Engineering Technological .t CHRISTINA ENROTH-CUGELL

Engineering Technological .t CHRISTINA ENROTH-CUGELL
J. Phy8iol. (1966), 187, pp. 517-552
With 17 text-ftgure8
Printed in Great Britain
517
THE CONTRAST SENSITIVITY OF RETINAL GANGLION
CELLS OF THE CAT
BY CHRISTINA ENROTH-CUGELL AND J. G. ROBSON*
From the Biomedical Engineering Center, Technological Institute,
Northwestern University, Evanston, Illinois, U.S.A .t and
the Department of Physiology, Northwestern University
Medical School, Chicago, U.S.A.
(Received 19 April 1966)
SUMMARY
1. Spatial summation within cat retinal receptive fields was studied by
recording from optic-tract fibres the responses of ganglion cells to grating
patterns whose luminance perpendicular to the bars varied sinusoidally
about the mean level.
2. Summation over the receptive fields of some cells (X-cells) was found
to be approximately linear, while for other cells (Y-cells) summation was
very non-linear.
3. The mean discharge frequency of Y-cells (unlike that of X-cells) was
greatly increased when grating patterns drifted across their receptive
fields.
4. In twenty-one X-cells the relation between the contrast and spatial
frequency of drifting sinusoidal gratings which evoked the same small
response was measured. In every case it was found that the reciprocal of
this relation, the contrast sensitivity function, could be satisfactorily
described by the difference of two Gaussian functions.
5. This finding supports the hypothesis that the sensitivities of the
antagonistic centre and surround summating regions of ganglion cell
receptive fields fall off as Gaussian functions of the distance from the
field centre.
6. The way in which the sensitivity of an X-cell for a contrast-edge
pattern varied with the distance of the edge from the receptive field centre
was determined and found to be consistent with the cell's measured
contrast sensitivity function.
7. Reducing the retinal illumination produced changes in the contrast
*
On leave from the Physiological Laboratory, Cambridge.
t Mailing address.
C. ENROTH-CUGELL AND J. G. ROBSON
sensitivity function of an X-cell which suggested that the diameters of the
summating regions of the receptive field increased while the surround
region became relatively ineffective.
518
INTRODUCTION
Kuffler (1952) found that the receptive fields of light-adapted cat retinal
ganglion cells are approximately circular and have functionally distinct
central and peripheral regions; he showed that stimulation of these two
regions produces opposite and antagonistic effects upon the activity of the
ganglion cells. This concentric arrangement of receptive fields seems to be
universal in both the cat and spider monkey (Wiesel, 1960; Hubel &
Wiesel, 1960) and has also been found in the frog (Barlow, 1953) and rabbit
(Barlow, Hill & Levick, 1964). It has been supposed that the receptive
fields of the ganglion cells of the human retina have the same organization
and it might therefore be expected that the characteristic behaviour of
retinal ganglion cells would be closely correlated with the characteristics
of human spatial vision, especially if measurements of the same kind were
considered.
There have been many investigations of human spatial vision in both its
acuity and contrast discrimination aspects (see reviews of Westheimer,
1965, and Boynton, 1962) but only one of the available methods of investigating the characteristics of spatial summation in the human visual
system has been at all extensively applied to retinal ganglion cells. This
method is the determination of the effect of size upon the increment
threshold for a circular test patch. Barlow (1953) has used incremental
threshold measurements of this kind to show that frog retinal ganglion
cells respond to a linear combination of signals proportional to light
intensity coming from all parts of their receptive fields. Barlow, Fitzhugh
& Kuffler (1957) and Wiesel (1960) have also successfully employed the
same method in studies of receptive fields in the cat retina and have briefly
discussed the relation of their results to visual acuity and simultaneous
contrast phenomena.
In studies on retinal ganglion cells the activity of the inhibitory surrounds of retinal receptive fields is clearly demonstrated by the existence
of an optimal diameter for the test patch. But psychophysical determinations of the threshold contrast for disks of various diameters (e.g.Barlow,
1958) show that there is no optimal diameter for a test patch. To explain
this difference it has been postulated that the inhibitory effects within the
receptive fields of individual ganglion cells in the human retina are obscured
by the mode of operation of the central mechanism responsible for detecting changes in the discharge in the optic nerve (Glezer, 1965). However,
it is obviously desirable to investigate spatial summation in animal retinas
519
CAT RETINAL CONTRAST SENSITIVITY
with techniques which, when applied to the human visual system, do not
obscure any inhibitory retinal interactions.
A particularly promising technique was introduced by Schade (1956)
who measured the visibility of grating patterns having a luminance
which varied sinusoidally with distance perpendicular to the direction of
the bars. He found that the threshold level of contrast for detecting such
patterns was a function of the spatial frequency of the grating and showed
a clear minimum at a spatial frequency which varied with the mean
luminance. He interpreted the fall in sensitivity at higher spatial frequencies as the joint effect of optical blurring and retinal summation and
the fall in sensitivity at lower spatial frequencies as the effect of retinal
inhibition.
We now report measurements of the responses of cat retinal ganglion
cells to sinusoidal grating patterns of the kind employed by Schade. In
particular we consider the relation between the contrast and spatial
frequency of grating patterns which evoke the same (small) response from
a ganglion cell; this relation provides a description ofthe spatial summation
within the receptive field of the cell which can be directly compared with
the psychophysical results of Schade (1956) and others. We also consider
'the usefulness of the 'contrast sensitivity function' of a ganglion cell (the
reciprocal of the relation described above) in predicting the sensitivity
of the cell to other patterns. This amounts to a consideration of the
linearity of the retinal summation process, for it is only within the limits
of linearity that the techniques of Fourier analysis and synthesis (the
techniques required for using the contrast sensitivity function) can be
applied.
METHODS
and
Preparation
recording. Experiments were conducted on adult cats anaesthetized with
an initial 40-S80 mg/kg intraperitoneal injection of thiopentone sodium. Additional thiopentone was given intravenously in single doses at an average rate of about 1*5 mg/kg. hr when
the experiments lasted more than 10-12 hr. Preliminary experiments (without muscle
relaxants) showed that this procedure maintained anaesthesia satisfactorily. To suppress
eye movements succinylcholine chloride was administered by continuous intravenous
infusion at rates of 7-5-25 mg/kg.hr in a glucose and dextran solution. For those experiments in which the effect of varying the position of a grating or an edge within the receptive
field was studied (see Figs. 1, 3, 12-14) immobilization of the eyes was particularly critical
and dose rates of approximately 20 mg/kg. hr were always required. Body temperature was
maintained at 380 C.
The cat's head was fixed in a stereotaxic instrument and a rectangular piece of bone
together with the underlaying dura was removed from the top of the skull. This opening lay
directly above the optic chiasm and that portion of the optic tract above which there is no
geniculate body (Jasper & Ajmone-Marsan, 1954). Tungsten electrodes with a tip diameter
of approximately 0 5 p (Hubel, 1957) were used. The electrodes were held in a manipulator
with hydraulically controlled vertical motion, modified after Hubel (1959). A vertical wall
of dental impression compound around the hole in the skull together withl the base plate
520
C. ENROTH-CUGELL AND J*. G. ROBSON
of the hydraulic electrode-positioner (pressed against the compound while this was still
soft) formed a closed chamber above the exposed cortex. This chamber was filled with
mineral oil through which the electrode entered the brain.
In preliminary experiments it was confirmed histologically that when the Horsley-Clarke
co-ordinates (Jasper & Ajmone-Marsan, 1954) indicated that the electrode tip was in the
optic tract it actually had been located there. No visual responses were obtained above
Horsley-Clarke H - 1-5 to H - 2-0 in those animals in which the location of the electrode tip
was not histologically determined. Further, in each experiment the positions of all the penetrations producing any visual responses were combined into a map which always corresponded to the known course of the optic tract. We are confident that the recordings obtained
in all our experiments originated in optic-tract fibres even when there was no direct histological confirmation of the electrode position.
Both eyes were atropinized and phenylephrine hydrochloride was applied to retract the
nictitating membranes. Contact lenses of + 5-5 D were applied to each eye with a standard
contact-lens fluid. The cat faced the stimulus screen at a distance of 23 cm. For most animals
the + 5-5 D contact lenses provided close to the best possible focus of the pattern on the retina.
If necessary, additional spectacle lenses were placed 1 cm in front of the eye. A 3-5 mm
diameter pupil was usually placed just in front of the contact lens whenever the receptive
field of the unit being studied was not more than about 30 deg from the optic axis of the eye.
When the receptive field was more eccentric than this it was not possible to locate an artificial
pupil in such a way as to be sure that there was no vignetting of the retinal image and in
these cases no artificial pupil was used. When it was desired to decrease the retinal illumination neutral-density filters were placed immediately in front of the cat's eye.
The action potentials from single optic-tract fibres were amplified in a conventional
manner, monitored over a loudspeaker and on an oscilloscope and recorded on magnetic
tape together with the necessary stimulus signals. During the experiment the mean frequency of the nerve discharge could be determined by counting the pulses with an electronic
counter for periods of 10 sec.
Recordings were obtained from a total of 128 optic-tract fibres in thirteen cats and the
behaviour of ninety-seven ganglion cells in response to grating patterns was studied. No
exact method of determining the location of a receptive field was employed but the angles
between the line connecting the eye with the centre of the receptive field and the horizontal
and vertical planes were estimated to within 5 deg. These angles were corrected for the
direction of the optic axes in cats paralysed with succinylcholine (Vakkur, Bishop & Kozak,
1963) to provide an estimate of the angular positioni of the projection of the receptive field
relative to the centre of the area centralis.
