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 email@example.com
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.
Three complex-color wave-field animations on double
single slit diffraction.
A complex-color plot of the electron phase-contrast transfer
function of a high-resolution electron microscope, as
a function of defocus setting, is here.
To try focussing a microscope image yourself, go here.
Complex-color animation of a Gaussian wavepacket, trapped
in a simple harmonic oscillator potential. The
calculation was done using the Feynman propagator. Click here
for a much larger complex-plane animation of same. To see
what might happen to Gaussian bumps in a 2D well, click here or here.
of a free electron's transverse/longitudinal coherence
widths and group/phase velocities.
Quantum-mechanical tunnelling with a standing wave on the
left, a barrier in the middle, and a wave past the
barrier on the right, might be vizualized using the complex-color
band below. Click here
to see a less-compact complex-plane animation of
the same process. See any Modern Physics book for a
wave method for obtaining these images.
Ask in class for the discussion password if you don't
have it. The pre-course login ID is [Physcs325.001],
while the pre-course password is [Physcs325.001].
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
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
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
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
Questions this course might help you answer...
Exactly how does the treble dial on your stereo tuner
alter Boston Philharmonic sounds?
What you look like with frequencies betwixt 1/2cm &
1/3cm removed from your face!
How can a computer guess what's just outside the
field of view of a picture?
How to remove noise from images without messing up sharp
What is it like to "tool around" in the
reciprocal space of relativistic electrons?
How can I quantify very weak periodicities in time or
How is the atomic lattice oriented within the silicon
wafer in the watch on your wrist?
Does an image with duck amplitudes and cat phases look
more like a duck, or a cat?
How can you image the relative deBroglie phase of
electrons passing through a solid?
Is it possible to hide messages in reciprocal space, and
if so how?
Where are the atoms, and tunnels between atoms, in a high
resolution TEM image?
How does the roughness fingerprint of a surface
undergoing CVD change with time?
What is a Kikuchi line, and why would you want to follow
Did Kahlil Gibran really discover the secret of the sea
in meditation upon the dew drop?
Diffraction-space clues led us to what
"impossible" discovery in the 1980's?
How and why use color to display complex 2D arrays in
What things might have ONLY first-order spots in their
How do Huygens, Rayleigh-Sommerfeld, & Fresnel
How may one reveal the
anatomy of an optical system, as in...
Some local resources of possible interest:
a high-res electron microscope image on-line!
and some interesting TEM facts.
for the Winter 1998 AAPT Conference.
for solving constant acceleration problems at any speed.
Michio Kaku, HyperSpace (Oxford University Press,
James Gleick, Chaos: Making a New Science (Penguin
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)
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
Approximate Distribution for Grade:
(1) Collected HomeWork / Quizzes - 15%
(3) Four 1-Hour Exams - 60%
(3) Comprehensive Final Exam - 25%
Sequence and Scope
zeroeth draft, by chapter number...
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
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