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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 1, Iss. 7 — Jul. 1, 1984
  • pp: 775–782

Physical limits of acuity and hyperacuity

Wilson S. Geisler  »View Author Affiliations

JOSA A, Vol. 1, Issue 7, pp. 775-782 (1984)

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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 −¼ power of spot intensity, but vernier acuity and separation discrimination vary in proportion to the −½ 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.

© 1984 Optical Society of America

Original Manuscript: October 26, 1983
Manuscript Accepted: March 13, 1984
Published: July 1, 1984

Wilson S. Geisler, "Physical limits of acuity and hyperacuity," J. Opt. Soc. Am. A 1, 775-782 (1984)

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  35. Figures 5 and 7 show, for the present ideal detector, that two-point resolution follows an inverse fourth-root law and that two-point separation discrimination and vernier acuity follow an inverse square-root law. It will be proved in a subsequent paper that these relations are not true just for point sources but hold for essentially arbitrarily shaped stimuli. Thus, for any stimulus shape, the measurement of resolution and some hyperacuity as a function of luminance will provide a strong, parameter-free test of the quantum-fluctuations hypothesis.

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