Fractional Fourier transform of coherent optical systems application

• Carlos Jiménez Ruiz Universidad de la Guajira-Colombia
• Jaime Castillo Pérez Universidad de la Guajira-Colombia
• Susana Salinas de Romero Universidad del Zulia-Venezuela

Palabras clave: Fractional Fourier transform, optical systems, signal processing

Resumen

In 1980 Namias presented the Fourier transform of Fractional order as a generalization of the well known Fourier transform, establishing the mathematic character of this with its set of theorems and properties. Initially he used it to solve problems with the harmonic oscillator quantum mechanics. Recently, the Fourier Optics area has expanded with new contributions related to non conventional transformation, the so called fractional ones. For example, it has been proposed the applications of fractional Fourier transforms (FFT), for spatially variant filtering, characters recognition, encryption, water marks, implementation of neural networks, etc. In this work, we present a mathematic development of continuous fractional Fourier transform. It is applied to optical systems coherent to the signal processing.