0000000000568087

AUTHOR

Felipe Mateos

Fractional Fourier transforms, symmetrical lens systems, and their cardinal planes

We study the relation between optical lens systems that perform a fractional Fourier transform (FRFT) with the geometrical cardinal planes. We demonstrate that lens systems symmetrical with respect to the central plane provide an exact FRFT link between the input and output planes. Moreover, we show that the fractional order of the transform has real values between 0 and 2 when light propagation is produced between principal planes and antiprincipal planes, respectively. Finally, we use this new point of view to design an optical lens system that provides FRFTs with variable fractional order in the range (0,2) without moving the input and output planes.

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Teaching Fourier optics through ray matrices

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics prov…

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