Effect of field size on red - green color mixture equations
Joel Pokorny and Vivianne C. Smith
Eye Research Laboratories, The University of Chicago, Chicago, Illinois 60637
(Received 24 January 1976)
Red-green color mixture equations were measured in 10 color-normal observers for fields of view varying
from 30' to 10°. The GIR mixture decreases continuously as field size is increased. The data are consistent
with the interpretation that the cone visual photopigments decrease exponentially in effective optical density as
the field size is increased.
In 1893 Hering' observed that reduction of the field size
of an anomaloscope set for the observer's Rayleigh
equation caused the mixture field to appear too "red."
A new mixture requiring a higher G/R ratio was necessary. Hering attributed the changes to variation in the
density of macular pigment. Quantitative data were obtained by Horner and PursIow2 using a filter anomaloscope. They showed that the G/R ratio increased as
viewing distance increased (and field size decreased).
The effect was 0. 07 log unit between a 2° field viewed
at 50 cm and a 20 min field viewed at 300 cm. They
remarked on intersubject variability but confirmed the
finding on 40 observers. They attributed the change to
chromatic aberration but, in the second paper, mentioned the Stiles-Crawford effect as an alternative explanation.
These studies show changes in metamers as field
size is varied. Such changes may also represent
variation of receptoral characteristics. 3 Pokorny,
Smith, and Starr4 explained differences in the unit coordinates for 20 and 100 field sizes5 ' 6 by postulating a
continuous exponential decrease in effective optical
density of the photoreceptors as field size is increased.
The direction of change of the G/R ratios is in the direction predicted by such a variation of effective optical
density in the retina. Baker 7 and Alpern and Torii8
demonstrated that Rayleigh matches are characteristic
of pigments in density. Following a bleach, the mixture field appears green. The G/R ratio must be decreased to maintain a match. The match recovers
within 60 to 90 sec.
The present experiment was designed to investigate
the Horner and Purslow results using a fixed viewing
distance, narrow-band spectral stimuli, andanextended
range of field sizes (30' to 100). A second aim was to
estimate the proportion of variability that might be
ascribed to receptoral variance, and to examine its
origin.
Equipment: A Moreland Universal Anomaloscope 9
was modified (in manufacture) to include the use of 3cavity filters (Ditric) and a 500 W tungsten halogen
lamp. Calibration of the instrument was performed by
Moreland. In experiments 1 and 3, the filters had
maximal transmission at 545. 5 am (G), 589. 0 nm (Y),
and 670 nm (R) with half-height bandwidths of 9. 0-9. 65
nm. For experiment 2, a 580 nm filter (Ditric) was
also used, placed in the system at 150 to the normal.
Maximal transmission was at 575 nm with a 9 nm halfbandwidth.
The field without apertures subtended 100 x 100 in
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J. Opt. Soc. Am., Vol. 66, No. 7, July 1976
visual angle. Circular apertures provided field sizes
of 30', 10, 20, 40, and 80.
The anomaloscope was used in a manner essentially
identical to that of the Nagel anomaloscope. 10 The spectral yellow was variable in luminance; the G/R mixture was variable from green to red. The primary
energies were set so that normal matches would fall
near a G/R of 1. 0. The luminances of the R and G
primaries were similar. The effective field luminance
was approximately 5 cd/M 2 .
Observers: Ten normal trichromats served as observers. They were drawn from laboratory personnel
and included naive observers and observers well practiced in making color matches. Their ages ranged
from 22 to 36 years.
