Diffraction Theory and Visual Hyperacuity∗

The implications of the diffraction theory of light are examined as they relate to visual acuity and hyperacuity. Two incoherent point sources of light give rise to a double‐peaked light distribution whose trough is 26% below the adjoining peaks when the sources are separated by the Rayleigh limit of resolution, but the dip has vanished when the separation is 80% of the Rayleigh limit. Diffraction theory, however, places no restriction on the precision with which any single source can be localized. No paradox is therefore involved in having a point‐spread function with half‐width one minute of arc and, at the same time, a localization threshold of a few seconds of arc, although the need for a sophisticated processing mechanism to achieve such low hyperacuity thresholds is emphasized.