Fourier transform, as one of the most influential mathematical method in various scientific fields, plays an indispensable role in computational optics. It is a key technology that connects different modeling domains in field tracing and, especially, it also determines the computational efficiency. Advanced Fourier transform techniques, namely the semi-analytical Fourier transform and the homeomorphic Fourier transform, are included in the field tracing concept, and that brings the boost in the simulation efficiency.

Pic-Advanced Fourier Transform for Optics
Fig. 1: Comparison of three Fourier transform techniques based on a truncated spherical wave with varying NA. In computational optics, it is a crucial question to sample the phase of electromagnetic fields. For the standard fast Fourier transform (FFT), the required sampling points increase dramatically with the NA; by using the semi-analytical Fourier transform with the quadratic phase part handled analytically, the required sampling points remains small in medium NA cases; for high-NA cases, the homeomorphic Fourier transform becomes applicable and can then take over the job.
(rights: IAP)


Z. Wang, S. Zhang, F. Wyrowski, The semi-analytical fast Fourier transform, Proc. DGaO (2017).

F. Wyrowski, C. Hellmann, The geometric Fourier transform, Proc. DGaO (2017).

Z. Wang, S. Zhang, O. Baladron-Zorita, F. Wyrowski, Semi-analytical fast Fourier transform and its application to physical-optics modeling, Proc. SPIE (2018).

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