<title>Diffractive centrosymmetric 3D-transmission phase gratings positioned at the image plane of optical systems transform lightlike 4D-WORLD as tunable resonators into spectral metrics...</title>

Abstract

Diffractive 3D phase gratings of spherical scatterers dense in hexagonal packing geometry represent adaptively tunable 4D-spatiotemporal filters with trichromatic resonance in visible spectrum. They are described in the (lambda) - chromatic and the reciprocal (nu) -aspects by reciprocal geometric translations of the lightlike Pythagoras theorem, and by the direction cosine for double cones. The most elementary resonance condition in the lightlike Pythagoras theorem is given by the transformation of the grating constants g<SUB>x</SUB>, g<SUB>y</SUB>, g<SUB>z</SUB> of the hexagonal 3D grating to (lambda) <SUB>h1h2h3</SUB> equals (lambda) <SUB>111</SUB> with cos (alpha) equals 0.5. Through normalization of the chromaticity in the von Laue-interferences to (lambda) <SUB>111</SUB>, the (nu) (lambda) equals (lambda) <SUB>h1h2h3</SUB>/(lambda) <SUB>111</SUB>-factor of phase velocity becomes the crucial resonance factor, the 'regulating device' of the spatiotemporal interaction between 3D grating and light, space and time. In the reciprocal space equal/unequal weights and times in spectral metrics result at positions of interference maxima defined by hyperbolas and circles. A database becomes built up by optical interference for trichromatic image preprocessing, motion detection in vector space, multiple range data analysis, patchwide multiple correlations in the spatial frequency spectrum, etc.