Vision Res. Vol. 31, No. 6, pp. 1021-1037, 1991 0042-6989/91 $3.00+0.00
Printed in Great Britain. All rights reserved Copyright © 1991 Pergamon Press pie
FOVEAL CONE DETECTION STATISTICS IN
COLOR-NORMALS AND DICHROMATS
MICHAEL F. WESNER, JOEL POKORNY, STEVEN K. SHEVELL a n d VIVIANNE C. SMITH
University of Chicago, Visual Sciences Center, 939 East 57th St, Chicago, IL 60637, U.S.A.
(Received 31 October 1988; in revisedform 25 April 1990)
Abstract--We measured for six male observers, the psychometric functions for the detection of two
simultaneously presented points of light. The test stimuli were two I min point sources separated by 17 rain
arc, and pulsed for 0.5 reset. The stimuli varied in wavelength from 500 to 620 nm. The psychometric
functions were fit with a model that assumes ideal detection and the following properties: (1) Poisson-dis-
tributed quantal absorptions; (2) binomial sampling of foveal long-wavelength-sensitive (LWS) and
middle-wavelength-sensitive (MWS) cones; (3) independent responses of the LWS and MWS cones; and
(4) the Smith-Pokorny fundamentals for cone spectral sensitivities. Based on X2 fits to the psychometric
functions for detecting neither, one or both of the two-point stimuli presented, estimates were derived for
the minimum quantal catch by a single cone for detection (C), the number of effective cones illuminated
by a point stimulus at threshold (N) and the proportion of central foveal cones of the LWS type (PL).
Three observers were color-normal, two were protanopes and one was a deuteranope. A second
deuteranope was included in the design but his data were too unreliable for an unambiguous solution.
The estimated quantal requirement C was consistently near 5 (4-6), and the effective number of illuminated
cones always was 1 or 2. The plausible range of PL (98% confidence interval) for the color-normal
observers was 0.48-0.68 (observer YY), 0.76--0.90 (observer MW) and 0.77-0.95 (observer DF). The best
fitting PL solution for these observers were 0.61, 0.82 and 0.88, respectively. These were comparable to
the values obtained from flicker photometric data. The best PL value for each of the protanopes was 0.00
and for the deuteranope the best PL value was 0.98.
Cones Fovea Dichromats Quanta Detection L/M cone ratios Spectral sensitivity
INTRODUCTION
Recently, a psychophysical technique similar to
that of the classic Hecht, Shlaer and Pirenne
(1942) study has been used to determine not
only the minimum number of quanta required
for detection by a foveal cone photoreceptor,
but also the L/M foveal cone ratio, or equiva-
lently, the proportion (PL) of foveal cones of the
LWS type (Vimal, Pokorny, Smith & Shevell,
1989). The quantal requirement per cone (5-7)
was found to be comparable to previous esti-
mates (Bouman & Walraven, 1957; Brindley,
1954; Cicerone and Nerger, 1989a, 1989b; Mar-
riott, 1963).
In the Vimal et al. (1989) threshold study,
estimates of the L/M cone ratio were deter-
*Note that the value PL is L/L +M which is not an
arbitrary metric. The statistic L/L + M is constrained
between 0 and 1.0 whereas L/M is between 0 and 1.0
when M > L, and between 1.0 and infinity when L > M.
Further, L/L + M (or PL) gives a normal population
distribution (as does log L/M) in photometric matching
(Lutze, Cox, Smith & Pokorny, 1990).
mined from the effect of test wavelength on the
shape and separation of two psychometric func-
tions. The ratio of LWS to MWS cones in the
fovea of the two observers was 1.6 (PL = 0.61)
and 4.0 (PL = 0.81), and agreed with estimates
of the L/M ratio determined independently
from Heterochromatic Flicker Photometry
(HFP) on the same observers.* Vimal et al.
(1989) assumed an idealized mosaic of LWS and
MWS cones randomly arranged in a hexagonal
lattice. Based on the relative spectral sensi-
tivities of the MWS and LWS cones, we can
describe qualitatively the effect of wavelength
on the probability of quantal catch for the two
cone types. At the shortest wavelength (500 nm),
MWS cones have a slightly higher probability of
quantal absorption than the LWS cones. At
546 nm, both types of cones in the mosaic have
an equal probability of quantal catch. At
600 nm, the MWS cones have a lower prob-
ability of quantal absorption than the LWS
cones, and at 620 nm the relative probability of
MWS cones absorbing quanta decreases fur-
ther. The areas of the fovea occupied by MWS
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