Fourier transforms of fractional order and their optical interpretation
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Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a=1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Fractional Fourier transforms can extend the range of spatial filtering operations.
Gradient index optics
Signal filtering and prediction
Quadratic graded index media
Spatial filtering operations