EXPERIMENT 1: THE EFFECT OF FIELD SIZE
Procedure: Each observer viewed with his preferred
eye. The 20 field was presented first. The observer
made 3 "free" matches, a procedure in which he is allowed to vary the luminance of the Yprimary and the
G/R mixture in order to obtain a perfect match. Between settings, the experimenter varied the control
knobs. After the free matches, the experimenter
established a match range by setting various G/R ratios
and asking the observer to state whether the ratios
constituted a match. The observer was allowed to make
minute adjustments of the Y control during this procedure. Observers could not achieve a perfect match with
the 80 and 100 x 100 fields. They were instructed to
set the G/R ratio so that the mixture half-field appeared
neither more "reddish" nor more "greenish" than the
spectral half-field. Each observer was cautioned not
to stare continuously at the field but rather to use a
glance technique in which he looked away every 10-12
sec.
Following the initial settings for the 20 field, the
other field sizes were presented in varied order, with
a brief break between field sizes. At the end of the
procedure, matches were rechecked for the 20 field.
Results and Discussion: The dial readings were converted into logG/R. In population studies, "1 the normal
mean is assigned a value of 0, with a range between the
2nd and 98th percentiles of ± 0. 15. Positive logG/R
ratios reflect an increase in G primary, negative ratios
an increase in R primary, needed for the match.
LogG/R ratios for the 10 observers are shown in Fig. 1
as a function of field size. All observers require more
red in their match as the field size is increased. The
Copyright © 1976 by the Optical Society of America
705
EXPERIMENT 2: THE VARIABILITY CONTRIBUTED
BY INERT OCULAR PIGMENTS
0.3
Procedure: The 20 aperture stop was used. Each
observer made two sets of matches, one at the standard
Rayleigh wavelength of 589 nm and one at a wavelength
of 575 nm. Free matches and match widths were
established as described above. The data were converted to logG/R.
02
0
FIELD SIZE (deg)
FIG. 1. Log G/R ratios for ten observers plotted as a function of the field of view.
logG/R ratios change most rapidly for small field
sizes, leveling off above 4°. The spread of individual
observers is approximately 0. 18 log unit for field sizes
greater than 30 min and 0. 205 for the 30 min field.
Chromatic aberration
2
Horner and Purslow ascribed their result to chromatic aberration. We found chromatic fringes evident
as the field size was reduced below 20. A red fringe
surrounding the mixture field may have interacted with
the match settings for the 30' and 10 fields. To check
this possibility, we introduced a 2 mm artificial pupil
2
containing an achromatizing lens' designed to compensate for chromatic aberration of the eye. Two observers (VP and JP) repeated experiment 1. The data
were within experimental variance.
Rod intrusion
The effect of rod intrusion, on a large-field Ray2
leigh match at 5 cd/M , is desaturation of the mixture
field. The desaturation appears more marked with a
100-fold reduction of luminance and the mixture field
appears "pinkish. " If a desaturant is allowed, a match
may be made and the R/G ratio will depend on the
choice of desaturant. We ascertained on four observers
that at 5 cd/M2 , neither the use nor choice of desaturant affected the G/R ratio. Thus, rod intrusion was
not a major source of contamination of the G/R ratios.
Further, had rod intrusion affected the G/R ratios, we
might have expected greater interobserver variability
in setting the G/R ratio at the 80 and 100 x 100 fields
as evident, for example, in the Stiles and Burch 10°
data. 6 However, the logG/R range was the same for
the 80 and 10° x 100 fields as for the 2° field, supporting the notion that rod intrusion did not interact with
the GIR setting. We note that any effect would have
been opposite in direction to the trend of data shown in
Fig. 3.
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J. Opt. Soc. Am., Vol. 66, No. 7, July 1976
Results and Discussion: Columns 1 and 2 of Table I
show the results of log G/R for the 589 and 575 nim
fields. The matches for 589 nm vary around 0, those
for 575 nm around 0. 427. Column 3 shows values obtained by subtracting log GIR at 589 nm from log G/R
at 575 nm. The effect of inert ocular pigments on
log G/R is to multiply the retinal match by the factor
T670/T 54 5 , where T670 is the transmission factor for the
inert pigments at the 670 nm primary and T745 is the
transmission factor for the inert pigments at the 545
nm primary.13 The matches are not affected by transmission factors for the test wavelength. Subtracting
logG/R at 589 nm from log G/R at 575 nm for each observer removes the effect of the observer's inert
pigments. The range of variation in the column 3 values reflects receptoral variability and repeatability
variance. In comparison, the range of variation in the
column 1 and 2 matches reflects, in addition, variation
contributed by inert pigments.
