Depth of focus, eye size and visual acuity

Abstract

We develop formulas for calculating the approximate depth of focus of any eye. They show that the magnitude of depth of focus is inversely proportional to the size of the eye and to its visual acuity. One particular implication of these quantitative relations, which is supported by previous data from rats and human infants, is that small eyes with low acuity should have large depths of focus. We show that the observed relation between defocus and contrast sensitivity in rats in predicted by our formulas. We also analyze recent findings in human infants and show that they demonstrate a good correspondence between the improvement in accuracy of the accommodative response with age and the reduction in depth of focus (predicted from our formulas) as acuity and eye size increase over the same age range. Optical factors such as astigmatism, refractive error and chromatic and spherical aberration should have no effect on visual resolution unless they exceed the depth of focus of an eye. Thus, our arguments imply that these factors may be relatively unimportant in small eyes with low acuity.