Prerequisite
- Graduate standing or consent of instructor
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 List
Introduction to Signals and Linear Systems
1. Discrete Systems
a.Matrix description of systems. Unitary and Hermitian systems. Modes
b.Example. Polarization device
c.Example. Modes of an optical resonator
d.Example. Coupled modes of a waveguide
2. Continuous 1D Systems (Temporal Systems)
a.Integral transforms. Shift-invariant systems
b.1D Fourier transform and its properties
c.Linear shift-invariant systems. Impulse response function. Convolution. Transfer function
d.Example: Propagation of an optical pulse in a dispersive medium
3. Continuous 2D Systems (Spatial Systems)
a.2D Fourier transforms and its properties
b.Projection-slice theorem. Application to CT tomography
c.2D linear systems. Point spread function. Transfer functions. Spatial filters
4. Coherent Optical Systems
a.Expansion of arbitrary waves in terms of plane waves. Angular spectrum
