Related Experiment Video
Updated: Oct 17, 2025

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
Published on: October 28, 2018
Freeform surface for light shaping by iterative design via Fourier domain
Abstract:
We extend our previous work [Yang et al., Opt. Express29, 3621 (2021)10.1364/OE.415649] and propose an iterative algorithm to design a freeform surface for far-field light shaping. The algorithm alternately performs a wavefront phase design step and a freeform surface construction step. The smooth wavefront phase is designed by the mapping-type Fourier pair synthesis method, and the freeform surface is constructed by using the obtained wavefront phase. The algorithm provides a solid approach that ensures the introduction of the required wavefront phase manipulation for light shaping. Moreover, the related physical effects such as the Fresnel effect and polarization effect are included in the algorithm. We demonstrate the flexibility of the algorithm by examples.
Related Concept Videos
Trigonometric Fourier series
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
Continuous -time Fourier Transform
Convergence of Fourier Series
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Properties of Fourier Transform II
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
Properties of Fourier Transform I
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
Parseval's Theorem for Fourier transform
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a...

