OPTI 512R

Linear Systems, Fourier Transforms (3 units). Mathematical background, convolution, the Fourier transform, linear filtering and sampling, two-dimensional operations, diffraction, image formation. Prerequisites: MATH 223, PHYS 142 & 241.

Lectures:
T/TH 12:30 to 1:45 | Room 305

Instructor:
Professor J. Scott Tyo
Meinel 623 | 626-8183
Email: tyo@optics.arizona.edu

Office Hours:
Monday 10:30 – 11:30, Thursday 10:00 – 11:00
On-Line Wednesday 8:30pm – 9:30pm

Topics Covered:

Mathematical Background and Linear Systems Theory
  1. Complex numbers
  2. Special functions, the impulse function and functions based on the impulse
  3. Harmonic Analysis and the Fourier Series, truncated Fourier series
  4. Operators and Linear Shift-Invariant Systems
  5. Convolution and its properties
  6. Fourier Transform and its properties
  7. Convolution Theorem and other special theorems for the Fourier transform (Rayleigh energy, moment, Wiener-Khinchine)
  8. Two-dimensional functions, Fourier transforms, and convolution. The Hankel transform and the Radon transform.
Signal Processing and Sampling
  1. Filters: Low Pass, High Pass, Band Pass; Amplitude and Phase Filters
  2. Signal processing, noise reduction, equalization
  3. Sampling and Reconstruction; Aliasing
  4. Discrete Fourier Transform and Discrete Convolution
Linear Systems applied to Electromagnetic Wave Propagation and Diffraction
  1. Plane waves, the plane wave spectrum
  2. Gaussian beam propagation
  3. Spherical waves and Fraunhofer diffraction
  4. Fresnel Diffraction, the Fresnel transform
  5. Fresnel diffraction from circular apertures, Fresnel zone plates
Imaging Systems and Fourier Optics
  1. Fresnel diffraction from Lenses and Fourier transforming properties of lenses
  2. Diffraction limited imaging systems
  3. Performance of optical imaging systems with coherent and incoherent illumination
  4. Optical transfer function, Modulation transfer function, Point Spread Function
  5. Impact of Aberrations
Recommended Textbooks:
Gaskill, Jack D. (). Linear Systems, Fourier Transforms, and Optics. Wiley Interscience

Goodman, Joseph W. (). Introduction to Fourier Optics. Roberts & Company.