch and
Hope1 show that in each subject a small
•error existed in each case between the defined center of maximum (photopic) sensitivity and the center of the exit pupil of
the eye. In that study, for theoretical and
practical reasons, the center of the dilated
entrance pupil of the eye was taken as the
reference origin. There are reports in the
literature which suggest that the center of
the entrance pupil shifts with contraction.2'3
In this paper, we simply ask whether the
alignment of the receptors was directed
toward the center of the constricted exit
pupil rather than the center of the dilated
exit pupil (or some point between). It was
assumed that the centers of the dilated and
constricted pupils represent the range of
pupil centers which might be encountered
in a given normal observer. In a sense, this
brief experiment represents a test of the
generality of the use of the center of the
entrance pupil as a reference in such
studies.
In the previous study, the projection of
the center of convergence of orientation
and directional sensitivity was estimated
for each of three subjects relative to the
geometric center of their dilated entrance
pupil. In this study, using foveal fixation,
the geometric centra of the dilated and
constricted entrance pupils of the same
three observers were determined relative to
each other. The corneal reflex was used as
the common reference point. By this means,
it is possible to relate the center of convergence of orientation and directional sensitivity to the geometric center of the constricted entrance or exit pupil.
Method
The Stiles-Crawford apparatus described by
Enoch and Hope1 was employed. The emmetropic
observer was fixed to the instrument by head rest
and bite bar. His foveal fixation was directed
toward the center of the combined test and background field. The experimenter centered the apertures of both fields on the reticule pattern. The
subject's entrance pupil (illuminated by infrared
light sources) was focused as sharply as possible
on the reticule and, hence, on the cathode of
the infrared image converter. Shutter 2 (see Fig.
4 in Enoch and Hope 1 ) was closed in order to
facilitate viewing of the superimposed corneal
reflexes of the test and background field in the
image converter. The focused entrance pupil was
translated until the corneal reflex was visible. It
was centered on the reticule pattern. The picture
seen on the phosphor of the infrared image converter was photographed using a special Burke
and James single lens reflex copy camera, f/1,
-l.Ox lateral magnification. The camera was indexed to the Stiles-Crawford device in order to
maintain constant object distance and image position. The eyepiece normally used to view the
cathode was removed. Polaroid film was employed.
The subject's pupil was dilated with repeated
doses of Euphthalmine 5 per cent. The experiment
was then repeated on a separate day at which
time the pupil was constricted with Pilocarpine
HC1 1 per cent. Data on refraction and angle
kappa on each emmetropic subject are presented
in the previous paper.
The corneal reflex caused by the incremental field
was not visible in the infrared viewer unless the
fixing left eye (and entrance pupil) was translated
laterally a bit to the left. A very small vertical
translation was also indicated on occasion. The
optimized corneal reflex appeared in the reticule
pattern at the same position as the image of the
apertures of the two fields. This suggests virtually
normal incidence and reflection. The latter conclusion was reinforced by the following observation. The entrance pupil was focused on the IR
cathode in this experiment. Hence, the corneal
reflex was blurred because its image lies behind
the plane of the entrance pupil. Focusing down on
the corneal reflex (about 1 mm.) caused no detectable translation of the beam relative to the
reticule. Thus, changing focus slightly did not
cause a meaningful parallactic error. This point is
important because the plane of the entrance pupil
probably shifts in a fore and aft direction with
constriction and dilation.
Four photographs each were taken of the constricted and dilated entrance pupils of each subject. The four photographs of the dilated pupils
were individually projected onto a reference surface by an opaque projector. The pupil circumference, position of the corneal reflex of the (superimposed) test and background beams, and reflexes of the infrared sources were traced onto
gridded paper. Each projection was compared with
the other three to provide an estimate of the
variability in the technique. Each of the four
constricted pupil photographs was then projected
and traced onto two of the previously traced
dilated pupils for each subject. Precise alignment
of the eye in the two projections was assured by
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Volume 11
Number 12
Analysis of retinal receptor orientation. IV. 1019
careful superimposition of the corneal reflex from
the test and background beams. The laterally
placed reflexes of the two infrared sources established a horizontal line providing a means of
avoiding rotation of one projection relative to the
other. The object-image distance of the projector
was maintained constant for all projections.