Stimulus. The stimulus pattern was provided by a cathode-ray tube display (Campbell &
Green, 1965). This gave great flexibility and ease of control and made it possible to change the
contrast of a pattern without affecting its mean luminance level. The cathode-rav tube
used was of the kind provided in the Tektronix 502 A oscilloscope but had a P-31 (blue-green)
phosphor. The tube was physically removed from an oscilloscope but it remained electrically connected by a flexible lead. The tube was contained in a magnetic screening shield and
mounted on a large adjustable stand so that its fluorescent screen could readily be placed at a
distance of 23 cm from the anterior nodal point of the cat's eye. It was positioned so that
the centre of the receptive field of the retinal unit from which recordings were being made
projected to the middle of the screen, which was perpendicular to the line joining the cat's
eye and the centre of the projection of the receptive field. The screen of the cathode ray
tube was masked so that only a square of 8-5 cm side was exposed; the illuminated area
subtended about 210 x 210 at the cat's eye.
The screen of the cathode-ray tube was apparently evenly illuminated to a level of
16 cd/M2 by deflecting the beam vertically at 150 kc/s with a triangular wave while the time
base provided a sawtooth wave form at 225 c/s to scan it horizontally. The frequency of the
CAT RETINAL CONTRAST SENSITIVITY
521
time base was much higher than the critical fusion frequency for retinal units in the cat
(Dodt & Enroth, 1954; Grusser & Reidemeister, 1959) and the number of vertical lines in
the raster (about 1500) was much greater than the number that could be resolved on the
screen of the cathode-ray tube. It thus seems reasonable to suppose that the screen was effectively steadily and uniformly illuminated for the cat as well as the experimenter.
To produce grating patterns upon the otherwise uniformly illuminated screen a suitable
periodic modulating voltage was applied to the grid of the cathode-ray tube. The time base
generator was normally triggered by a signal derived from the modulating voltage generator
so that the time base and modulating voltage were synchronized to produce a steady pattern
on the screen. The phase relation between the trigger signal and the modulating voltage was
continuously variable, allowing the position of the pattern on the screen to be continuously
varied. The variable phase relation between trigger signal and modulating voltage was
achieved by supplying the field vindings of a synchro resolver (e.g. Ahrendt, 1954) with
sine and cosine waves from the modulating voltage generator and using the output signal
from the rotor winding to trigger the time base. The relative phase of the output from the
rotor was directly determined by the angle between the rotor and stator of the resolver and
hence the displacement of the pattern on the screen could be read directly as a relative phase
angle from a scale on the shaft of the resolver.
For some experiments the resolver was driven at a constant speed by a synchronous motor.
This caused the grating pattern to drift at constant velocity across the screen. With this
arrangement the velocity of the movement of the grating was such that at any spatial
frequency the temporal fluctuation of luminance at any point on the screen was equal to the
rotational frequency of the resolver (drift frequency).
The contrast pattern on the oscilloscope screen was presented in two forms-stationary
or moving. When stationary, the pattern was not continuously present but was alternately
introduced and withdrawn by switching on and off the modulating voltage. Thus the screen
was alternately patterned and uniformly illuminated. In describing the results of experiments with stationary contrast patterns the expression 'phase angle of the pattern' will
be used in the specific sense of indicating the position of the cosine grating pattern relative
to the centre of the receptive field of the cell (see right-hand sketches in Fig. 1).
The amplitude of the modulating voltage could be adjusted to vary the contrast of the
pattern. Contrast is defined as (Lm.. -Lmin)I(L..x + Lmin.), where L is the stimulus luminance.
The contrast of the grating was standardized with a calibrated neutral-density filter
(Campbell & Green, 1965). It was found that there was a proportional relation between the
modulating voltage and the contrast of the pattern for contrasts of up to 0 45, the maximum
value used in these experiments. The modulating voltage was arranged to have a mean of
zero and so the mean luminance of the screen was not changed when the modulating voltage
was switched on.
Data analysis. The change in the discharge in an individual optic nerve fibre produced by
the presentation of a visual stimulus is not usually well defined, particularly when the
stimulus is small. It is therefore useful, when investigating the activity of a single ganglion
cell, to consider some kind of average response to repeated presentations of a stimulus. The
form of average that has previously been used (e.g. Kozak, Rodieck & Bishop, 1965) is the
averaged response histogram. This function is the average number of impulses that occur
in each unit time interval after the stimulus presentation. In the limit (as the unit time
interval is made vanishingly short) this becomes an estimate of the average 'pulse density'
of the response. In a practical situation it is necessary to compromise between decreasing
the unit time interval to achieve adequate time resolution and increasing the time interval
to provide a usefully smooth function. As an alternative to increasing the unit time interval
it is possible to use a very short time interval and a separate linear low-pass filter to provide
the smoothing. In this way no extra loss of information is introduced by the smoothing.
The filter can, of course, precede the averaging mechanism and this is the arrangement that
we have adopted.
522
C. ENROTH-CUGELL AND J. G. ROBSON
The nerve impulses were used to trigger a pulse generator giving current pulses of 0-5 msec
duration. The current pulses were fed into a capacitor which discharged through a fixed
resistor, the time constant of the combination generally used being 20 msec. The voltage
across the capacitor was applied to an 'averaging' computer which formed the sum of a
number of responses (generally eighty) with a time resolution of 1 or 2 msec. This sum was
scaled to give a smooth estimate of the average pulse density of the response.
RESULTS
Stationary patterns
General. In initial experiments the response of ganglion cells to the presentation of stationary patterns was examined. It was found, as expected,
that the magnitude of the response was dependent upon the position of
the pattern with respect to the receptive field centre, i.e. upon the phase
angle of the grating (as defined on p. 521). However, it was evident that the
way in which the response changed as the phase angle of the pattern was
varied was not the same for all ganglion cells but rather that there were two
types of cell exhibiting distinctly different behaviour. Cells of the two types
will be referred to subsequently as X-cells and Y-cells; both on-centre and
off-centre varieties of both cell types were found (X-cells: nineteen oncentre and six off-centre;. Y-cells: forty-six on-centre and fifty-seven
off-centre).
The difference in the behaviour of X- and Y-cells can be seen by comparing Figs. IA and lB which show, respectively, typical responses of
off-centre varieties of the two types of cell. As a general description of the
difference of form of the two sets of responses it may be said that the
responses of the Y-cell are more complex than those of the X-cell; in
particular the responses of the X-cell to the introduction and withdrawal
of the pattern are more nearly the inverse of each other than is the case
for the Y-cell. However, the most characteristic difference in behaviour
is to be seen by comparing the responses for the grating phase angles of
90 deg and 270 deg (see Fig. 1). These are the positions in which the
pattern lies with odd symmetry about a diameter of the receptive field
and in which the changes in luminance over one half of the receptive field
are the exact inverse of the changes over the other half. For these two
positions X-cells do not respond at all to introduction and withdrawal of
the pattern while Y-cells respond with large increases in pulse density
both when the pattern is introduced and when it is withdrawn. Moreover,
the particular phase angles at which grating patterns do not stimulate
X-cells are not dependent upon the contrast of the pattern. This is
exemplified by the finding that whenever 'null positions' for a grating
can be shown to exist they always occur 180 deg apart; that is, the phase
angle of a null position does not depend upon the sign of the contrast.
523
CAT RETINAL CONTRAST SENSITIVITY
Furthermore, neither the existence nor the phase angle of a null position
depends upon the mean luminance of the pattern.
100
Phase angle
(deg)
_
-o
100
90
100
--f
I
Q(
\NP A
0
180
100 _
O
270
L
A
,X,
0
B
Fig. 1. Responses of an off-centre X-cell (A) and an off-centre Y-cell (B) to the
introduction and withdrawal of a stationary sinusoidal grating pattern. The
contrast (0.32) was turned on and off at 0 45 c/s. Downward deflexion of the
lowest trace in both A and B indicates withdrawal of the pattem (contrast turned
off), upward deflexion indicates introduction of the pattern (contrast turned on).
The upper line in each pair is the pulse density of the ganglion cell discharge (scale
at left: pulses/sec); the length of the zero line represents a duration of 2 sec. The
'phase angle of the pattern', i.e. the angular position (in degrees) of the (cosine)
grating relative to the mid point of the receptive field centre, is given at the right
of the figure and is illustrated by the sketches. A: X-cell (no. 84); spatial frequency
0-13 c/deg. B: Y-cell (no. 13); spatial frequency 0-16 cideg.
X-cells. From these findings relating to the existence of null positions
for grating patterns it is possible to draw certain conclusions about the
characteristics and interaction of the photoreceptor signals which sum to
affect the discharge of X-cells. At this point it may be helpful to recall in a
simple diagrammatic fashion (Fig. 2) the picture that we have in mind when
discussing the implications of these null position findings. We assume that
each retinal ganglion cell is influenced by signals coming from elementary
areas of its receptive field (photoreceptors) and that each receptive field is
organized into an approximately circular central region with a concentric
surround (Kuffler, 1953; Rodieck & Stone, 1965b). We assume that signals
from all the elementary areas that together constitute the 'centre summating region' are summed to provide one signal (C in Fig. 2) while signals
524
C. ENROTH-CUGELL AND J. G. ROBSON
from all the elementary areas that constitute the 'surround summating
region' are separately summed to provide another signal (S of Fig. 2). The
summated signals C and S have antagonistic effects upon the ganglion
cell. Although retaining the term 'surround' we visualize the surround
and centre summating regions as being co-extensive in the central part
of a receptive field (cf. Rodieck & Stone, 1965b). This notion is illustrated
by the way in which the weighting functions of the centre and surround
summating regions have been drawn in Fig. 2.
