Department and Course Number CEG 428  Course Coordinator Abdul Ahad S. Awwal
Course Title Linear Optical Systems for Computer Engineers Total Credits 4

Catalog Description

Introduction to linear optical systems, transformation properties of optical systems, correlation, convolution, diffraction, applications related to optical computers, such as beam steering for optical interconnection, digital multiplication by analog convolution, and parallel optical algorithm for pattern search, neural network. Prerequisites : EE 321, 322.

Text Books and Other Source Materials

  1. J. D. Gaskill, Linear Systems, Fourier Transforms and Optics, John Wiley & Sons, Inc. New York, 1978, ISBN 0-471-29288-5.
  2. J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, 1996, ISBN 0-07-024254-2.
  3. Selected papers published in refereed journals such as Applied Optics, Optical Engineering.

Course Goals

The student should have learned the following:

  1. Complex representation of optical signals.
  2. Optical linear systems theory and point spread function
  3. correlation and convolution
  4. 1-D and 2-D Fourier transform and its properties
  5. Linear Optical filtering: amplitude filter, phase filter and complex filter
  6. Simulation of optical filtering using Matlab.
  7. Propagation of optical information
  8. Fourier transform using lenses
  9. Optical pattern recognition.
  10. Optical holography: recording and generation

The student should be able to apply the concepts above to the following:

  1. Manipulation of optical signals as complex quantities.
  2. 3-D representation and visualization of optical functions. Transformation of optical function. Mathematically manipulate expressions involving these functions.
  3. Harmonic decomposition of simple signals and its optical importance and/or interpretation.
  4. Optical impulse function or point spread function.
  5. Conditions for a linear shift invariant system.
  6. Complex exponentials as eigenfunctions
  7. Graphical and mathematical convolution, correlation of complex and complicated optical signals.
  8. Fourier transforms of real and complex signals and their optical representation.
  9. Important properties of optical Fourier transform and its relationship with geometrical optics.
  10. Analyze linear shift invariant system using Fourier transform technique.
  11. Linear optical filtering – effect of an amplitude, phase and complex filter.
  12. Optical techniques of extracting signal from signal plus noise.
  13. Sampling theorem and recovery of optical sampled signals.
  14. Signal detection using matched filter.
  15. Analyze propagation of light as a linear system phenomenon.
  16. Analyze light propagation under different boundary condition and different transmittance function.
  17. Analyze the coherent optical system using linear systems tools based on wave-optics.
  18. Analyze effect of a lens in an optical system, when the position of the input object is varied.
  19. Design and analysis of an optical information processing system such as phase-contrast microscopy.
  20. Design and analysis of a VanderLugt filter.
  21. Analysis of a joint Fourier transform correlator.
  22. Analysis of a phase only filter and complex matched.
  23. Implement optical correlators using Matlab.
  24. Optical techniques of recording and reconstruction of holograms.
  25. Computer simulation of a holographic memory.

Prerequisites by Topic

  1. Complex algebra.
  2. Impulse response.
  3. Linear system theory and convolution
  4. Discrete Fourier transform using Matlab.
  5. Fourier transform.
  6. Matlab tools.

Course Content

Wk

Topics

Read

1

Review of transforms and linear systems, Optical functions and representation

Gaskill – Ch 2-5

2

Optical linear system theory: Correlation and convolution

Gaskill – Ch. 6

3

Fourier transform and properties

Gaskill – Ch 7

4

Linear filtering applications: complex, amplitude and phase filter

Gaskill – Ch 8

5

2-D Fourier transforms, simulation using digital computers (2D FFT)

Gaskill – Ch 9; Goodman – Ch 2

6

Propagation of lasers: short distance (Fresnel) and long distance (Fraunhoffer)

Goodman – Ch 4

7-8

Optical information processing I: Fourier transform using lenses, pattern recognition algorithm

Goodman – Ch 5,8

9-10

Optical information processing II: optical holography, computer generated holograms.  Advanced topics in fiber optics.

Goodman – Ch 9, and notes

Laboratory Projects

There are projects for the course.  

Estimate CSAB Category Content

Core Advanced Core Advanced
Data Structures Concepts of PL 0
Algorithms 0.5 Comp Organization + Architecture 2.5
Software Design Other (Theory) 1.0

Oral and Written Communications

There are no oral presentations.  Students submit  projects along with a "ReadMe", a text file that highlights the design details as well as problems and defects in their implementation.

Social and Ethical Issues

None.

Theoretical Content

None.

Problem Analysis

The projects are about Optical Systems reduced in size  and sophistication to fit a 10-week course.  Detailed analyses of the requirements of the project are performed by the student before implementing them.

Solution Design

The projects are about a component of Optical Systems reduced in size and sophistication to fit a 10-week course.  Skeletal solutions of the project are given by the instructor at the conceptual level in the lectures, and also in source code files.  The student needs to design further details and implement them.