A perfect circle of the average diameter of each
dilated or constricted pupil was used as a template
for locating the center of the pupils. The template
was overlaid on the tracings. It was then adjusted
to provide the best match to the pupil circumference, and the point on the pupil tracing corresponding to the center of the template was
marked precisely. Repeated matches of the template to the tracings indicated that the technique
was quite reliable. The displacement of the center
of the constricted pupil relative to that of the
dilated pupil was determined in the horizontal and
vertical directions and converted to millimeters
through the use of a millimeter scale placed at
the plane of the entrance pupil, photographed, and
projected precisely as for the pupils. Eight comparisons of a dilated to a constricted entrance
pupil (of the 16 possible in the 4 by 4 matrix)
were made for each subject.
Results
Fig. 1 presents the results of the analysis
described above. The center of the constricted entrance pupil (small crosses) was
displaced from that of the dilated entrance
pupil (center of X and Y coordinates) for
all three subjects. The mean centrum of
the Stiles-Crawford curves (from seven
retinal loci) for each of these subjects1 is
depicted by Xs. The shift of the constricted
pupil was such that it essentially coincided
with the mean Stiles-Crawford centrum for
subject SH, was generally in the right direction, and the range of variabilities for
the two data sets overlapped slightly (compare with Fig. 10, HE, Enoch and Hope1)
for subject HE, but was in exactly the
opposite direction for subject BL. When
the mean data points across all three subjects were considered, the three centers fell
very close to each other. All three points
could be covered by a circle of radius
equal to 0.25 mm. and having an area of
less than 0.2 mm.2. This area comprised
less than 6.5 per cent of a constricted
entrance pupil (2 mm. diameter) and less
than 0.3 per cent of a dilated entrance
pupil (9 mm. diameter).
MEANS
ALL SUBJECTS
IOS)
lmm
0
lmm
lmm
0
lmm
-^—NASAl(Rr)
TEMPORAL ( U ) — » X
MEAN CENTRUM
CURVES
OF
STILES-CRAWFORD
I-J-H MEAN CENTER OF CONSTRICTED
PUPIL (WITH RANGE)
ENTRANCE
Fig. 1. Centers of the dilated and constricted
entrance pupils and of the projection in the entrance pupil of the center of convergence of orientation and directional sensitivity. The centers of
the dilated entrance pupils are depicted by the
intersection of the X and Y coordinates of each
part of the figure. The centers of the constricted
entrance pupils are indicated by small + symbols,
the length of the arms of which indicate the
range of variability of eight comparisons. The position of the projection of each center of convergence of orientation and directional sensitivity is
indicated by an X. The large circle on each set of
coordinates depicts a 2 mm. diameter schematic
entrance pupil centered on the objectively determined constricted entrance pupil center. Individual data for three subjects and their mean are
shown in the four quadrants of this figure.
Another factor considered was the position of the corneal reflex of the superimposed test and background beams relative
to the centers of the constricted and dilated
pupils (Fig. 2). The corneal reflex maintained a fairly consistent relationship to the
center of the dilated entrance pupil across
the three subjects, lying slightly less than
0.5 mm. nasal and very slightly above or
below ( < 0.2 mm.) the pupil center. For
subject SH, the center of the constricted
entrance pupil and the corneal reflex were
in fairly good register. For the other two
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Investigative Ophthalmology
December 1972
1020 Enoch and Hope
SH
(OS)
HE
(OS)
BL
(OS)
MEANS
ALL SUBJECTS
(OS)
lmm
lmm
lmm
1mm
— « r - N A S A L (Rr.)
TEMPORAL ( L t . ) — * —
°
CORNEAL REFLEX FROM STIMULUS ARRAY
•4-* CENTER OF CONSTRICTED PUPIL
Fig. 2. Centers of the dilated and constricted entrance pupils compared to the position of the
corneal reflex. The corneal reflexes for foveal fixation on the stimulus array are depicted by open
circles. Other details are as for Fig. 1.
subjects however, this was not the case. If,
however, one considered the mean values
across the three subjects, the three points
were quite tightly grouped.
Discussion
Here we have compared the centration of
the dilated and constricted entrance pupils
of the eye with the mean centrum of the
Stiles-Crawford functions (the projection
in the entrance pupil of the center of convergence of orientation and directional sensitivity) for the individual observers. Taken
as an average across the three subjects,
the three points were in very good register,
suggesting that, in the normal observers
included in this sample, the centers of the
constricted and dilated exit pupils and the
center of convergence of orientation and
direction sensitivity are, on the average,
probably virtually coincident. A slight shift
of the constricted pupil relative to the
dilated pupil was seen in all three of the
observers. The tendency was nasal and
slightly upward.3 Finally, the relationship
of the corneal reflex of the stimulus array
maintains a fairly consistent relationship to
the center of the dilated entrance pupil in
the individual observers.
