Montana State University

Department of Electrical and Computer Engineering

EE581 -- Fourier Optics and Imaging Theory

 Fall 2011


lens and jinc function

Class is Monday, Wednesday, Friday 11:00-11:50 in EPS 110.

The professor this term is David Dickensheets, davidd@ee.montana.edu, (406) 994-7874, 530 Cobleigh Hall.

David's Office Hours are Tues. 10:00-12:00.

What is Fourier Optics?

The way your camera lens collects and focuses light is governed by the physics of diffraction. Under many situations we can cast this diffraction problem in the form of a Fourier integral. Furthermore, since optical systems tend to be linear over a large range of light intensities, we can take advantage of all that we know about linear systems theory and Fourier transforms to analyze and better understand optical systems. Concepts such as convolution and transfer functions that electrical engineers are accustomed to applying to electrical systems are central to the understanding of optical imaging systems as well. This systems-view of the diffraction problem has come to be known as "Fourier optics", and the concepts and tools covered in this class find wide application in optical instrument design and system analysis.

Announcements

Welcome to EE581! 


Handouts

Reading Assignments

To be completed prior to lecture on the indicated dates

Lecture Date Reading Assignment Lecture Topic
8/29   Introduction, Review of Fourier Transforms
8/31 Chapter 1 and Chapter 2, sect. 2.1 Fourier Transform properties review
9/2 2.1,2.2  2D Fourier transforms; Fourier Bessel Transforms
9/5No Class - Labor Day
9/7 2.3,2.4 Linear Shift Invariant Systems; 2D sampling
9/9 Chapter 3:  3.1 Huygen's principle; scalar wave equation; monochromatic waves
9/12 3.2,3.3 Green's function applied to diffraction
9/14 3.4,3.5,3.6 Kirchoff Diffraction
9/16 3.7,3.8,3.9 Rayleigh Sommerfeld Diffraction
9/19 3.10 Angular Spectrum of Plane Waves, Numerical Techniques
9/21 4.1,4.2 Fresnel Diffraction
9/23 4.3 Fresnel and Fraunhofer Diffraction
9/26 4.3 Fraunhofer Diffraction of rectangular and circular apertures
9/28 4.4 Far field diffraction from phase gratings
9/30 4.4 Periodic apertures using Fourier series
10/3catch up
10/5 4.5 Fresnel diffraction - rectangular symmetry; paraxial transfer function
10/7 4.5 Fresnel diffraction example with circular symmetry
10/10 4.5 Talbot planes
10/12 5.1,5.2 Young's interferometer demo; Lenses as a phase transformation
10/14no class meeting
10/17 Midterm #1 (first 4 chapters of Goodman)
10/19 5.2,5.3Fourier transforming properties of lenses
10/21 5.3image formation as a convolution
10/24 5.3more on image formation
10/265.3,5.4 (operator notation optional)more examples of image formation, more complex systems
10/28  6.1, 6.2 Geometrical Optics Review, first look at ATF
10/31 6.1, 6.2 Diffraction Limits for maximum resolvable frequency: Abbe's limit, exit pupil diffraction and the Amplitude Transfer Function
11/2 6.1, 6.2 Temporal and Spatial Coherence; Correlation and Coherence of Functions
11/4 6.3 Derivation of system response for coherent and incoherent cases
11/7 6.3 Optical Transfer Function and Modulation Transfer Function
11/9  6.4  Examples comparing OTF and ATF for imaging systems; physical view of OTF; Aberrated systems
11/11 No Class - Veterans' Day
11/14 6.5, 6.6 Wrap-up of Frequency Domain Analysis
11/16 catch up
11/18 Midterm #2 (chapters 5 and 6 of Goodman)
11/21  7.1-7.2 Introduction to wavefront modulation; LCD spatial light modulators
11/23, 11/25No Class - Thanksgiving Holiday
11/28   LCD SLMs
11/30   MEMS display technologies
12/2    Diffractive Optics
12/5   Diffractive optics wrap-up
12/7
  synthetic aperture systems
12/9 synthetic aperture systems
12/15 8:00-9:50 am  Final Exam

Problem Sets

set # Due Date Problems Solutions                   
1 9/7 2-1, 2-2, 2-3, 2-5 handed out in class
2 9/14 2-6, 2-8, 2-11 handed out in class
3 9/23 3-2,3-5,3-7 handed out in class
4 9/28

1D angular spectrum propagation

my version of 1D code in Matlab: oneDdiffract.m

simple Rayleigh Sommerfeld integral calculation for reference: RSintegral.m  RSkernel.m

 
 5 10/5 2D angular spectrum propagation  
 6 10/10 Fresnel and Fraunhofer diffraction homework  handed out in class
 7 10/26 5-2, 5-3  handed out in class
8 11/2 5-10, 5-11, 5-14  handed out in class
9 11/14 6-2, 6-4, 6-7  handed out in class
10 11/14 6-10, 6-13, 6-15  handed out in class
11  12/2 psf and OTF for aberrated systems

 

Demonstration Schedule

Date Group Demo Title 
9/30
B 2D FFT and Fourier domain filtering
10/7 C Spot of Arago
10/14 A Young's two pinhole interferometer
10/21 D Talbot Self Imaging
10/28 C Acousto-optic Modulator
11/4 B Optical Fourier Transforms
11/30 A Computer Generated Hologram 1xN Beam Fan-Out
12/2 D

 

 

Links


This page is maintained by David Dickensheets.