Absorption of white light in photoreceptors

The fraction F of incident light absorbed by a photoreceptor of length l has traditionally been given by F = 1 - e-kl, where k is the absorption coefficient of the photoreceptor. Unfortunately, this widely-used expression is incorrect for absorption of the type of light most common in natural scenes--broad spectrum "white" light--and significantly over-estimates absorption. This is because the measured values of k are only valid at the absorbance peak wavelength of rhodopsin, whereas at other wavelengths (which the eye may also see) k is lower. We have accounted for the wavelength dependence of k and calculated the absorption of white light from four different natural radiant sources: the quantal irradiances of natural daylight and a patch of very blue sky, and the quantal reflections of soil and green foliage irradiated by natural daylight. Based on these results, a simple averaged correction for white light stimulation is derived, F = kl/(2.3 + kl), which is valid for a wide range of k and l, and therefore applicable to both vertebrate and invertebrate photoreceptors.