Wc (r)
W(r)
s
Fig. 2. Diagrammatic representation of signal summation over a retinal ganglion
cel receptive field. The upper diagram illustrates the assumption that signals
from elementary areas constituting the centre summating region and signals from
elementary areas constituting the surround summating region are separately
summed and that the resulting signals C and S have antagonistic effects upon the
ganglion cell. For an on-centre cell the two signals would be described by + C and
- S, for an off-centre cell by - C and + S. In the lower half of the figure are shown
the Gaussian weighting functions assumed to describe the sensitivities of the
centre and surround summating regions respectively; Wj(r) = kc exp [- (r/rc)2].
W,V,(r) = k,exp[ - (r!r,)2] (see pp. 534-535). Note that the weighting functions for
both centre and surround summating regions have maxima in the middle of the receptive field. The bars drawn below the centre and surround weighting functions are
5rc and 5r, long respectively. These bars indicate the assumed 'anatomical'
diameters of the regions.
From the very existence of null positions it can be argued that the time
course of changes in the signals from photoreceptors whose illumination is
suddenly increased must be substantially the inverse of that of changes in
signals from photoreceptors whose illumination is suddenly decreased for
the sum of such signals can evidently remain constant. This implies either
that the signals from photoreceptors are linearlyrelated to their illumination
525
CAT RETINAL CONTRAST SENSITIVITY
or that they are non-linearly related in a way which is symmetrical
about the mean luminance. The latter alternative can be ruled out by the
observation that the null positions for grating patterns are not changed
when the mean luminance is changed. It can therefore be concluded that
X-cells respond to the sum of a number of signals from different parts of
their receptive field, each proportional to the local retinal illumination.
This is not to say that the response of an X-cell is linearly related to the
contrast or luminance of the stimulus (it clearly is not so related) but only
that the initial processes of photoreception, signal transmission and signal
summation are linear. A proviso is in fact required if it is assumed, as we
have, that the excitatory and inhibitory signals (C and S of Fig. 2) that
interact to affect the ganglion cell result from two separate processes of
spatial summation; in this case, although we can certainly conclude that
the separate processes of summation are linear we have not demonstrated
that the interaction of the summed excitatory and inhibitory signals is also
linear (subtractive).
Y-cells. Y-cells clearly respond to both the introduction and the withdrawal of grating patterns whatever the position of the pattern (Fig. 1B).
There is, however, considerable variation in the form of the response that
is evoked by such a stimulus; indeed, for each cell the form of the response
is usually dependent upon both the contrast of the grating as well as its
spatial frequency. Many of the cells respond with a large transient increase
in pulse density to both the introduction and withdrawal of the pattern
(Fig. 3). These transient responses become more nearly the same at every
position of the pattern as the spatial frequency is raised (cf. Figs. 3A
and B) although this is accompanied by a general reduction in the magnitude of the response.
The behaviour of the Y-cells is evidently very non-linear and indeed it
seems likely that these cells respond to any change in the light distribution over their receptive fields. If linear summation of signals from the
photoreceptors which influence these cells occurs at all it must do so only
over small regions of the whole receptive field.
Moving patterns
The magnitude of the response of a ganglion cell to the presentation and
withdrawal of a stationary grating pattern was found to be dependent not
only upon the position of the pattern but also upon its contrast and spatial
frequency. A few determinations were made of the effect of changing the
spatial frequency and contrast of the gratings upon responses to the presentation of stationary patterns (e.g. Fig. 3), but it was found difficult to
achieve the long-term positional stability of both the stimulus display and
the cat's eye which was necessary for studying the higher spatial frequencies.
°oEAhX~ ~270/
526
C. ENROTH-CUGELL AND J. G. ROBSON
A simplified technique was therefore adopted; this was based upon the use
of sinusoidal grating patterns drifting steadily in a direction perpendicular
to their bars.
Under these conditions of stimulation the luminance at each point of the
receptive field of a ganglion cell is modulated sinusoidally in time about
some mean level, the depth of modulation of the luminance being the same
as the contrast of the pattern. Since the responses of ganglion cells are
evidently the result of time-dependent processes in the retina, it is
100
ELj
Phase angle
(deg)
V\f
VA
900
100
100
L2
11
0
180
o0
B
016 c/deg
0 64 c/deg
Fig. 3. Responses of an on-centre Y-cell (no. 20) to the introduction and withdrawal of a stationary grating pattern of low spatial frequency (A) and higher
frequency (B). The contrast (0-32) was turned on and off at a temporal frequency
of 0-45 c/s. The upper line in each pair is the pulse density of the ganglion cell
discharge (scale at left: pulses/sec); the length of the zero line represents a duration of 2 sec. The lowest traces indicate the introduction (upward deflexion) and
withdrawal (downward deflexion) of the pattern. The phase angle of the pattern
is given to the right of the records.
A
essential that the temporal characteristics of stimuli whose effects are to
be compared should be the same. For grating patterns of different spatial
frequency drifting at constant velocity this is achieved if the velocity is
inversely proportional to the spatial frequency; in this way the temporal
(drift) frequency of luminance changes is kept constant.
By using a moving pattern as a stimulus, the magnitude of the response
of a cell to a grating having certain contrast and spatial frequency is
defined by just one measurement instead of by a series of measurements for
different positions of the pattern.
W~ ~ 25
527
CAT RETINAL CONTRAST SENSITIVITY
In the experiments reported here the velocity was generally such as to
produce a temporal fluctuation of 1 c/s. At times it was adjusted to produce
a temporal fluctuation of 4 c/s. These frequencies were chosen because they
appeared to be in the approximate frequency region in which the maximum
amplitude of response was obtained. The amplitude of the responses always
fell off markedly at temporal frequencies above 15 c/s and appreciably at
frequencies below 1 c/s.
-
70
0L
0.12
10080
10L
7
10:
O
-
100
-
0
_
100
70
_
0/04
100
0136
024
20
1 0
~~~~~~~~~~7
A
B
Fig. 4. Responses from (A) an on-centre X-cell (no. 128) and (B), an off-centre
Y-cell (no. 103) to sinusoidal grating patterns of different spatial frequencies but
the same contrast (0 4) drifting across their receptive fields. For each spatial frequency the velocity at which the grating drifted was such as to modulate the
luminance of any point at 4 c/s (the 'drift frequency'). The upper line of each pair
is the pulse density (scale at left: pulses/sec); the length of the zero line represents
1 sec. The spatial frequency (c/deg) is shown at the right of each zero line. The
lowest records in (A) and (B) show responses to a uniformly illuminated field.
The mean pulse density of the discharge (pulses/sec) is given to the left of each pulse
density trace.
Figure 4 shows the responses of one X- and one Y-cell to the passage
across their receptive fields of gratings of various spatial frequencies but
of fixed contrast. The pulse density is modulated with an obvious periodicity at 4 c/s, the drift frequency in this particular experiment. The
amplitude of the modulation is clearly greatly reduced at high.spatial
frequencies and somewhat reduced at spatial frequencies below an intermediate optimum value.
The wave form of the Y-cell (Fig. 4B) response is typically more distorted than that of the X-cell (Fig. 4A), in much the same way as with the
C. ENROTH-CUGELL AND J. G. ROBSON
stationary patterns. However, the most striking difference between Xand Y-cell behaviour lies in the effect of the drifting pattern upon the
mean pulse density. X-cells respond to movement of the pattern with a
periodic modulation of the pulse density of their discharge without producing any change in its mean value. Y-cells on the other hand respond
with a large increase in the mean pulse density upon which background
discharge the periodic modulation is superimposed. Indeed some Y-cells do
not discharge at all when steadily illuminated, only doing so when there
is some temporal variation in the retinal illumination. It should be noted
that although the X-cell of Fig. 4 has an on-centre and the Y-cell an offcentre the differences in behaviour of X- and Y-cells are not simply a
question of different centre types. This is exemplified by the differences in
the responses to stationary patterns shown in Fig. 1 where the X- and the
Y-cell have the same type of centre. It is, however, true that the majority
of the X-cells had an on-centre (see p. 522).
528
100 F
10
80
0-32
0
0-02
78
100 F
V 0-16
100F
0-01
7
86
8
[0.08
0005
E 004
0-0025
0
Fig. 5. Responses from an on-centre X-cell (no. 128) to drifting sinusoidal grating
patterns of constant spatial frequency (0-36 c/deg) but different contrasts (contrast
given at the left of each record). The drift frequency was 4 c/s. The upper line of
each pair is the pulse density (scale at left: pulses/sec); the length of the zero line
represents 1 sec. The number to the right of each record is the mean pulse density
(pulses/sec) of the discharge of the cell. Note that in no case does the peak-to-peak
response amplitude double when the contrast is doubled and that the wave form of
the pulse density modulation does not appear to become more sinusoidal as the
contrast is reduced to very low values. The experimenter could hear the modulation of the frequency of the discharge when the contrast was greater than 0-015.
