Abstract
The methods of dihedral Fourier analysis are introduced and applied to describe the data-analytic properties of rotators, gyrators, separable fractional Fourier, and shearing operators in phase-space. The methods are also applied to introduce the notion of dihedral field orbits in phase-space as experimental designs or protocols for the statistical study of optical information, and to describe and classify these operators according to their response to field (dihedral) rotations and reversals.
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