Develop the fundamental understanding of how Fourier theory is used to explain a range of phenomena in optical physics and how Fourier techniques apply to the analysis and synthesis of different optical systems.

Prerequisites

• Familiarity with Fourier analysis or appropriate graduate level

Textbooks

• J. W. Goodman, Introduction to Fourier Optics, 2nd Ed.
• A. Papoulis, Systems and transforms with applications in optics
• R. Bracewell, The Fourier transform and its applications
• H. Stark, Applications of optical Fourier transforms

Topics

• Fourier series
• Fourier integral transformation

• Fourier transform theorems
• 2D transforms
• Hankel transforms
• Higher dimensionality transforms
• Sampling theorem

• Signal analysis
• Linear systems
• Spectral analysis
• Asymptotic expansion of Fourier transforms
• Wave propagation and angular spectrum filtering

• Thin spherical lens as a pure phase transformation
• Image formation – a system approach
• Coherent imaging systems / light focusing / Fresnel zone plates
• Resolution criteria / coherent vs incoherent imaging
• Incoherent optical processing / optical computing

• Phase contrast imaging
• Filter synthesis
• Joint transform correlator
• Scale and rotation-invariant optical processing
• Synthetic aperture imaging
• Holography
• Wavelet transforms