Moreland' 3 discussed the role of inert ocular pigments in accounting for interobserver variability in
Rayleigh matches. The macular pigment does not ab2 4
sorb at wavelengths above 540 nm' " and would not
contribute to variability in this study. The inert ocular
pigment that may affect Rayleigh matches is that in the
lens. Moreland suggests that lens variation in observers ranging in age from 20 to 60 years might account for 0. 1 log unit of published log G/R ranges. His
5
calculation was based on Said and Weale's data' suggesting a linear change of lens density with age. Coren
and Girgus' 6 suggest that a second degree polynomial is
a better fit to the age data. Use of the polynomial would
TABLE I.
Comparison of 2° matches at 589 and 570 nm.
Observer
Column 1
Column 2
Column 3
Log G/R
for 589 nm
Log G/R
for 575 nm
Difference
(Column 2 - 1)
+ 0.545
+ 0.390
DHL
DL
+0.140
+0.030
+ 0. 092
+0.080
JP
KP
VP
- 0.025
+0.005
+0.070
0.355
0.370
0.465
RB
CH
+ 0.470
+
+
+
+
0.495
+ 0.405
+ 0.360
+ 0.378
+
+
+
+
0.415
0.380
0.365
0.395
GS
-0.045
+ 0.340
+ 0.385
HW
+0.030
+ 0.370
+ 0.340
JW
+0. 075
+ 0.470
+ 0.395
Mean
+0.045
+ 0.427
+
0.185
0.205
0.382
Range of
observations
0.075
J. Pokorny and V. C. Smith
We used the procedure described by Alpern and
Torii8 : Following the bleach, the observer viewed
either the 20 or the 8° field and attempted to track the
recovery following one of two criteria-tracking between
"too red" and "match" or tracking between "too green"
and "match. " Three repetitions were made for each
criterion.
080
o 0.70
z 0.60
0
~05
LL0
0.40
TIME (min)
z 0.60
0
, 0.50
LL
0
05
TIME (min)
10
1.5
FIG. 2. Recovery of a match after bleach. Upper panel
shows fraction red as a function of time for a 20 field. Lower
panel shows recoveries for an 8° field. The solid line shows
the midpoint of the steady state match (experiment 1). The
arrows show the predicted fraction red for dilute pigments.
The upper 3 traces are red runs; the lower are green runs.
increase Moreland's expected log G/R range due to age
to 0. 18. Our observers ranged in age from 20 to 36
years, which would predict no more than a 0. 1 variation
in log G/R due to differences in age. Examination of
Table I shows that the ranges in columns 1-3 are 0. 185,
0. 205, and 0. 075, respectively, confirming that the
major portion of the interobserver range at 20 (about
0. 1) may be ascribed to population variation in inert
lens pigment.
We can calculate the variance of the match at 589 nm
expressed as percent green normalized at 575 nm for
comparison with data of Stiles. 5 The standard deviation
was 0.008 compared with Stiles' report of an average
deviation of 0. 0075 in the same spectral region.
EXPERIMENT 3: RECOVERY FROM BLEACH
Procedure: A silicon photocell (UDT PIN10) was
used to sample the fraction R in the R/G output. The
photocell output was amplified and displayed on a chart
recorder. A 3200 0 K light of luminance 6000 mL was
used to present a uniform bleach over 200 in extent.
One observer (VP) viewed this field for 45 sec with a natural pupil. The pupil constricted to about 2 mm giving
an estimated 60 000 tds, providing a substantial bleach
of the cone pigments.
