The sharpness of our senses is defined by the finest detail we can discriminate. Visual acuity is measured by the smallest letters that can be distinguished on a chart and is governed by the anatomical spacing of the mosaic of sensory elements on the retina. Yet spatial distinctions can be made on a finer scale still: misalignment of borders can be detected with a precision up to 10 times better than visual acuity, as already shown by Ewald Hering in 1899. This hyperacuity, transcending by far the size limits set by the retinal 'pixels', depends on sophisticated information processing in the brain.
How does hyperacuity differ from traditional acuity?
The best example of the distinction between acuity and hyperacuity comes from vision, for example when observing stars on a night sky. The first stage is the optical imaging of the outside world on the retina. Light impinges on the mosaic of receptor sense cells, rods and cones, which covers the retinal surface without gaps or overlap, just like the detecting pixels in the film plane of digital cameras. Each receptor accepts all the light reaching it but acts as a unit, representing a single location in visual space. This compartmentalization sets a limit to the decision whether an image came from a single or a double star (resolution). For a percept of separately articulated stars to emerge, the images of the two must be wide enough apart to leave at least one intervening pixel relatively unstimulated between them. This defines the resolution limit and the basis of visual acuity.
A quite different mechanism operates in hyperacuity, whose quintessential example and the one for which the word was initially coined, is vernier acuity: alignment of two edges or lines can be judged with a precision five or ten times better than acuity. In computer graphics the phrase "sub-pixel resolution" is sometimes used in discussions of anti-aliasing and geometrical superresolution. Though what is in fact involved is not resolution (is it one or two? – a qualitative distinction) but localization (exactly where? – a quantitative judgment) it captures the process. When an image spreads across several pixels, each with graded intensity response but only a single spatial value, the position of the image center can be located more exactly than the width of the pixel, much like the mean of a histogram can be calculated to a fraction of the bin width.
In the figure on the right, the retinal mosaic has superimposed on it, at top, the images of two stars at resolution limit when the intervening gap assures judgment that there are two stars and not a single elongated one. Shown below are the images of two separate short lines; the precision of the read-out of their location difference transcends the dimension of the mosaic elements.
Analysis of hyperacuity mechanism
Details of the neural apparatus for achieving hyperacuity still await discovery. That the hyperacuity apparatus involves signals from a range of individual receptor cells, usually in more than one location of the stimulus space, has implications concerning performance in these tasks. Low contrast, close proximity of neighboring stimuli (crowding), and temporal asynchrony of pattern components are examples of factors that cause reduced performance. Of some conceptual interest are age changes and susceptibility to perceptual learning which can help in understanding underlying neural channeling.
Two basic algorithms have been proposed to explain mammalian visual hyperacuity: spatial, based on population firing rates, and temporal, based on temporal delays in response to miniature eye movements. While none of them gained empirical support so far, the plausibility of the former had been critically questioned by the discrete nature of neural firing
The optics of the human eye are extremely simple, the main imaging component being a single element lens which can change its strength by muscular control. There is only limited facility for correction of many of the aberrations which are normally corrected in good quality instrumental optical systems. Such a simple lens must inevitably have a significant amount of spherical aberration, which produces secondary lobes in the spread function. However, it has been found by experiment that light entering the pupil off-axis is less efficient in creating an image (the Stiles-Crawford effect), which has the effect of substantially reducing these unwanted side lobes. Also, the effects of diffraction limits can, with care, be used to partially compensate for the aberrations.