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The geometric Fourier transform |
F. Wyrowski1, C. Hellmann2
1Institut für Angewandte Physik, Friedrich-Schiller-Universität Jena; 2Wyrowski Photonics UG
frank.wyrowski@uni-jena.de |
The Fourier transform of the electromagnetic field components in different planes of a system is a frequent operation in physical optics modeling which connects the space and k domains. An important example is the shift from the space to the k domain in the exit pupil of a lens system to obtain the PSF by, for example, the Debye integral, which we show to be just a special case of a more general theoretical approach: the geometric Fourier transform. We introduce the so-called geometric zone of a field, in which the Fourier transform can be obtained without integration and, in conclusion, in a very numerically efficient manner. We prove that, in its geometric zone, the physical optics propagation of an electromagnetic field can be performed, without tangible loss of accuracy, by geometric field propagation. If we propagate between the geometric and the focal region of a field, then the well-known far-field and Debye integrals are recovered as special cases. The concept of a geometric Fourier transform provides a solid theoretical fundament and practical algorithm for the inclusion of geometric techniques in a physical optics treatment of electromagnetic fields in homogeneous media. |
Keywords:
Theoretische Grundlagen, Beugungstheorie, Optische Systeme |
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