Both the center of the dilated entrance
pupil and the corneal reflex have been used
as primary references in conducting StilesCrawford research (e.g., Safir, Hyams, and
Philpot* and Enoch and Hope1). Given the
brief time-bound defined in this study, the
present comparisons suggested that either
is acceptable in this respect as long as the
direction of view is toward the stimulus
array, or very close to it. With oblique
viewing, the corneal reflex changes its position relative to the center of the entrance
pupil dramatically. It is, of course, precisely
this feature which recommends the use of
this reference for .certain types of visual
task. In the present research, however, the
Stiles-Crawford data were taken over a
large span of retinal points and fixation
directions. Since the corneal reflex from the
stimulus array shifts considerably over such
a range,- a comparison of the Stiles-Crawford data and the position of this variable
was carefully avoided.
Departure from concentricity for the
constricted and dilated entrance pupils has
been described previously.2-3 The present
data demonstrated small shifts of the constricted pupil in all three of our emmetropic
subjects. Comparisons of each projection of
a dilated pupil photograph with the other
three for each subject indicated that there
was no detectable variability in the photographs. This was not the case for the photographs of the constricted pupil. However,
this source of variability was incorporated
with any experimentor measurement error
which may have existed, and was shown in
Fig. 1. The fact that the range of variability
did not overlap the center of the dilated
entrance pupil attests to the reality of the
shifts. The constricted pupil centers clearly
shifted nasalward in two subjects and upward in all three. The mean data, reflecting the nasalward and upward shift, compares almost perfectly with the 0.28 mm.
shift predicted by Gullstrand3 for spherical
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Volume 11
Number 12
Analysis of retinal receptor orientation. IV. 1021
corneas! The corneas of these emmetropic
observers were virtually spherical. For
foveal fixation, the mean center of the constricted entrance pupil tended to shift toward the location of the corneal reflex.
Enoch and Hope1 suggested that one
possible cause of the small eccentricities of
the transretinally-determmed Stiles-Crawford centra might be due to a shift of the
constricted pupil relative to that of the
dilated one. This hypothesis received no
definitive support in the present experiment. For only one subject was there any
indication that this factor may account for
the Stiles-Crawford eccentricity and this
case was offset by another observer for
whom the pupil shift was in the opposite
direction to that required. In the mean
data, the Stiles-Crawford centrum was
about equidistant from the centers of the
dilated and constricted entrance pupils
(0.40 and 0.35 mm., respectively). In the
exit pupil these values would be 0.36 and
0.32 mm., respectively. In fact, the rather
good register of the three points is much
more impressive than their separation and
is a further illustration of the precision with
which the several factors contributing to
the directional sensitivity of the system
function.1-5
The reader is reminded that a shift of
the Stiles-Crawford peak in the entrance
pupil by 1.0 mm. reflects only a 2.5° dif-
ference in alignment measured at the retina. One must consider an array of millions
of receptors only tens of microns long, remotely placed and oriented relative to the
plane of the pupillary aperture, a distance
measured in tens of millimeters. This precision of alignment is not a chance occurrence. The amazing thing is the limited
magnitude of discrepancy between the
transretinally-determined peaks of the
Stiles-Crawford functions and the center
of the exit pupil, not the fact that small
discrepancies exist. As pointed out in previous papers in this series,1'6 it is clearly
necessary to define mechanisms establish
ing, influencing, and maintaining appropriate receptor alignment and anomalies related to these processes.
REFERENCES
1. Enoch, J. M., and Hope, G. M.: An analysis
of retinal receptor orientation: III. Results of
initial psychophysical tests, INVEST. OPHTHALMOL. 11: 765, 1972.
2. Le Grand, Y.: Optique Physiologique I ,Ed. 2,
Paris, 1952, Editions de la Revue D'Optique,
p. 45.
3. Gullstrand, A.: in Von Helmholtz, H.: Physiological Optics, Ed. 3, New York, 1962, Dover,
Vol. I, pp. 356 and 396.
4. Safir, A., Hyams, L., and Philpot, J.: Movement of the Stiles-Crawford effect, INVEST.
OPHTHALMOL. 9: 820, 1970.
5. Enoch, J. M.: Retinal receptor orientation and
the role of fiber optics in vision, Am. J. Optom.
49: 455, 1972.
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