ECE 665: Fourier Optics and Holography

Spring, 2004

Preliminary Course Description and Syllabus

4 December 2003

Instructor:  : Dr. Thomas Fowler, Adjunct Professor

Office:             235, S&T II, by appointment

                        703-610-2944

                        email: tfowler@mitretek.org or tfowler@gmu.edu

This course is offered at Ft. Belvoir in the Spring of 2004.

COURSE OBJECTIVE: To provide an understanding of optical systems for processing temporal signals as well as images. Topics include use of coherent optical systems for image processing and pattern recognition, principles of holography, and acousto-optic systems for radar-signal-processing optical computers.  Course is based on use of Fourier analysis in two dimensions to understand the behavior of optical systems.  We will start with a review of one dimensional Fourier analysis, as many students may have forgotten some of this material.  Then we will move on to two-dimensional Fourier analysis, followed by its application to optical systems analysis.

DESIRED BACKGROUND: Electromagnetics, Semiconductor Devices, Basic Optics, Photonics, Fourier Analysis in one dimension, as covered in undergraduate math, physics, or engineering courses.

TEXT: Introduction to Fourier Optics, Second Edition, Joseph W. Goodman, McGraw-Hill, 1996.  Be sure to copy the errata file for the text from the course web page!

OTHER REFERENCES.

 

For some material, students may also wish to refer to the text used for ECE 565, Saleh & Teich, Fundamentals of Photonics.

 

Reynolds, et. al., The New Physical Optics Notebook: Tutorials in Fourier Optics, SPIE, 1989.

 

G. Fowles, Introduction to Modern Optics, 2nd edition, Dover, 1989.

 

Kock, Lasers and Holography, 2nd edition, Dover, 1981.

http://www.vislab.usyd.edu.au/CP3/Four456.html.  Includes programs for 2D Fourier transform. 

 

Other material to be added to this list later:
Lecture 1 Review of one dimensional Fourier analysis in PPT or SXI.

 

 

COURSE TOPICS:

·        Two-dimensional Fourier analysis

·        Diffraction theory

·        Fresnel and Fraunhofer approximations

·        Fourier transforming properties of lenses

·        Transfer functions

·        Image formation with coherent and incoherent light

·        Transform functions of imaging systems

·        Optical data processing

·        Holography

 

ABBREVIATED SYLLABUS:

Week 1:           Background: Review of one-dimensional Fourier analysis.  Refer to your undergraduate texts on this subject.

Week 2:           Two-dimensional Fourier analysis.  Linear systems and Fourier analysis.  Two-dimensional sampling theory.  (Goodman, ch. 2)

Weeks 3-4:      Scalar diffraction theory.  Helmholtz equation, Green's theorem.  Kirchoff formulation of diffraction.  Rayleigh-Sommerfield formulation of diffraction.  Non-monochromatic waves.  Diffraction at boundaries.  Angular spectrum of plane waves.  (Goodman, ch. 3)

Weeks 5-6:      Fresnel and Fraunhofer diffraction.  Background.  Fresnel and Fraunhofer approximations and examples.  (Goodman, ch. 4)

Week 7:           Transfer functions and wave-optics analysis of coherent optical systems.  Thin lenses and Fourier transforming properties of lenses.  Image formation.  Analysis of complex coherent optical systems. (Goodman, ch. 5)

Weeks 8-9:      Frequency analysis of optical imaging systems.  Frequency response for coherent and incoherent imaging.  Aberrations and their effect on frequency response.  Comparison of incoherent and coherent imaging.  Resolution beyond classical limit. (Goodman, ch. 6)

Week 10:         Wavefront modulation.  Photographic film.  Liquid crystals and other modulators.  Diffractive optical elements.  (Goodman, ch. 7)

Week 11:         Analog optical information processing.  Background.  Incoherent and coherent image processing systems.  (Goodman, ch. 8, sec. 1-3 only)

Weeks 12-13:  Holography.  Wavefront reconstruction problem.  Gabor and Leith-Upatnieks holograms.  Thick holograms.  Recording materials.  Computer-generated holograms.  Incoherent light.  Applications.

 

GRADING: 20% homework, 40% midterm exams, 40% final exam.

Syllabus

ECE 665—Fourier Optics and Holography

Spring, 2004

 

Week

Topics

Text Reading

26 January

•         Review of one-dimensional Fourier analysis

Refer to your undergraduate books on this subject

2 February

•         Analysis of two-dimensional signals and systems

•         Fourier analysis in two dimensions

•         Localization

•          

Goodman, ch. 2, sec. 2.1-2.2

9 February

•         Analysis of two-dimensional signals and systems (continued)

•         Linear systems and Fourier analysis

•         Two-dimensional sampling theory

Goodman, ch. 2, sec. 2.3-2.4

 

16 February

•         Foundations of Scalar Diffraction Theory

•         Introduction

•         Mathematical preliminaries

•         Kirchoff and Rayleigh-Sommerfield formulations

Goodman, ch. 3, sec. 3.1-3.5

23 February

•         Foundations of Scalar Diffraction Theory (continued)

•         Comparison of Kirchoff and Rayleigh-Sommerfield theories

•         Huygens-Fresnel principle

•         Non-monochromatic waves

•         Diffraction at boundaries

•         Angular spectrum of plane waves

Goodman, ch. 3, sec. 3.6-3.10

1 March

•         Fresnel and Fraunhofer Diffraction

•         Background

•         Fresnel approximation

•         Fraunhofer approximation

Goodman, ch. 4, sec. 4.1-4.3

8 March

*** Spring Recess – No Class ***

 

15 March

•         Fresnel and Fraunhofer Diffraction (continued)

•         Examples of Fraunhofer diffraction patterns

•         Examples of Fresnel diffraction calculations

•         Midterm Exam

Goodman ch. 4, sec. 4.4-4.5

22 March

•         Wave-optics Analysis of Coherent Optical Systems

•         Thin lens as phase transformation

•         Fourier transforming properties of lenses

•         Image formation: monochromatic illumination

•         Analysis of complex coherent optical systems

Goodman, ch. 5, sec. 5.1-5.4

29 March

•         Transfer Functions and Frequency Analysis of Optical Imaging Systems

•         Generalized treatment of imaging systems

•         Amplitude transfer function

•         Frequency response for coherent and incoherent imaging

Goodman, ch. 6, sec. 6.1-6.3

5 April

•         Transfer Functions and Frequency Analysis of Optical Imaging Systems (continued)

•         Aberrations and their effect on frequency response

•         Comparison of coherent and incoherent imaging

•         Resolution beyond classical diffraction limit

Goodman, ch. 6, sec. 6.4-6.6

12 April

•         Wavefront modulation

•         Photographic film

•         Liquid crystals and other modulators

•         Diffractive optical elements

Goodman, ch. 7, sec. 7.1-7.3

Reference: Saleh & Teich, ch. 6

19 April

•         Analog Optical Information Processing

•         Historical background

•         Incoherent image processing systems

•         Coherent optical image processing systems

Goodman, ch. 8. sec. 8.1-8.3

26 April

•         Holography

•         Introduction

•         Wavefront reconstruction problem

•         Gabor and Leith-Upatnieks holograms

•         Image locations and magnification

•         Different types of holograms

Goodman, ch. 9, sec. 9.1-9.6

3 May

•         Holography (continued)

•         Thick holograms

•         Recording materials

•         Computer-generated holograms

•         Degradation of holographic images

•         Holography with spatially incoherent light

•         Applications

Goodman, ch. 9, sec. 9.7-9.12