EE581 -- Fourier Optics and Imaging Theory
Class is Monday, Wednesday, Friday 11:00-11:50 in EPS 110.
The professor this term is David Dickensheets, [email protected], (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
- Course syllabus (PDF)
- Fourier Transform Relationships (PDF)
- Talbot's Facts relating to Optical Science in December 1836 Philosophical Magazine (pdf)
- Cardinal planes of a paraxial imaging system (pdf)
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Lecture Date
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Reading Assignment
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Lecture Topic
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8/29
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Introduction, Review of Fourier Transforms
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8/31
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Chapter 1 and Chapter 2, sect. 2.1
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Fourier Transform properties review
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9/2
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2.1,2.2
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2D Fourier transforms; Fourier Bessel Transforms
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9/5
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No Class - Labor Day
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9/7
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2.3,2.4
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Linear Shift Invariant Systems; 2D sampling
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9/9
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Chapter 3: 3.1
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Huygen's principle; scalar wave equation; monochromatic waves
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9/12
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3.2,3.3
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Green's function applied to diffraction
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9/14
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3.4,3.5,3.6
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Kirchoff Diffraction
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9/16
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3.7,3.8,3.9
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Rayleigh Sommerfeld Diffraction
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9/19
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3.10
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Angular Spectrum of Plane Waves, Numerical Techniques
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9/21
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4.1,4.2
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Fresnel Diffraction
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9/23
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4.3
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Fresnel and Fraunhofer Diffraction
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9/26
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4.3
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Fraunhofer Diffraction of rectangular and circular apertures
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9/28
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4.4
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Far field diffraction from phase gratings
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9/30
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4.4
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Periodic apertures using Fourier series
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10/3
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catch up
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10/5
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4.5
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Fresnel diffraction - rectangular symmetry; paraxial transfer function
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10/7
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4.5
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Fresnel diffraction example with circular symmetry
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10/10
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4.5
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Talbot planes
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10/12
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5.1,5.2
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Young's interferometer demo; Lenses as a phase transformation
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10/14
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no class meeting
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10/17
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Midterm #1 (first 4 chapters of Goodman)
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10/19
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5.2,5.3
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Fourier transforming properties of lenses
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10/21
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5.3
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image formation as a convolution
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10/24
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5.3
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more on image formation
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10/26
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5.3,5.4 (operator notation optional)
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more examples of image formation, more complex systems
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10/28
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6.1, 6.2
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Geometrical Optics Review, first look at ATF
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10/31
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6.1, 6.2
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Diffraction Limits for maximum resolvable frequency: Abbe's limit, exit pupil diffraction
and the Amplitude Transfer Function
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11/2
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6.1, 6.2
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Temporal and Spatial Coherence; Correlation and Coherence of Functions
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11/4
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6.3
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Derivation of system response for coherent and incoherent cases
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11/7
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6.3
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Optical Transfer Function and Modulation Transfer Function
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11/9
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6.4
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Examples comparing OTF and ATF for imaging systems; physical view of OTF; Aberrated
systems
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11/11
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No Class - Veterans' Day
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11/14
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6.5, 6.6
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Wrap-up of Frequency Domain Analysis
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11/16
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catch up
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11/18
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Midterm #2 (chapters 5 and 6 of Goodman)
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11/21
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7.1-7.2
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Introduction to wavefront modulation; LCD spatial light modulators
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11/23, 11/25
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No Class - Thanksgiving Holiday
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11/28
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LCD SLMs
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11/30
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MEMS display technologies
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12/2
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Diffractive Optics
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12/5
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Diffractive optics wrap-up
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12/7
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synthetic aperture systems
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12/9
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synthetic aperture systems
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12/15
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8:00-9:50 am Final Exam
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set #
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Due Date
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Problems
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Solutions
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|---|---|---|---|
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1
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9/7
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2-1, 2-2, 2-3, 2-5
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handed out in class
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2
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9/14
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2-6, 2-8, 2-11
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handed out in class
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3
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9/23
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3-2,3-5,3-7
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handed out in class
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4
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9/28
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1D angular spectrum propagation my version of 1D code in Matlab: oneDdiffract.m simple Rayleigh Sommerfeld integral calculation for reference:RSintegral.m RSkernel.m |
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5
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10/5
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6
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10/10
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handed out in class
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7
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10/26
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5-2, 5-3
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handed out in class
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8
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11/2
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5-10, 5-11, 5-14
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handed out in class
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9
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11/14
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6-2, 6-4, 6-7
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handed out in class
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10
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11/14
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6-10, 6-13, 6-15
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handed out in class
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11
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12/2
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Date
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Group
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Demo Title
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|---|---|---|
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9/30
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B
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2D FFT and Fourier domain filtering
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10/7
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C
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Spot of Arago
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10/14
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A
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Young's two pinhole interferometer
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10/21
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D
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Talbot Self Imaging
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10/28
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C
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Acousto-optic Modulator
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11/4
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B
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Optical Fourier Transforms
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11/30
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A
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Computer Generated Hologram 1xN Beam Fan-Out
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12/2
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D
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- demonstration information