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 1021