Fraccional Fourier transform in the case of an inclined image plane (2010)
The well-known Fresnel diffraction formula relates the distribution of complex amplitude of a wave in the object plane (input wave field) with the distribution of complex wave amplitude in the image plane (output wave field) when it comes to propagation in space free; This means that if the object and image planes are parallel to each other, the corresponding image system is said to be a linear invariant displacement system (LSI). This advantageous property is essential for the development of phase sensitive imaging techniques; however, if the image plane is inclined with respect to the incident beam, the effective propagation distance will change over the image plane, consequently the image system will not be invariant to displacement. In this article, an extension of the Fresnel diffraction formalism to the case of an inclined image plane using the Fourier transform of fractional order is proposed.