Applications of fast algorithms for the numerical calculation of optical signal transforms

John J. Healy; John T. Sheridan

doi:10.1117/12.662446

25 April 2006 Applications of fast algorithms for the numerical calculation of optical signal transforms

John J. Healy, John T. Sheridan

Proceedings Volume 6187, Photon Management II; 618713 (2006) https://doi.org/10.1117/12.662446
Event: SPIE Photonics Europe, 2006, Strasbourg, France

Abstract

Any paraxial optical system which can be implemented using only thin lenses and propagation through free space or through sections of graded index (GRIN) media, belongs to the class of systems known as Quadratic Phase Systems (QPS). Given some input optical wave field, the output of any QPS can be described using the linear canonical transform (LCT), a unitary, additive, three-parameter class of linear integral transform first discovered in the 1970s. The terminology used in relation to the LCT is not at all consistent across the literature, and it is frequently called by other names, such as Quadratic-phase Integral and Generalized Fresnel Transform. In this paper, we examine a new, more flexible numerical implementation of the FLCT. This algorithm is similar to the Sande-Tukey FFT algorithm, and is of general radix. We demonstrate the savings possible in terms of required samples with the flexibility inherent in a general radix algorithm.

Citation Download Citation

John J. Healy and John T. Sheridan "Applications of fast algorithms for the numerical calculation of optical signal transforms", Proc. SPIE 6187, Photon Management II, 618713 (25 April 2006); https://doi.org/10.1117/12.662446

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