The semi-analytical Fast Fourier Transform

Z. Wang, S. Zhang, F. Wyrowski
Institut für Angewandte Physik, Friedrich-Schiller-Universität Jena
wangzongzhaotc@gmail.com
 
Physical optics modeling requires frequent shifting from the space into the k domain and vice versa. This is achieved by performing a Fourier transform of the electric and magnetic field components. Therefore, the Fast Fourier transform (FFT) algorithm constitutes the backbone for fast physical optics modeling. The numerical effort of the FFT technique is approximately linear with the required number of sampling points of the complex amplitude of a field component. However, in optics we often deal with field components which possess a strong wavefront phase, whose complex sampling leads to a huge numerical effort even in the case of the FFT. We propose a way to handle the Fourier transform which does not require the sampling of second-order polynomial phase terms, but rather treats them analytically. This is achieved by replacing the FFT of the fully sampled field by two FFTs of complex functions which require significantly fewer sampling points. We present the theory of the semi-analytical FFT alongside several examples to demonstrate the great potential of this approach.
Keywords:
Theoretische Grundlagen, Beugungstheorie, Optische Systeme
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118. Tagung, Poster: P2