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Retinal response to departure from perfect power coupling: implications for the Stiles–Crawford effect

Maximum power transfer occurs in an oscillatory system driven by an external periodic force matching the natural frequency. Here, we analyze the role of matching in the biological phenomenon of waveguiding of light in a photoreceptor cone. When the fraction of light power that is not able to be coupled to a fundamental mode of a foveal cone is computed, it is found that the mismatch is proportional to the degree of departure from the perfect matching for one hundred percent coupling. Thus, Stiles–Crawford effect of the first kind is shown to be the response of the retina to departure from perfect matching. We show by correlating how the diminution in luminous efficiency recorded in psychophysical measurements for beams entering the pupil mm from the point of optimum efficiency in Stiles–Crawford effect of the first kind is due to a departure of either six or one-sixth times from this perfect match. The Stiles–Crawford function is recreated by interpreting perfect matching for axial entry of the beam and proportionate mismatching for corresponding degree of peripheral entries. Now the fundamental question is: Does a biological system respond by decreasing the efficiency by same amount irrespective of increase or decrease so long the product of departures from the value for optimum efficiency is unity?