A Quantitative Basis for the Relation between Visual Acuity and Illumination

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Abstract
There exists no explanation of the dependence of visual acuity on illumination. The region of variation of visual acuity with increasing illumination is such that one must assume either that the number of sensitive elements per unit retinal area can vary nearly a hundredfold or that the number of elements in the retina can be varied functionally. Since the number of rods and cones in the retina is fixed anatomically the latter is the assumption of choice. The author plots the integral frequency curves giving the total number of functioning elements per unit area at the different retinal illuminations. At the lowest illuminations vision is mediated by the rods. The number of rods which function is small, which is equivalent to a resolving surface with the receiving elements sparsely distributed. The retinal distance between 2 just discriminable contours must be large, and visual acuity is low. As the illumination increases, more and more rods become functional. The average distance between the functional elements becomes smaller and visual acuity becomes larger. Presently an intensity is reached at which the cones begin to function. The cones come into play nearly 10 times as fast as the rods because of their greater number in the fovea. Visual acuity then becomes a function of the foveal cones and continues to increase until all the cones are active. This curve corresponds well with the curve showing the relation between visual acuity and illumination as originally given by Koenig. Further, this theory satisfies the data obtained from completely color blind individuals in which with increasing illuminations the cone portion of the curve disappears and only the lower rod limb remains. Koenig computed that the whole range of intensities visible to the eye is made in only 572 discrete steps in intensity recognition. About 30 of these steps are mediated by the rods; the rest by the cones. If there is a minimal retinal area which carries out all the functions of the retina as a whole, Hecht concludes that the minimal retinal area must contain 542 cones or some multiple of that number. The lowest visual acuity corresponds to a minimal retinal area of 0.04 sq. mm. and since there are 13,500 cones per sq. mm. of fovea it appears that the minimal retinal area of 0.04 sq. mm. contains 540 cones in the fovea, which is a striking agreement from 2 independent sources. This same assumption of the statistical distribution of rod and cone thresholds is also applied to a basis for color vision.

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