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Semi-analytical Fourier transform and its application to physical-optics modelling
Author(s): Zongzhao Wang; Site Zhang; Olga Baladron-Zorita; Frank Wyrowski
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Paper Abstract

The Fast Fourier Transform (FFT) algorithm makes up the backbone of fast physical optics modeling. Its nu- merical effort, approximately linear on the sample number of the function to be transformed, already constitutes a huge improvement on the original Discrete Fourier Transform (whose own numerical effort depends quadrati- cally on the sample number). However, even this orders-of-magnitude improvement in the number of operations required can turn out to fall short in optics, where the tendency is to work with field components that present strong wavefront phases: this translates, as per the Nyquist-Shannon sampling theorem, into a gigantic sample number. So much so, in fact, that even with the reduced effort of the FFT, the operation becomes impractica- ble. Finding a workaround that allows us to evade, at least in part, the stringent sampling requirements of the Nyquist-Shannon theorem is then fundamental for the practical feasibility of the Fourier transform in optics. In this work we propose, precisely, a way to tackle the Fourier transform that eschews the sampling of second-order polynomial phase terms, handling them analytically instead: it is for this reason that we refer to this method as the “semi-analytical Fourier transform”. We present here the theory behind this concept and show the algorithm in action at several examples which serve to illustrate the vast potential of this approach.

Paper Details

Date Published: 18 June 2018
PDF: 8 pages
Proc. SPIE 10694, Computational Optics II, 106940O (18 June 2018); doi: 10.1117/12.2315776
Show Author Affiliations
Zongzhao Wang, Friedrich-Schiller-Univ. Jena (Germany)
Wyrowski Photonics UG (Germany)
Site Zhang, Friedrich-Schiller-Univ. Jena (Germany)
LightTrans International UG (Germany)
Olga Baladron-Zorita, Friedrich-Schiller-Univ. Jena (Germany)
LightTrans International UG (Germany)
Frank Wyrowski, Friedrich-Schiller-Univ. Jena (Germany)


Published in SPIE Proceedings Vol. 10694:
Computational Optics II
Daniel G. Smith; Frank Wyrowski; Andreas Erdmann, Editor(s)

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