where [A] is the analyte concentration and Kd is the dissociation constant. As the photophysical translation of a binding event depends on the exciton diffusion length, as well as the exciton size, we assumed a non-linear relationship (exponent n) between the observed fluorescence change ([I-I0]/I0) and the surface coverage. Incorporating a factor to account for the offset factor between the end (IE) and the non-zero start response/signal (IS) of the sensors we get: