Analytical and numerical analysis of ABCD systems

John J. Healy; John T. Sheridan

doi:10.1117/12.780306

25 April 2008 Analytical and numerical analysis of ABCD systems

John J. Healy, John T. Sheridan

Proceedings Volume 6994, Photon Management III; 699402 (2008) https://doi.org/10.1117/12.780306
Event: SPIE Photonics Europe, 2008, Strasbourg, France

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.

Citation Download Citation

John J. Healy and John T. Sheridan "Analytical and numerical analysis of ABCD systems", Proc. SPIE 6994, Photon Management III, 699402 (25 April 2008); https://doi.org/10.1117/12.780306

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