For drifting gratings of any given spatial frequency the magnitude of
the response of a ganglion cell increases with increasing contrast of the
pattern. Figure 5 illustrates the effect of changing the contrast of a drifting
grating of fixed spatial frequency upon the discharge of an on-centre Xcell. An obviously non-linear distortion of the wave form of the modulation
529
CAT RETINAL CONTRAST SENSITIVITY
of the pulse density is evident for the higher contrast levels when the pulse
density becomes zero over part of each cycle. The great sensitivity of this
ganglion cell is indicated by the fact that when the temporal and spatial
frequencies are both approximately optimal (as they were in this experiment) a contrast of little more than 0 1 is sufficient to cause the pulse
density to fall to zero for part of each cycle. Even at the lowest contrast
levels, however, the wave form of the modulation of the pulse density is
also clearly not sinusoidal. This is not surprising in view of the obviously
non-linear relation between the amplitude of the pulse-density modulation
and the contrast of the stimulus pattern. Insufficient measurements were
made to define this relation well but the response amplitude was approximately proportional to the square root of the stimulus contrast. We have
found no evidence at all for a threshold type of non-linearity in the
stimulus-response relation for those cells which discharge spontaneously
in the absence of any temporal variation of retinal illumination. These
findings are in accord with those of Fitzhugh (1957), who studied the
response of retinal ganglion cells to incremental flashes.
The contrast sensitivity function of X-cells
Since the initial processes of spatial summation in the cat's eye have
been shown to be effectively linear for the X-cells, we can investigate and
describe these initial processes by methods applicable to linear systems.
Thus, if we measure, for gratings of different spatial frequencies, the
contrast required to evoke a certain fixed response from an X-cell we can
derive an estimate of the relative 'contrast sensitivity function' of the cell.
This will in effect be the (arbitrarily scaled) spatial contrast transfer
function of the linear mechanisms involved.
Objective measurements of contrast sensitivity. Direct determination of the
contrast sensitivity function of a ganglion cell can be made by recording
the response of the cell to a series of gratings of different spatial frequencies
each at several contrast levels. From these recordings the contrast required at each spatial frequency to evoke a response of a given magnitude
can be found by interpolation. Of course, the interaction at the ganglion
cell level of the summated centre and surround signals has not been shown
to be linear (subtractive) even though these signals themselves (C and S
of Fig. 2) appear to be the resultants of linear summation. Thus it is not
necessarily possible to evoke exactly the same response even from an Xcell with gratings of different spatial frequency whatever the relative
contrast levels of the gratings.
However, as can be seen from Fig. 6 which shows the responses of an
X-cell to a series of gratings of different spatial frequencies and contrast,
gratings of different frequencies do in fact evoke substantially the same
34
Physiol. I87
530
C. ENROTH-CUGELL AND J. G. ROBSON
responses when their contrast levels are appropriately adjusted. It thus
seems reasonable to assume that the interaction of the summated centre
and surround signals is approximately linear for X-cells, at least at these
contrast levels.
100~
-
F 0G35
007
014
100
0
0
L 0015
003
006
100:
10
012
_
0
002
004
032
10 0-0075 °.1°0°03
0 64
-/
[0
10
010
020
040
1-6
Fig. 6. Responses of an on-centre X-cell (no. 68) to a series of drifting sinusoidal
grating patterns of different spatial frequencies and contrasts. The drift frequency
was 4 c/s. The upper line of each pair shows the pulse density (scale at left: pulses/
sec); length of the zero line represents 0 5 sec. The spatial frequency (c/deg) is shown
at the right of each row and the contrast under each pulse density trace.
From the recordings shown in Fig. 6 the contrast sensitivity function
of Fig. 7 was derived. The response amplitude for every contrast at each
frequency was measured and plotted versus contrast. From these individual amplitude versus contrast curves the reciprocal of the contrast
needed to evoke a modulation of the pulse density of amplitude 10/sec
at the different spatial frequencies was obtained and are shown as filled
circles in Fig. 7. The contrast sensitivity of this cell had a maximum at
about 0 5 c/deg; it fell off rapidly at higher spatial frequencies and more
slowly at lower frequencies.
Subbjective measurements of contrast sensitivity. The objective determination of contrast sensitivity functions by this method is too time consuming to be practicable as a routine procedure and we have adopted a
subjective method similar to that employed by other investigators to
determine equality of response. In this method the experimenter listens
to the discharge of a cell and adjusts the contrast of the stimulus pattern
so that the modulation of the discharge frequency is barely detectable.
Two kinds of check have been made to find whether this procedure results
in an adequate determination of the contrast required to produce a constant response amplitude.
531
CAT RETINAL CONTRAST SENSITIVITY
In Fig. 7 a direct comparison of objectively and subjectively determined
contrast sensitivity functions for the same cell is illustrated. The sensitivity scale is essentially arbitrary for both determinations and hence the
curves have been shifted relative to each other along the contrast scale to
facilitate direct comparison.
100
c~~~~~~~~
e OQ10 _
L I1 1|1 1 1 1111111
01
I
1.0
Spatial frequency (c/deg)
Fig. 7. Objectively and subjectively determined contrast sensitivity functions for
an on-centre X-cell (no. 68). Objective measurements (filled circles): these are
based on the responses of the cell to sinusoidal gratings drifting at 4 c/s (shown in
Fig. 6). Response amplitude versus contrast curves were drawn for each spatial
frequency and from these curves the contrast required to evoke a pulse density
modulation of amplitude 10/sec was estimated. Reciprocals of these values are
plotted here. Subjective measurements (continuous line): at different spatial frequencies the experimenter determined the contrast required for a barely audible
modulation of the ganglion cell discharge synchronous with the drift. The reciprocals
of these contrast values were plotted (Fig. 9 C) and the experimental points were
fitted with a curve conforming to eqn. (9) (p. 536). This curve is shown here.
Another type of check upon the validity of the method is to measure
objectively the amplitudes of the responses previously judged by the
experimenter to be at threshold. Figure 8 illustrates the results of a check
of this kind. The responses of an X-cell to various gratings having twice
the contrast subjectively found to produce a barely audible modulation
of the impulse density are found to be very similar in amplitude though
having slightly different wave forms. We also established that the repeatability of such subjective contrast sensitivity determinations for an
individual cell was satisfactory even when the individual determinations
were separated in time by as much as 2 hr. In Fig. 9 are some representative samples to illustrate this. From these various tests we conclude that
the subjective method of measuring contrast sensitivity functions can be
employed satisfactorily for X-cells.
34-2
C. ENROTH-CUGELL AND J. G. ROBSON
Rotational symmetry of receptive fields. Kuffler (1953) found that the
contours of constant sensitivity of cat retinal ganglion cell receptive fields
(mapped out with a small spot of light) were approximately concentric
circles. Approximate rotational symmetry of receptive fields was also
found by Rodieck & Stone (1965 b). This implies that the sensitivity of such
cells to grating patterns should be independent of the orientation of the
grating.
532
100[
'
0
0-15
0-04
0
008
012
0
0-037
0-36
0
100
0*17
Fig. 8. Responses of an on-centre X-cell (no. 68) to sinusoidal gratings drifting at
4 C/s across the receptive field. The upper trace of each pair is the pulse density
(scale at left: pulses/sec); the zero line represents 1 sec. The spatial frequency of the
drifting grating pattern (c/deg, shown at the right of the records) increases from
above downwards. At each spatial frequency the contrast was set to twice the value
found to produce a just-audible modulation of the discharge frequency. These
contrast values are given at the left of each record. Note that the peak-to-peak
response amplitudes were very similar at the four different spatial frequencies,
though there were slight differences in the wave forms.
Some confirmation that the contrast sensitivity function of an X-cell
is independent of the orientation of the grating was provided by measurements of the contrast sensitivity function made with horizontal and
vertical gratings. Figure 10 shows for an on-centre X-cell that withinthe
precision of the measurements there appears to be no significant difference
between the effectiveness of vertical and horizontal gratings. In the rabbit
(Barlow et al. 1964) and squirrel (Cooper & Robson, 1966), retinal ganglion
cells which respond selectively to the motion of patterns in some particular
preferred direction are quite common. In this study it was always established
CAT RETINAL CONTRAST SENSITIVITY
533
100
10
.9 100
.
- Cell no. 68
0-1
I
0-1
1
100
10
w
10
,, 1 0
0
b
- cX
, I H......
01
I II 111111
I
III
I
100
100
- Cell no. 124
10 -E
10
J
0
- F
1
0-1
Spatial frequency (c/deg)
Fig. 9. Subjectively measured contrast sensitivity functions for five on-centre
X-cells (A-E) and one off-centre X-cell (F). Sinusoidal grating patterns of different
spatial frequencies drifted past the receptive field of each ganglion cell at a drift
frequency of 1 c/s. Each point represents a single determination of the contrast
which was required for the experimenter to hear a modulation of the discharge
frequency at c/s (i.e. synchronously with the temporal luminance modulation).
Where there are two sets of symbols these represent two complete runs of contrastsensitivity determinations each proceeding from the lowest to the highest spatial
frequency. Filled circles, first determination; open circles, second determination.
Time between first and second run in A, 40 min; in CT, 1 hr; in D, 2 hr 40 min; in E,
1 hr 45 min. The points located to the left of the vertical axis in D-F indicate the
contrast sensitivity at 'zero spatial frequency'. To determine this point the luminance of the uniformly illuminated stimulus field was modulated sinusoidally at
1 c/s and the minimum amplitude of the luminance modulation required to evoke
an audible modulation of the discharge frequency was determined. The mean luminance remained the same as when the stimulus was spatially modulated. All the
curves in this figure conform to eqn. (9) (p. 536), the parameters chosen being
shown in Table 1. The cells can be identified by their numbers (given at the top
left of the curves). Cell no. 64 had the highest spatial resolution of all cells studied.
