Fourier Transforms
March 22nd, 2005 | No Comments »My son Alexander contributes that of the three primary Fourier transforms that I have claimed represent the image forming mechanisms used by the eye only the long wavelength transform at the fovea represents a “true” FT as it is detected on the actual (or “fundamental”) Fourier plane. The other two (exact mid-band and short wavelength) do not lie on this plane and therefore are somewhat “imagey” representing (due to their extension in space) characteristics of both a Fourier and image plane. The fact that the foveal long wavelength transform represents the “purest” FT is the reason why the image from this region contains the greatest outline detail (the “Marr” sketch). Image information from the outlying “less pure” FT regions would naturally be “smudged” - as is in fact observed phenomenologically in visual imagery. We are studying the connection of this predicted behavior with the geometrically determined structure of the retina.
One must always keep in mind that wavelength falling on the retina is determined by the refractive properties of the structure of the eye, i.e., before interacting with the retina. Retinal receptors themselves are only responsive to (”tuned” to) three cardinal wavelengths.(as described) from whence the image is computed. Detectors on the retina surface then compute (via the giant dipole mechanism proposed) light intensity (amplitude), and phase (that encodes directionality). The aspect of encoding directionality can also seemingly be used to interpolate wavelengths falling between the three cardinal points as the position where individual wavelengths fall is known (fixed by the refractive properties of the eye).