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J. Opt. Soc. Am., Vol. 66, No. 7, July 1976
Results and Discussion: The sets of recoveries,
superimposed on each other, are shown in Fig. 2. The
fraction R in the match is shown as a function of time.
In panel (a) are shown the data for the 20 field and in
panel (b) the 8° field. For the 2° field, the upper three
traces are the red runs, the lower three traces are the
green runs. For the 80 field, the sets of traces are
not clearly separated. The solid line shows the midpoint of the steady-state match (experiment 1). The arrows show the fraction red predicted for dilute pigments
assuming optical densities of 0. 45 for LWS, 0. 35 for
MWS for the 2° field. 4 We have chosen to reproduce
the actual tracings of the chart recorder to demonstrate
the variability of the technique. The widening of match
width noted by Alpern and Torii8 is evident in the 20
field recoveries but not in the 80 field recoveries; the
red runs for the 20 and 8° fields are quite different,
while the green runs are similar. The sets of green
runs for the 20 and 80 fields are initially overlapping
but draw apart at full recovery. The data support the
hypothesis that for observer VP, the 20 field is characterized by visual pigments in higher densities than
those characterizing the 80 field. However, the variability is too great to allow estimation of optical density or pigment kinetics for either field.
We were also able to demonstrate informally that the
field size effect for four other observers reflected pigments in different densities: The observers state that
the mixture field for a match made at 10° appears too
red when viewed with the 20 field stop. Following a
bleach, this mixture field viewed with a 20 stop appears
initially greener than the spectral yellow, passes
through the 10° match at about 45-60 sec, and then appears too red at full recovery.
THEORETICAL TREATMENT
While the inert pigments do contribute to interobserver variability, we would not expect them to interact with the field size for a given observer. We therefore reduced the matches for all field sizes by subtracting the Table I column 2 match for each observer
and adjusting matches to set the mean log G/R at 20 to
zero. Means and standard deviations were computed
and are shown in Fig. 3. Error bars are ± one standard deviation. The solid line is a theoretical prediction for log G/R, calculated for an observer whose
visual pigments show a continuous exponential decrease
in effective optical density as field size increases. The
effective densities are those derived previously. 4We
assume that effective optical density for the long-wavelength sensitive pigment varies as ODLWS =0.25 + 0.8825
x e</1.333, and that for the middle wavelength varies as
ODMws = 0.15 + 0. 8825 ed/ 1333, where d is the diameter
of the viewing field in degrees. These equations preJ. Pokorny and V. C. Smith
707
iI
.
I
I
I
.
I
.
I
02
M
0I
0
-J
0
I
I
-0.1
I
0
I
I
I
2
4
6
FIELD SIZE (deg)
I
I
I
I
I
8
I-
,
I
10
FIG. 3. Average log G/R ratios for ten observers (circles,
and error bars, ± one standard deviation) compared with theoretical prediction (solid line).
dict effective optical densities of 0. 45 for LWS, 0. 35
for MWS for the 20 field. The prediction passes within
one standard deviation of the observed results for all
field sizes. However, the average data fall below the
prediction for the 30' and 10 fields and above the prediction for 40, 80, and 100 x 100 fields suggesting that
the exponential should be more compressed. For example, OD =k + 0. 75 e-d/ 1.333 would provide a better fit
for the G/R mixture data.
We conclude that these data provide experimental
confirmation that the effective optical density of the
visual photopigments decreases continuously as field
size increases.
ACKNOWLEDGMENT
We thank Frank W. Newell, M.D. for a critical reading of the manuscript.
*Supported in part by NIH, USPH, NEI Grant Nos. EY70652,
EY00901, and EY00523.
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R. G. Horner, and E. T. Purslow, "Dependence of anomalo-
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J. Opt. Soc. Am., Vol. 66, No. 7, July 1976
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4
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5
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13
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15
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J. Pokorny and V. C. Smith
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