0-1
I
C. ENROTH-CUGELL AND J. G. ROBSON
that the cell under investigation was not selectively motion-sensitive
before obtaining data with moving sinusoidal contrast patterns. No
directionally selective cells were encountered, a finding which agrees well
with the results of others in the cat (Rodieck & Stone, 1965a, b).
534
100
1
0
0~~~~~~~
I
I HI11
I11
I~~~~~
0.1
10
Spatial frequency (c/deg)
Fig. 10. Check of radial symmetry of a ganglion cell receptive field. Two subjectively determined contrast sensitivity functions for an on-centre X-cell (no.
116). Open circles: the bars of the drifting sinusoidal pattern were vertical and
motion was from left to right in the cat's visual field. Filled circles: bars of pattern
were horizontal and motion was from above down.
Interpretation of contra8t-8en8itivity functionV. Before discussing the characteristics of the
contrast-sensitivity functions of individual retinal ganglion cells (X-cells) and the effects
upon them of changing the mean level of illumination, it is convenient to consider whether
a simple analytic expression can be fitted to all the measured contrast sensitivity functions.
It is clearly advantageous to be able to describe the spatial summation over each receptive
field by an expression of standard form with appropriate parameters, especially if this
relates in a simple manner to the sensitivity at different points over the receptive field.
We assume (cf. Ratliffe, 1965) that the response of a ganglion cell is related (not necessarily in a linear way) to R1 where
r+
Jo+ oo L(x, y)
RI = -j
W(r)dxdy.
L(x, y) is the luminance over the stimulus plane and W(r) is the 'point weighting factor' for
a unit area at a distance r from the centre of the receptive field. By making W a function of r
alone we assume perfect rotational symmetry of the receptive field.
For the simpler case in which the luminance varies in the x direction only (i.e. a 'line'
pattern) the ganglion cell response is determined by R2 where
r+ o
R.= JL(x)(q)dx.
-
(1)
00
L(x) is the luminance along the line at x and w(q) is the 'line weighting function' for a
strip of unit width at a distance q from the centre of the receptive field.
The line and point weighting factors can be related:
_=
n
W(r) r
- ~
dr.
Ioq \\I(r2
-q2)
(2)
CAT RETINAL CONTRAST SENSITIVITY
535
Now consider a ganglion cell stimulated by a sinusoidal grating pattern whose luminance
L(x) is defined by
L(x) = Lo (1 + m cos 27Tvx),
where m is the contrast of the grating, v its spatial frequency (c/unit x) and Lo its mean
luminance. In this case the cell responds to R3 where, from eqn. (1),
R3= fJ
r+ o
Lo[I +mcos (27rrq+ 0)] wo(q)dq,
q5 being the distance from the centre of the receptive field to the origin of x expressed as a
phase angle (at the spatial frequency v). Then, taking into account the symmetry of W(q)
about q = 0,
R3 = 2Lo
co(q) dq + 2Lmcosq fo(q) cos 2iwqdq.
2 f co(q)cos27Tvqdq = C(v)
But
(3)
can be identified as the cosine (Fourier) transform of the line weighting function so that
dq+ Lomcosgs>Cl(v).
0
R3= 2Lo fw(q)
(4)
If the grating moves at constant velocity so that
0 = 2nft,
where f is the temporal frequency of the motion ('drift frequency') and t is time then,
substituting in equation (4), gives
R4
=
2Lof &(q) dq + Lom cos 27fftC(v).
(5)
In the experimental investigation, determinations were made for each ganglion cell of the
contrast m' required at different spatial frequencies to produce a particular amplitude of
modulation of the pulse density of the discharge. These determinations were used to
estimate the contrast sensitivity function S(v) thus:
(6)
8(v) m'(v)
Assuming that a constant amplitude of the modulation of the pulse density is equivalent to
a constant amplitude of modulation of R4 then, from eqns. (5) and (6),
S(v)
=
KC(v),
(7)
where K is an arbitrary constant determined by the chosen amplitude of modulation of the
pulse density. The contrast sensitivity function of a ganglion cell can thus be interpreted in
terms of the cosine transform of its line-weighting function.
It is convenient to assume an analytic form for the point-weighting function of a ganglion
cell and then to derive from this the line-weighting function and contrast sensitivity function
of the cell. In general agreement with previous authors (e.g. Schade, 1956; Rodieck, 1965)
we assume that the point-weighting functions of both centre and surround summating
regions of a typical ganglion-cell receptive field are Gaussian in form and that the signals
from these regions subtract arithmetically, i.e.
W(r) = W,(r) - W,(r)
= kc exp [-(r/rc)2]-ksexp [-(r/r,)2],
where the subscripts c and 8 refer to the centre and surround summating regions of the
receptive field, these regions having respectively characteristic radii rc and r8 and pointweighting functions with maximum values of kc and k, (see Fig. 2).
The line weighting functionl is given by
It(q) = w)c(q) - (oj(q),
536
C. ENROTH-CUGELL AND J. G. ROBSON
and then from eqn. (2)
w(q) = kcrc0rexp[-(q/rc)2]-k.r7T4exp [-(q/rs)2]
and from eqn. (7) the contrast sensitivity function
(8)
(9)
S(v) = K7T{k,r02exp[-(7Trrv))2]-k8r82exp[-(7Tr8v)2]}.
Thus it can be seen that if the point-weighting function of a ganglion cell is the difference
of two Gaussian pulses then so also is the line-weighting function, and the contrast sensitivity function is the difference of two Gaussian spectra.
To see if the measurements of contrast sensitivity at different spatial
frequencies could be fitted by curves conforming to eqn. (9), families of
such curves with various ratios of r/IrC and kcr,2Ikcr,2 were plotted in double
logarithmic co-ordinates. These were compared (by eye) with the measured
values of contrast sensitivity plotted in similar co-ordinates for each of
the X-cells encountered. By suitable displacement of the curves relative
to the experimental points, it was always possible to select a curve which
fitted satisfactorily.
TABLE 1. Parameters of curves (conforming to eqn. 9) selected to fit contrast
sensitivity measurements for X-cells
Cell no.
1
40
43
55
56
57
64
66
rc(deg)
0-32
037
053
r,(deg)
0-76
2-2
1-6
14
3-3
1-4
0.91
3-3
1-6
2-4
3-6
6-4
1-8
2-5
4-0
2-9
40
1-6
0-96
1-6
r,Ir,
ks rslkc rc
2-4
0-92
0-90
3-0
0.95
0-21
6-5
0-78
0-14
23
0-98
0-20
7-1
0 73
0-16
5-7
0-94
0 49
6-8
0-80
68
0-29
5.5
0 90
0-29
70
8-5
0-98
71
049
7-5
093
79
0-64
10
0 90
0-42
83
4-2
0-93
84
0-88
2-9
0.95
96
0*40
10
0-87
020
98
11
095
101
0-64
6-3
0-86
112
0 45
3-6
0-88
116
0-24
40
0-96
124
0 40
3-8
0-95
128
0 37
1-5
3.9
0-90
Cells 84, 101, 112 and 124 had off-centres, all the others had on-centres. The mean luminance of the stimulus screen was 16 cd/m2. A 3-5 mm diameter pupil was used with all cells
except nos. 43, 55, 84, 101 and 124.
5-9
Measured contrast sensitivity functions. Satisfactory measurements were
made of the contrast sensitivity functions for twenty-one X-cells (seventeen on-centre and four off-centre units). Examples of these measurements
and of the fit of the selected curves can be seen in Fig. 9. Table 1 gives the
values of the parameters which define the shape of the fitted contrastsensitivity functions. We have omitted giving the values for all four parameters independently because unfortunately objective determinations of
537
CAT RETINAL CONTRAST SENSITIVITY
the sensitivities of most of the cells were not made and thus the relative
positions of the different curves along the sensitivity axis depend upon the
subjective criterion of response adopted by the experimenter for each
determination. Although not directly investigated, it seems very likely
that there would be appreciable variation in the citerion chosen on different occasions according to the mean discharge frequency of the individual cells. Even at the one luminance level at which the parameters of
Table 1 were obtained the mean impulse frequencies of the ganglion cells
involved ranged between 10 and 100 impulses/sec.
20
0
Iel
20
40
I
60
I
Right
20
20
Down
Fig. 11. Approximate visual field locations of the receptive field centres of
twenty X-cells whose axons ran in the left optic tract; these are the cells listed in
Table 1 except for one off-centre cell (no. 112) whose location was not recorded.
The positions of the receptive field centres relative to the projection of the middle
of the area centralis were estimated to within 5 deg. The axes are marked in angular
distance (deg) from the projection of the centre of the area centrals. Filled circles,
on-centre cells; open circles, off-centre cells. The diameter of each symbol is equivalent to 5 times the characteristic radius of the central summating region of the
receptive field.
Despite the wide variation in the parameters of the contrast-sensitivity
functions of the various ganglion cells it is clear that the parameters
chosen to define the ganglion-cell receptive fields are partially correlated.
For example, the variation in the ratio of the total weights of centre and
surround summating regions (klsr82/klcrc2) is obviously much less than that
of the individual parameters.
