Topics in Applied Physics - Harmonic Analysis (3)

This is a course on applications in nature of reciprocal/direct, frequency/period, momentum/position, covariant/contravariant, and wave/particle complementarity in fields as diverse as: (i) electron optical exploration of nano-materials, (ii) infrared spectroscopy of gigascale integrated circuit silicon, (iii) light optical computing, (iv) electronic circuit design, (v) crystallography, (vi) classical geometrodynamics, (vii) photonics, (viii) algorithms for data compression, (ix) visual and voice pattern recognition, and (x) music. The focus will be on applications in optics of present economic impact, although we will discuss and illustrate connection to the other areas also, in language consistent with the background of participants. Guest presentations on applications could involve regional experts in areas as diverse as optometry, Bach, silicon science, diffraction, telescope making, circuit theory, electron microscopy, and digital analysis of images. This course will include some hands-on experience with light and electron optical systems (including an atomic resolution 300kV TEM), and will we hope complement related lab course offerings the department is considering this semester as well. For more information contact

UM-StL Physics 325 - Spring '01

Boiler plate specific to this version of the course might read: Prerequisite - Physics 201, Mathematics 202. Harmonic analysis; phase, complex-color, & momentum representations; Fourier transforms, spectroscopy, & filtering; Transfer, point-spread, & transmittance functions, Wave field scattering & optics, plus Applications. Three hours of (interactive) lecture and one hour (web-based) discussion per week.

New, Answer What?, Local Pages, External Links, More Books, OverView, HomeWork

What's New?

complex-color quantum harmonic oscillator

complex-color tunnel barrier animation

color map for the complex plane

The Story: The department asked me to put together a course on topics in applied physics. In fact, the catalog description of Physics 325 will likely be changed to reflect this in years ahead. Fortuitously, the version of the course I am teaching this winter/spring will be about Reciprocal World. This will let me use a book previously used by both Mary Leopold and Frank Moss for Physics 325, but will integrate exciting applications for these tools that we presently use in the lab, from the very beginning of the course. Those tools include things like instrument transfer functions, periodicity analysis, roughness spectroscopy strategies, electron diffraction, darkfield imaging, and Bayesian inference of both Fourier backgrounds and imagined surroundings. I'm hoping some of our regional collaborators, including current and ex-graduate students, will volunteer to share their expertise in these areas as well.

Perhaps the theatre of operations is best illustrated by the figure below, from my recent presentations on "Play and work in the NanoWorlds of St. Louis".

If your computer hardware and browser can handle VRML (virtual reality markup language), you can visit the reciprocal half of this image (in which color corresponds to Fourier phase) here. The shape transform regions around each reciprocal lattice peak are particularly fun for hikes, as well as cross-country skiing if your virtual-reality hardware supports such serious gross-motor activity. If not, call up Nordic Track and tell them you would like a beta-test version of their VRML skiier, as soon as it becomes available!

Puzzler: What are the Miller (reciprocal lattice) indices of the blue structures, and the zone (direct lattice) index of the projection? If you take the trouble to correctly figure out the integer answers to the last question, which we might refer to as uvw, then you can check your answers to all questions by looking over the relabeled image at:

A second puzzler might be: Below find a pattern that comes not from the imagination of a human, but from the scattering of electrons through a cubic-lattice crystal. But how would the mathematics of a cubic crystal allow one to predict this pattern?

VLSI Si [100] ZAP

Questions this course might help you answer...

AnySpeed Engineering Complex ColorMath Information Physics NanoWorld Explorations Reciprocal World Silicon River StarDust in the Lab Web Puzzlers

Atomic Physics Lab Center for Molecular Electronics Center for NeuroDynamics Physics & Astronomy Scanned Tip and Electron Image Lab

Some local resources of possible interest:

A few of the many web resources...

...on transforms

...on circuit analysis

...on Fourier transform spectroscopy

...on diffraction and contrast analysis

...on lenses and wavefield optics

...on propagators

...on Bayesian inference

...on other stuff

  • Press below for Alta-Vista's Dynamic Link-Lists on these topics...

