Physical limits of acuity and hyperacuity.

An ideal detector is derived for the discrimination of arbitrary stimuli in the two-alternative forced-choice paradigm. The ideal detector's performance is assumed to be limited only by quantal fluctuations, the optics of the eye, and the size and spacing of the receptors in the retinal mosaic. Detailed predictions are presented for two-point acuity and hyperacuity tasks. The ideal detector's two-point resolution, over a wide range of luminances, is approximately 10 times worse than its two-point vernier acuity or separation discrimination. Furthermore, two-point resolution is shown to vary in proportion to the -1/4 power of spot intensity, but vernier acuity and separation discrimination vary in proportion to the -1/2 power of spot intensity. It is shown that this ideal detector can be implemented by the use of appropriately shaped receptive fields. The derivation provides a simple way to determine the shapes of these optimal receptive fields for arbitrary stimuli. The sensitivities of real (human) and ideal detectors are compared.