538
C. ENROTH-CUGELL AND J. G. ROBSON
Figure 11 shows how the X-cell receptive fields were distributed over
the visual field. The size of the symbols plotted indicates the relative size
of the centre summating regions of the receptive fields. Wiesel (1960)
stated that 'ganglion cells with small field centres were most often recorded
in the area centralis' and that 'larger field centres were more common for
ganglion cells recorded in the periphery of the retina'. For our sample of
X-cells the same seems to hold true.
Sensitivity of a cell to a contrast edge
The sensitivity of a ganglion cell to patterns other than sinusoidal
gratings should be calculable from a knowledge of its contrast sensitivity
function assuming that the superposition principle is applicable. As an
independent check of the applicability of the superposition rule we
examined the responses of an X-cell to a simple contrast edge pattern and
have compared the cell's measured sensitivity to the edge with the sensitivity predicted from the contrast sensitivity function.
A voltage having a rectangular wave-form and a zero mean was used to modulate the
luminance of the screen of the cathode-ray tube which provided the stimulus. The presence
of the modulating voltage caused the luminance of one half of the screen to increase and the
luminance of the other to decrease by an equal amount. The two halves of the screen were
divided about a vertical straight edge whose distance from the centre of the screen could be
altered. The modulating voltage was switched on and off at 0-45 c/s and the pattern consequently appeared and disappeared at this frequency.
Figure 12 shows responses of an on-centre X-cell to the introduction and
withdrawal of the edge pattern for various positions of the edge with
respect to the centre of the receptive field. It is clear that the magnitude
of the response depends upon the position of the edge, that the polarity
of the response changes as the edge is moved from one side of the receptive
field centre to the other and that when the edge is in the centre, i.e. when
it forms a diameter of the receptive field, there is virtually no response at
all. The existence of a position for the edge in which changes in contrast
do not evoke a response from the cell provides confirmation of the linearity
of the processes of spatial summation occurring over the receptive field
of this X-cell.
For various positions of the edge it was possible to determine what contrast had to be introduced or withdrawn to produce an audible increase
in the discharge frequency of this cell. The results of this determination
are shown in Fig. 13. The contrast sensitivity of the cell for the edge pattern
is shown as a function of the distance of the edge from the receptive field
centre. The sensitivity was least when the edge passed through the centre
of the receptive field, and greatest when it lay on either side of the centre.
Also shown in Fig. 13 is the sensitivity of the cell to the edge pattern
CAT RETINAL CONTRAST SENSITIVITY
539
calculated from its contrast sensitivity function previously determined with
drifting sinusoidal grating patterns. The calculation has been performed
by convoluting the line weighting function of the cell (Fig. 13 at bottom)
with the luminance distribution in the stimulus pattern for different
positions of the pattern. The equation of the cell's line weighting function
was assumed to be of the standard form (eqn. (8)) and the parameters were
'100
C
A
100
_
Fig. 12. Response of on-centre X-cell (no. 68) to introduction and withdrawal
of an edge pattern. The edge was vertical and its contrast was 0-2. It was held
stationary in three different positions while the contrast was turned on and off at
0-45 c/s. Upward deflexion of the lowest trace indicates introduction of the edge
pattern, downward deflexion indicates its withdrawal. The upper line in each pair
is the pulse density (scale at left: pulses/sec); the length of the zero line indicates
a duration of 2 sec. The three positions of the edge relative to the receptive field
centre are indicated in the sketehes to the right of the records. In A the edge was
located 7.5 mmn to the right of the mid point of the receptive field centre, in B it
passed through the mid point, in C the edge was displaced 7-5 min to the left. The
records show average responses to twenty stimnulus presentations.
derived from fitting a curve of the form of eqn. (9) to the contrast sensitivity measurements (see Fig. 9 C). Allowiing for an apparent slight
asymmetry in the effect of moving the edge from one side of the centre to
the other, the fit can be regarded as satisfactory and as justifying the
application of a linear analysis.
This ganglion cell had a rather well maintained response to the pre-
540
C. ENROTH-CUGELL AND J. G. ROBSON
sentation of a stationary edge pattern and, for various positions of the
edge, measurements were made of the average pulse density of the discharge over the period between 10 and 20 sec after introducing the pattern.
In Fig. 14 the average pulse density of the discharge has been plotted as a
function of the distance of the edge from the centre of the receptive field
for two contrast levels. When the edge was positioned in the centre of the
100
>1~~~~~~~
0
~ ~
~
~
0~~~~~~~
~
z
~
0
o
AQ
10
I
I
I
I
I
I
I
I
I
I
I
5
3
4
2
1
0
1
2
Angular displacement of the edge from centre of receptive field (deg)
5
4
3
Fig. 13. Contrast sensitivity of an on-centre X-ceU for an edge pattern. This is
the same cell as in Fig. 12 (no. 68). A vertical edge was alternately introduced and
withdrawn at 1 c/s while held stationary in different positions. For each position
the minimuim edge contrast which resulted in a just-audible change in the discharge
frequency was determined. The reciprocals of these contrast values are plotted here.
The open circles indicate responses of one polarity (Fig. 12 C), the filled circles indicate responses of opposite polarity (Fig. 12 A). Note the reversal of response polarity
at the midpoint of the receptive field. The full line through the points is the edge
contrast sensitivity of this cell calculated from its previously determined contrast
sensitivity function for sinusoidal grating patterns (Fig. 9 C). At the bottom is
shown the line weighting function of the receptive field also calculated from the
contrast sensitivity function.
field no effect on the cell's discharge was produced while the maximum
change in pulse density was obtained when the edge was a short distance
(about 0-3 deg) to either side of the centre. It is interesting to note that
the maximum increase in the pulse density of the discharge was larger
than the maximum decrease. If the response of the cell (in terms of the
change in the mean pulse density of its discharge) had been proportional
CAT RETINAL CONTRAST SENSITIVITY
541
to its sensitivity then the relative response for different edge positions
calculated from the measured contrast sensitivity function and the experimentally determined response should have been the same. In fact the way
in which the mean pulse density depended upon the edge position was
quite similar to what would have been expected assuming linearity. This
can be seen by comparing the experimental points of Fig. 14 with the full
curve which shows the expected response based upon the contrastsensitivity function measurements.
100~~~~~~~~~~~~0
8.90
i.
80 90~~~~
_-/
~~~
~~~~~
80~~~~~~~~~~0
70
-
670
-
-
------------
o-
-
g 50
0
I
I
I
I
4
2
1
3
5
3
1
0
2
4
5
Angular displacement of edge from centre of receptive field (deg)
Fig. 14. 'Static' response of an on-centre C-cell to a contrast edge. This is the
same cell (no. 68) as in Figs. 12 and 13. The vertical edge was held stationary at
different distances from the receptive field centre and the contrast was alternately
turned on and off. The average pulse density over the period 10-20 sec after the
introduction of the edge was measured for each edge position. Two different contrast levels were used: filled circles, 0 4; open circles, 0-2. The edge sensitivity of
the same cell calculated from the contrast sensitivity function obtained with
sinusoidal gratings (Fig. 9C) is shown below the experimental results for com-
parison.
Mean level of illumination
For two X-cells the effects of changing the mean level of illumination
were studied. The retinal illumination was varied by placing different
neutral density filters in front of the cat's eye, ensuring that stray light
did not enter the eye behind the filter. On placing a filter in front of the
eye (or on taking one away), there was a marked transient change in the
mean discharge frequency. After a few minutes the discharge frequency
542
C. ENROTH-CUGELL AND J. G. ROBSON
reverted in both cases to approximately its previous level (Kuffler,
Fitzhugh & Barlow, 1957). When the cell that was being studied had
adapted to the new level of illumination the contrast sensitivity function
was determined in the usual way. Figure 15 shows the effect upon the contrast sensitivity function of an X-cell of changing the mean illumination.
Each reduction results in a decrease in the contrast sensitivity, especially
at higher spatial frequencies. The other cell studied behaved in a similar
manner.
100
10
001
01
1
Spatial frequency (c/deg)
Fig. 15. The effect upon the contrast sensitivity function of an on-centre X-cell
(no. 71) of changing the mean retinal illumination. The contrast sensitivity
function was subjectively measured at four luminance levels of the stimulus
screen: 0, 16; A, 0 5; 0, 1V6 x 10-2; A, 5 x 10-4 cd/M2. The pupil diameter was
3-5 mm in each case.
Clearly the shape of the contrast sensitivity function changes as the
illumination changes. The fall-off in sensitivity at low spatial frequencies
disappears at reduced illumination levels. This can be interpreted as a
disappearance of the effect of the antagonistic surround of the cell's
receptive field at low light levels as described by Barlow et al. (1957). It is
not possible, however, to fit the experimental points satisfactorily by a
series of curves of standard form (eqn. 9, p. 536) which differ only in the
maximum values of the weighting functions of centre and surround summating regions (i.e. which have different values of kc and kJ). To achieve
a satisfactory fit in the high-frequency region it is necessary to assume
that decreasing the mean illumination not only decreases kl and ks but
also increases the characteristic radius of the centre summating region
(re). Over the range of illumination studied here (4.5 log. units) a 2-fold
change in r, is required to fit the results.
It also seems necessary to assume that there is a similar change in the
characteristic radius of the surround summating region. The curves in
543
CA T RETINAL CONTRAST SENSITIVITY
Fig. 15 have in fact all been drawn with rI/r, = 9, but though the fit is
satisfactory it is not critically dependent upon this parameter.
