The relative cone contribution is expected to increase from 0 to 1 as adapting intensity increases, owing primarily to the desensitization of the rod system with increasing intensity. We attempted to model this increase with an equation that has a simple rationale described below:
The adaptation level is expressed here in terms of the scotopic sensation luminance
S′, which is based on the individual observer's scotopic sensitivity (Kaiser,
1988; Raphael & MacLeod,
2011; and see
Appendix). On the simple model described in Raphael and MacLeod (
2011; appendix B), from which
Equation 2 is derived, the absolute weight for rods is proportional to rod sensitivity. The transition from scotopic to photopic vision is driven by the decrease of rod system sensitivity as the adapting intensity seen by rods increases across the mesopic intensity range. The parameter
k is equal to the log-log slope of the rod threshold versus intensity curve (TVI-curve), according to which rod sensitivity varies inversely as the
kth power of luminance. In particular, a value of
k = 1 is expected where rod sensitivity conforms to Weber's law. The parameter
M is the
mesomesopic luminance in scotopic cd/m
2, which is the luminance at which rods and cones contribute equally to luminance so that
WP = 0.5. The best fitting
M and
k values for the averaged cone weights are 0.33 sc cd/m
2 and 0.81 sc cd/m
2, respectively (black curve,
Figure 4), with an average root mean squared error of the fit of 0.1. The individual values for each subject are shown in
Table 2 along with the fitted individual
M and
k values of the dark adaptation curves measured with minimum motion (Raphael & MacLeod,
2011) for nearly the same observers (six out of eight observers from the minimum motion experiment took part in the MDB experiment).