    Some Suggested Supplementary Reading

    ...on the subject matter of this course...

  • Enrique Gonzalez-Velasco - Fourier Analysis and Boundary Value Problems (Academic Press, San Diego CA, 1995).
  • A. Bruce Carlson - Communication Systems - an intro to signals & noise in electrical communication (McGraw-Hill, NY, 1986).
  • Gerald Folland - Fourier Analysis and its Applications (Wadsworth & Brooks, Pacific Grove CA, 1992).
  • John M. Cowley - Diffraction Physics (North-Holland, Amsterdam, 1981).
  • John C. H. Spence - Experimental High-Resolution Electron Microscopy (Oxford University Press, Oxford 1988). that may prove useful...

  • The Web
  • MathCAD, Mathematica, Maple.
  • Numerical Recipes by Press, Teukolsky, Vetterling, and Flannery (Cambridge U. Press, 1988, 1992).

    ...on subjects of more general interest...

  • Galileo Galilei - Dialog Concerning the Two Chief World Systems (1632, translated by Stillman Drake, UC Press, 1962)
  • Roman Vinokur - The science of the jump shot: Kinematics on the basketball court, Quantum (Jan/Feb 1993) 46-50.
  • McBeath et. al. - How baseball outfielders determine where to run to catch fly balls, Science 268 (28 April 1995) 569-573.
  • Larry Gonick & Art Huffman, The Cartoon Guide to Physics (HarperPerennial, NY, 199_).
  • Larry Gonick & Woollcott Smith, The Cartoon Guide to Statistics (HarperPerennial, NY, 1993).
  • Thomas Kuhn, The Structure of Scientific Revolutions, 2nd edition (U. of Chicago Press, Chicago IL, 1970)
  • Joel A. Barker, The Business of Paradigms (ILI Press, Lake Elmo MN, 1985)
  • K. Eric Drexler, Engines of Creation (Anchor Doubleday, New York NY, 1986)
  • Stephen W. Hawking - A Brief History of Time
  • Jearl Walker, Flying Circus of Physics (John Wiley & Sons, 1975)
  • Michio Kaku, HyperSpace (Oxford University Press, 1994)
  • James Gleick, Chaos: Making a New Science (Penguin Books, 1987)
  • Stuart Kauffman, At Home in the Universe (Oxford University Press, 1995)
  • Kip S. Thorne, Black Holes & Time Warps (W. W. Norton & Co., 1994)
  • Mark Slouka, War of the Worlds (BasicBooks, 1995)
  • Richard Dawkins, The Selfish Gene (Oxford University Press, 1976)


    Assumed Background:


  • Physics 201, Math 202


    Prof: Phil Fraundorf 516-5933; Benton Hall 421 (office)
    Office Hours: after class and by appointment
    Text: Linear Systems, Fourier Transforms, and Optics, by Jack D. Gaskill (John Wiley & Sons. NY, 1978)
    Lectures: Section E01 TR 6:55-8:10pm Benton Hall B115.

    Approximate Distribution for Grade:

  • (1) Collected HomeWork / Quizzes - 15%
  • (3) Four 1-Hour Exams - 60%
  • (3) Comprehensive Final Exam - 25%

    Syllabus: Sequence and Scope
    zeroeth draft, by chapter number...

    2. Representing Physical Quantities w/Math, to which we add Complex Color & aTan2.
    3. Special Functions, to which we add Ray-Tracing, and Image Distortions w/Semper.
    4. Harmonic Analysis, plus stuff on FFT's, Roughness Spectroscopy, Errors, & 7,9.
    5. Operators & Physical Systems, plus stuff on electron CTF's & HREM analysis, & 8.
    6. Convolution, plus stuff on Interferograms, & Cross-Correlation Displacement Measures.
    10. Optics and Diffraction, to which we add Crystallography, Kikuchi Maps, and Darkfield.
    11. Images & Coherence, plus stuff on Holography & Inferring Background/Surroundings.

    Note: 7 is on Fourier Transform Pairs, 8 on Filters, 9 on 2D convolutions/transforms.

    first draft...

    Current Draft of the UM-StL Physics 325 Syllabus

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