'Contrast-sensitivity functions' of Y-cells
Although the use of contrast-sensitivity functions to describe the spatial
characteristics of retinal ganglion cells can only be fully justified for those
cells which demonstrate linear spatial summation (X-cells), it is, of course,
possible to determine what contrast is required for gratings of different
spatial frequencies to produce a given effect upon Y-cells. There are,
however, two distinct effects to be considered: an increase in the mean
Spat. freq.
0 09
100
Eo F
A
A
A
(c/deg)
Average
pulse density
0.04
30
070
30
06
33
10
30
F
L
100
008
O
_
100
014
/0\
~
O0
100
0 42
0L
100
0
~~~~~~~~~~~~~~(pulse/sec)
0
.6
Fig. 16. Responses of an off-centre Y-cell (no. 103) to drifting sinusoidal grating
patterns of different spatial frequencies. Upper line in each pair is the pulse
density (scale at left: pulses/sec); the length of the zero line represents 1 sec.
Drift velocity 4 c/s. The lowest record is the response to a uniformly illuminated field.
Four spatial frequencies were chosen and for each frequency the contrast was
adjusted so as to yield as nearly as possible the same mean pulse density. The
contrasts required are given at the left of the records. The mean pulse densities that
were achieved during the experiment are given at the extreme right of the figure.
Note that the amplitude of the pulse-density modulation is greater at low spatial
frequencies even though the mean pulse density is increased by the same amount
at all frequencies.
C. ENROTH-CUGELL AND J. G. ROBSON
impulse density and a modulation of the impulse density predominantly
at the drift frequency of the stimulus. But these two effects do not go
hand-in-hand, as is demonstrated in Fig. 16. Gratings with different
spatial frequencies whose contrasts have been chosen to produce the same
increase in the mean pulse density obviously do not all produce the same
amplitude of modulation of the pulse density, the dominant effect at high
spatial frequencies being the increase in mean pulse density. There is thus
no unique contrast sensitivity function for a Y-cell. However, it is possible
using the subjective method to make consistent determinations of two
relations between contrast and spatial frequency for Y-cells. These two
544
100
:1
cii
10
_
a
_
b
w
0
~
0
Spatial frequency (c/deg)
Fig. 17. 'Contrast sensitivity' of an off-centre Y-cell (no. 103, same as in Fig. 16)
for sinusoidal grating patterns. The procedure was similar to the subjective
measurement of the contrast sensitivity function for an X-cell. For each spatial
frequency, the experimenter determined (a) the contrast required for an audible
modulation of the discharge frequency of the cell synchronous with the temporal
luminance modulation; the reciprocals of these contrast values are plotted as open
circles. He also determined (b) the contrast required for an audible increase in mean
discharge frequency as the grating was set in motion. The reciprocals of these
contrast values are plotted as filled circles. The triangles are the reciprocals of
the contrasts required to increase the mean discharge frequency of the cell from
6 to 30 impulseslsec. These values are taken from Fig. 16.
relations are obtained when the experimenter finds for each spatial frequency what contrast is required for him to detect either a periodic
modulation of the pulse density of the discharge of the cell or an increase
in the mean pulse density when the grating is set in motion. The two
contrast-sensitivity relations determined in this way differ considerably at
high spatial frequencies (Fig. 17) as would be expected from the effect
illustrated in Fig. 16. The contrast sensitivity as judged by the effect of a
drifting grating upon the mean impulse density is relatively greater at
higher frequencies. In Fig. 17 the contrast-sensitivity curves obtained
when using the two different subjective criteria for threshold contrast are
CAT RETINAL CONTRAST SENSITIVITY
545
shown and for comparison four objective determinations of the contrast
needed to evoke an increase in the mean pulse density of 25/sec.
Receptive field centres of Y-cells tended to be larger than those of X-cells
(centres of both types mapped with the same small flashing light) and
Y-cell centres had less tendency than X-cell centres to be located centrally
in the visual field. This makes it likely that Y-cell axons generally are
larger than X-cell axons. Possibly this explains why some of our electrodes
only recorded the discharges from Y-cells.
DISCUSSION
Spatial summation in the retina
Linear summation. In our experiments with stationary patterns it was
found that for certain ganglion cells (designated X-cells) in the cat's
retina a decrease in the illumination over one half of a receptive field could
completely nullify the effect of simultaneously increasing in the same way
the illumination over the other half of the receptive field. Upon this
observation we primarily base our conclusion that the signals from photoreceptors in the cat's retina are effectively linearly related to the incident
illumination and that the signals from photoreceptors in both the centre
and surround summating regions of an X-cell receptive field add linearly
before they affect the discharge of the ganglion cell.
Barlow (1953) demonstrated approximate linearity of addition over the
receptive field centres of some frog ganglion cells though he did not consider the interaction of simultaneous increments and decrements of
luminance in different parts of a receptive field. Barlow also demonstrated
that, for a ganglion cell with a concentric type of receptive field, the
luminance of a peripherally positioned spot which just inhibited the effect
of a central one was linearly related to the luminance of the central spot.
He concluded that this indicated approximately linear action in the
inhibitory surround region of a receptive field as well as in the central
region. It should be noted that Barlow's conclusion that there is linear
addition of signals in the retina was based upon measurements of the
sensitivity of ganglion cells; that is, upon finding stimuli that were equivalent to each other in producing a certain response from a cell. Barlow did
not claim, and we make no claim, that the response of a ganglion cell is
linearly related to the stimulus magnitude. Moreover, Barlow does not
provide evidence for asserting that the interaction between summated
signals from centre and surround regions is subtractive. It seems that the
assumption of a divisive process of interaction would be equally consistent
with his experimental results and ours.
Rodieck (1965), on the other hand, assumed that the principle of super35
Physiol. i87
546
5C. ENROTH-CUGELL AND J. G. ROBSON
position could be applied in interpreting the responses of cat retinal ganglion cells to various stimuli (Rodieck & Stone, 1965a, b). In our experience, however, even for those cells (X-cells) with receptive fields over
which the initial process of spatial summation appears to be linear there
are always signs of markedly non-linear behaviour evident in the relation
between stimulus and response amplitudes. This non-linear relation appears
to hold down to very low contrast levels and suggests that there is a fundamentally non-linear mechanism in the retina. It is interesting to note that
in experiments with drifting sinusoidal gratings the distortion of the wave
form of the modulation of the pulse density of the discharge of the responding cell does not appear to be reduced as the contrast of the stimulus
approaches zero; indeed, in some instances it even probably increases.
In our analysis of spatial summation over the receptive fields of X-cells
we have assumed (with Rodieck, 1965) the existence of separate processes
of summation in the central and surround regions of the receptive fields.
We have also assumed that the sensitivities of both centre and surround
summating regions fall off as Gaussian functions of the distance from the
middle of the receptive field. Our only justification for making these
assumptions is that they lead to a particularly simple mathematical
formulation of the process of spatial summation which gives a satisfactory fit with our experimental results.
In the interpretation of the measurements of the contrast-sensitivity
function of ganglion cells it has been assumed that the effects of the
optics of the cat's eye are negligible. In particular the fall-off in sensitivity
at high spatial frequencies has been assumed to result from spatial integration in the retina rather than from optical blurring. Support for this
assumption comes from Westheimer's (1962) measurements of the
ophthalmoscopically observed fundal image in a cat's eye. These measurements indicate that even with a 6 mm diameter pupil little attenuation
of contrast occurs at spatial frequencies below 2 c/deg. With a smaller
pupil even less contrast attenuation would be expected as most of the
(in-focus) blurring can probably be ascribed to spherical aberration
(Morris & Marriott, 1961). With a small pupil also the effects of focus
errors are minimized; in any case these are relatively slight at the relevant
spatial frequencies and are unlikely to have contributed significantly to
the measured fall-off in contrast sensitivity at the higher spatial frequencies.
Non-linear summation. On the basis of experiments with drifting grating
patterns whose spatial frequency approached the upper limit at which the
retinal ganglion cells would still respond we classified the cells into two
types: Y-cells whose response was evident as an increase in the mean
pulse density of their discharge and X-cells whose response was evident
as a modulation of their pulse density at the drift frequency. We never
547
CAT RETINAL CONTRAST SENSITIVITY
had any difficulty in distinguishing between these two cell types. The Ycells were also characterized by the impossibility of finding for them any
position for a grating of low spatial frequency in which the pattern could
be turned on or off without evoking a response. Upon the latter observation
we base our conclusion that Y-cells do not respond to the sum of signals
proportional to luminance coming from all parts of their receptive fields.
This direct test for non-linear action was not applied to all those ganglion
cells classified as Y-cells on the basis of their response to drifting gratings.
However, in every case where it was applied it gave the same result. No
other consistent differences in the behaviour of X- and Y-cells were
observed.
Whether our classification of ganglion cells into two distinct classes
would be upheld by objective measurements of the detailed behaviour of a
large sample of ganglion cells under a wide range of conditions (e.g. of
mean luminance) cannot be answered, but there can be no doubt that under
the conditions of our experiments there was a very big difference in the
behaviour of typical members of the two classes.
Diameter of receptive fields
From our measurements of the contrast sensitivity of X-cells to sinusoidal grating patterns of different spatial frequencies it has been possible
to calculate the characteristic radius, rc, of the central summating region
of the receptive fields of these cells; rc is the radius at which the sensitivity
of the central summating region falls to 1/e (37 %) of its maximum value.
