The luminance and chromatic discrimination data are presented in the results as the change in L-cone luminance (ΔL cd/m
2) as a function of pedestal L-cone luminance. Note that the L-cone luminance is equivalent to 0.665 of the luminance value for luminance discrimination data, which were fitted by a physiological based contrast response model for MC and PC pathways.
31,33 The achromatic contrast response is described by a Michaelis-Menten saturation function
32:
where
Rmax is the maximum response rate,
Csat is the half-maximum contrast response, and
C is the stimulus Michelson contrast. Contrast gain is defined as
Rmax/
Csat, the derivative of
equation 1 at 0 contrast (
C = 0). Therefore, contrast gain expressed in logarithmic units is linearly related to −log(
Csat). A contrast discrimination threshold can be obtained when the differential responses to two contrasts (
C and a [
C + Δ
C]) reaches the criterion, δ. Therefore, the pulsed-pedestal luminance discrimination threshold can be derived from
equation 1:
where ΔL is the discrimination threshold (L-cone cd/m
2),
Kp_a (p denotes pulsed, a denotes achromatic) is the vertical scaling parameter in logarithmic unit that represents PC-mediated absolute threshold (therefore, −
Kp_a represents contrast sensitivity), and
k represents δ/
Rmax, which is typically small and was set as 0 when fitting the pulsed-pedestal data. There are two free parameters for the achromatic pulsed-pedestal condition (
Kp_a and
Csat_a). Note that the 0 contrast data were not used for pulsed-pedestal model fitting because the pulsed- and steady-pedestal conditions have the same (0 contrast) stimulus, and detection was empirically established to be mediated by the inferred MC pathway. The steady-pedestal luminance discrimination data for a pedestal luminance, L (in L-cone cd/m
2), are described by
where
Ks_a is the vertical scaling parameter in logarithmic units, which represents absolute threshold in logarithmic units. Therefore, −
Ks_a represents MC-mediated absolute sensitivity.