Advanced Fourier Transform for Optics

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. 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. Picture: IAP, F.Wyrowski

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.

Publications Expand entry

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).