Conventionally, however, the diameter of the central region of a receptive
field is equated either with the diameter of the disk of light which has the
lowest increment threshold (e.g. Wiesel, 1960) or with the diameter of the
boundary between the receptive field regions from which responses of
opposite polarity can be evoked by a small spot of light. In our formulation
the radius of the conventional receptive field centre, rj', is the radius at
which the sensitivities of central and surround summating regions are
equal, i.e. Wc (rc') = W, (r,'). Using this relation we have calculated the
diameter of the conventional centres of our sample of twenty-one X-cells.
The range was 0-55-2-9 deg as compared to 0 5-4 deg reported by Rodieck
& Stone (1965b) for all retinal ganglion cells from which they recorded.
The modal value of the diameters in our sample was between 1 and 1.5 deg
which is in accord with the value found by Wiesel (1960) recording directly
from the retina with micropipettes. In Wiesel's experiments the retinal
illumination was probably 2-3 times greater than in ours.
In relating the diameters of receptive field centres to the histologically
determined structure of the cat's retina, Brown & Major (1966) compared
the diameters of ganglion-cell dendritic fields with the diameters of con35 -2
C. ENROTH-CUGELL AND J. G. ROBSON
ventional receptive field centres as reported by Wiesel (1960) and Rodieck
& Stone (1965b). If the partial coextension of centre and surround summating regions is accepted, then dendritic field diameters might more
reasonably be related to the diameters of the central summating regions
than to the diameters of the conventional field centres. Since the sensitivity of each centre summating region is assumed to fall off continuously
from its maximum value these regions do not have a well-defined diameter,
but a value of 5 times the characteristic radius (Fig. 2) probably provides a
fair estimate of their anatomical diameter. Using this factor the diameters
of the central summating regions of the twenty-one X-cells which were
studied ranged from 0-7 to 4-5 deg without any clear indication of the
bimodal distribution reported by Brown & Major (1966) for the diameters
of ganglion-cell dendritic fields. It is interesting to note, however, that
the central summating region of no X-cell significantly exceeded the diameter of the largest dendritic fields. The diameters of the surround summating regions (5 r8), on the other hand, varied from a minimum of about
4 deg up to about 30 deg. Thus even the smallest surround region was as
large as the largest dendritic field and most of the surround regions were
much larger.
Because of the obviously non-linear behaviour of Y-cells we have not
attempted to interpret measurements of their relative sensitivity to
grating patterns of different spatial frequencies in terms of a linear model.
We therefore do not have estimates of the diameters of the central summating regions of Y-cells comparable to those for X-cells. For many
Y-cells, however, the diameter of the conventional receptive field centre
was measured with a small spot of light. Diameters between 1 and 7 deg
with a modal value of about 3 deg were found. These values are considerably larger than those for X-cells measured with the same small spot
or calculated from their contrast sensitivity functions. Many of the Y-cells
had conventional centres of greater diameter than the largest ganglion cell
dendritic field (Brown & Major, 1966).
We have interpreted changes in the contrast sensitivity function of
X-cells brought about by adaptation to lower mean luminance levels as
indicating an increase in the diameters of centre and surround summating
regions. If this interpretation is correct the rationale behind a comparison
of the diameters of receptive field regions and ganglion-cell dendritic fields
becomes obscure.
Visual acuity
It might be expected that the visual acuity of the cat could be related to
the characteristics of its retinal ganglion cells. Unfortunately, no satisfactory behavioural measurement of the visual acuity of the cat has been
reported. Smith (1936) found that cats could distinguish (though not per548
549
CA.T RETINAL CONTRAST SENSITIVITY
fectly) between vertical and horizontal gratings composed of equal width
black and white bars at a spatial frequency of 5X5 c/deg when the mean
luminance was probably about 250 cd/M2 (our estimate from Smith's
description). Although Smith did not use higher frequency gratings it
seems likely that the cat's resolution limit was not much higher than
5*5 c/deg, at which frequency the performance of the animals appears to
have been appreciably impaired.
Before comparing Smith's results with our findings it is important to
note that his observations were made on cats with natural pupils. From
Kappauf's (1943) data on the relation between pupil width and environmental luminance it seems likely that Smith's cats had pupil widths of a
little less than 2 mm; the retinal illumination of these cats was therefore
probably about 5 times higher than the maximum achieved in our experiments with a 3-5 mm diameter pupil, and the retinal image in Smith's cats
may have been a little sharper than in our experiments.
Figure 9B shows the contrast sensitivity function of the retinal ganglion
cell which responded at the highest spatial frequency. By extrapolation
it can be estimated that this cell would have produced a detectable
response to a square-wave grating with a contrast of 1 (equivalent to a
sinusoidal grating with the same spatial frequency and a contrast of 1.27)
at spatial frequencies of up to about 4 c/deg. Allowing for the difference in
pupil size and retinal illumination this cell might well have produced a
detectable response at 5 5 c/deg under conditions similar to those of Smith's
(1936) experiments. This makes it seem unlikely that ganglion cells with
much smaller centres than that of the cell of Fig. 9B (r, = 0-16 deg,
corresponding to a conventional centre diameter of 0.550) are present in
the cat's retina. It is, of course, difficult to assess the relation between
the stimulus which will evoke from a ganglion cell a response that can be
detected by an experimenter listening to its discharge and the stimulus
which will produce a certain behavioural effect.
Psychophysical correlates
The contrast sensitivity function of the human visual system is derived
from psychophysical measurements of the minimum contrast required for
a subject to detect sinusoidal gratings of different spatial frequencies. The
contrast sensitivity function for central vision has been shown to be partly
determined by the dioptric mechanism of the eye and partly by neural
mechanisms (see Campbell & Green, 1965). It has not, however, been
possible to decide by direct experiment on humans to what extent the
neural mechanisms involved are retinal. It is therefore of interest to compare the psychophysical results with the contrast sensitivity function of
retinal ganglion cells as determined from animal experiments.
550
C. ENROTH-CUGELL AND J. G. ROBSON
Assuming that the human retina is similar to the cat's the problem
immediately arises whether the psychophysical measurements reflect the
behaviour of retinal ganglion cells of the X- or Y-types. Since X-cells have
been found to occur predominantly in the more central regions of the
retina and the Y-cells predominantly in the more peripheral regions it
seems possible that central human vision may be mediated by ganglion
cells of the X-type. This interpretation is supported by some evidence that
the psychophysically measured contrast sensitivity function (for central
vision) is determined by a linear mechanism (Robson & Campbell, 1964).
Moreover, Merchant (1965) has noted certain characteristics of human
peripheral vision and suggested that it may be mediated by a mechanism
whose behaviour would bear a close resemblance to that of Y-cells.
The form of the contrast sensitivity function of a typical X-cell (Fig. 9)
resembles that of the human visual system (e.g. Schade, 1956) in that it
shows a rapid fall-off at high spatial frequencies and a less rapid fall-off
at spatial frequencies below some optimum value. It must be noted, however, that the form of the human contrast sensitivity function at low
spatial frequencies is dependent upon the temporal frequency at which the
observations are made (Robson, 1966).
It is difficult to compare in absolute terms the contrast sensitivity of a
human subject with the contrast sensitivity of a ganglion cell which does
not exhibit a threshold non-linearity. However, the discharge of many of
the X-cells from which we recorded was clearly modulated (so as to be
obvious to an experimenter listening to the discharge) by grating patterns
of optimal spatial frequency and contrast of little more than 0.01. At the
same retinal illumination a human subject can see grating patterns when
the contrast is about 0-005. Thus it seems likely that a cat can detect patterns at contrast levels comparable to -those required by a human subject.
An obvious difference between the human contrast sensitivity function
and the contrast sensitivity function of any of the cat retinal ganglion
cells that we have studied is that they occupy very different positions
along the spatial frequency scale. The maximum observed value for the
optimum spatial frequency of a cat ganglion cell was about 0-8 c/deg,
while the optimum frequency for human central vision with the same
retinal illumination is about 5 c/deg. The human thus seems to operate in a
higher spatial frequency range than the cat. Consequently it might be
expected that the human contrast sensitivity at low spatial frequencies
would be less than the sensitivity of some of the cat retinal ganglion cells.
Indeed in our experiments it was sometimes possible for the experimenter
to detect the presence of a grating pattern by listening to the discharge
of a cat retinal ganglion cell when he could not see the pattern on the
stimulus screen.
551
CAT RETINAL CONTRAST SENSITIVITY
Campbell & Green (1965) showed that at high spatial frequencies the
human contrast sensitivity function falls off exponentially with increasing
frequency while Kulikowski, Campbell & Robson (1966) have noted that
it can be fitted by the difference between two exponential functions. The
human contrast sensitivity function thus appears to be broader than the
contrast sensitivity function of individual cat ganglion cells. It must be
remembered that human contrast sensitivity at any one spatial frequency
is probably determined by those ganglion cells which are most sensitive at
that frequency. Thus if the human central retina contains receptive fields
of different sizes the psychophysically measured contrast sensitivity
function may well be broader than the contrast sensitivity functions of
the individual ganglion cells. Measurement of the characteristics of cat
ganglion cells support the general hypothesis that in each part of the
retina there exist ganglion cells with a relatively wide size range. The
existence of receptive fields of different sizes in the central human retina
may also account for Campbell & Robson's (1964) observation that simultaneously presented sinusoidal grating patterns with harmonically related
spatial frequencies appear to be detected independently.
This investigation was supported by U.S. Public Health Service Research Grants B-2208,
National Institute of Neurological Diseases and Blindness and FR 00018, Division of
Research Facilities and Resources. C. E.-C. was supported by Career Development Award
5.K3-NB-18,537, National Institutes of Neurological Diseases and Blindness.
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