Fraccional Fourier transform in the case of an inclined image plane

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C O Torres
L Mattos
C Jiménez
Jaime Castillo Pérez
Y Torres


Fresnel diffraction, inclined image plane, fractional Fourier transform.


The well-known Fresnel integral relates a known complex wave defined in the object plane (the input wave field) to the observable complex wave (the output wave field) defined in the image plane after free-space propagation; this means that if the object and image plane are parallel to each other, corresponding imaging system is said to be linear-shift-invariant (LSI). This advantageous property was 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 vary over the image plane, consequently, the imaging system is not shiftinvariant. In this paper an extension of the theoretical formalism of Fresnel diffraction to the case of an inclined image plane is proposed using the fractional Fourier transform.

MSC: 33D15, 33D90, 33D60, 34M03,  62E15


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