Abstract

BACKGROUND
In the specification of visual targets and their transmission through the eye's optics to form retinal images, the spatial distribution of energy and its Fourier transform, the spatial-frequency spectrum, are equivalent, so long as linearity constraints are obeyed. The power spectrum, in which phase has been discarded, is an insufficient descriptor; it does not enable the original object to be reconstituted.
PROCEDURE
Not so well known, and explored here, are joint representations in the space and spatial-frequency dimensions. Their properties are outlined for some sample targets and for transforms of the Gabor, Difference-of-Gaussians and Wigner types. A related approach is one in which other kernel functions, such as the Gaussian or its derivative, are substituted for the cosines in the Fourier transform; here also graphs can be generated which jointly display properties both of the target and of its point-by-point representation in a size-tuned domain.
APPLICATIONS
This kind of study has application in matching the performance characteristics of optical devices to the eye's, in optical superresolution, and in the analysis of the demands placed on neural processing in, for example, visual hyperacuity.

Links

Publisher Full Text

Authors

Westheimer G

Institution

Division of Neurobiology, University of California, Berkeley, CA, USA. gwestheimer@berkeley.edu

Source

Ophthalmic & physiological optics : the journal of the British College of Ophthalmic Opticians (Optometrists) 32:4 2012 Jul pg 271-81

MeSH

Fourier Analysis
Humans
Models, Biological
Optical Processes
Photic Stimulation
Psychophysics
Visual Acuity

Pub Type(s)

Journal Article
Review

Language

eng

PubMed ID

22697214