Blur Unblurred—A Mini Tutorial

Abstract

Optical blur from defocus is quite frequently considered as equivalent to low-pass filtering. Yet that belief, although not entirely wrong, is inaccurate. Here, we wish to disentangle the concepts of dioptric blur, caused by myopia or mis-accommodation, from blur due to low-pass filtering when convolving with a Gaussian kernel. Perhaps surprisingly—if well known in optometry—the representation of a blur kernel (or point-spread function) for dioptric blur is, to a good approximation and disregarding diffraction, simply a cylinder. Its projection onto the retina is classically referred to as a blur circle, the diameter of which can easily be deduced from a light-ray model. We further give the derivation of the relationship between the blur-disk’s diameter and the extent of blur in diopters, as well as the diameter’s relation to the near or far point, and finally its relationship to visual acuity.