本課程詳細探討傅氏轉換之特性,著重物理意義之闡釋,以能靈活處理頻譜問題為目標,並將二維系統與二維傅氏轉換的觀念應用於空間中光波傳播,繞射,成像及影像處理問題。討論主題如下：
I. Fourier transform and related topics:
1. Definition, basic properties, and theorems of Fourier transforms
2. Measure of width, the uncertainty relation, the central limit theorem
3. Linear filters and transfer functions, sampling theory, DFT and FFT
4. Hilbert transform and other transforms
5. Two-dimensional Fourier transforms and two-dimensional systems
6. Reconstruction from projections, Abel transform and Radon transform
II. Fourier optics:
1. Scalar diffraction theory, angular spectrum of plane waves
2. Fresnel and Fraunhofer diffraction
3. Fourier transforming and imaging properties of lenses
4. Frequency analysis of optical imaging systems
5.Spatial filtering and optical information processing
6. Introduction to holography (or wavefront-reconstruction imaging)