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Proceedings Paper

Analytical and numerical analysis of ABCD systems
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Paper Abstract

The numerical simulation of linear, lossless, paraxial, quadratic phase systems using the linear canonical transform (LCT) presents significant challenges due to the high sampling rate associated with the chirp function in the kernel. However, such simulations are significant for the design and analysis of optical systems and other signal processing purposes. Furthermore, such systems can be optically implemented using only lenses and free space. In this paper, we implement a recently proposed technique for calculating the discrete LCT. We review the existing literature on sampling the linear canonical transform. We apply a space-spatial frequency representation of the signal, the Wigner-Ville distribution function (WDF), and the space bandwidth product (SBP) of the signal (or system) to identify suitable sampling rates for simulation. We apply this method to simulate the effect on a 1D rectangular waveform of the fractional Fourier transform (FRT). The numerical results are compared with analytical expressions for the same system.

Paper Details

Date Published: 25 April 2008
PDF: 8 pages
Proc. SPIE 6994, Photon Management III, 699402 (25 April 2008); doi: 10.1117/12.780306
Show Author Affiliations
John J. Healy, Univ. College Dublin (Ireland)
John T. Sheridan, Univ. College Dublin (Ireland)


Published in SPIE Proceedings Vol. 6994:
Photon Management III
John T. Sheridan; Frank Wyrowski, Editor(s)

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