Topics in Applied Physics - Harmonic Analysis (3)

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?

• Notes on molecule harmonic analysis and diffraction in action.
• Check out a flyer about "hands-on physics" for Spring 2001!
• An application of darkfield decomposition to nano-material images.
• Square-aperture darkfield (sinc wavelet?) direct<=>reciprocal glide (.5MB).
• A big What Ray Optics Left Out animation (1MB).
• A workshop on using reciprocal world to save a mission to mars. VQM
• What does ray optics leave out? A 238kB JPEG, under the stream at right, illustrates in detail.
• Might analytical Fresnel diffraction curtains (at left) spice up YOUR dining room?
• Steps 1, 2 and 3 to the beautiful equations that let us calculate such curtains.
• A nomogram for lenses, to shed light on the steps above.
• Check out our microscopy course overview, as well as sem, tem and spm course pages.
• Try amplitude-surfing focussed double and multi slit diffraction runs to see what it's like!
• This worksheet does discrete 1D FFT's with MathCAD and their free browser!
• Sample exams: First(a,b,c,d), Second(a,b,c,d), Third(a,b,c,d), Final(a,b,c,d,e).
• On finding the details of signal buried in noise.
• A little exercise with the quadratic phase function.
• A physical introduction to the basics of FTIR.
• Three complex-color wave-field animations on double and narrow/wide 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.

• Complex-color animation of a free electron's transverse/longitudinal coherence widths and group/phase velocities.
• A handout on various paths to and from reciprocal space.
• 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 piecewise-continuous Schrodinger wave method for obtaining these images.

• This course now has a university-wizarded webpage and discussion area.
• 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 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:

http://www.umsl.edu/~fraundor/p325/zone_uvw.gif

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?

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 edges?
• What is it like to "tool around" in the reciprocal space of relativistic electrons?
• How can I quantify very weak periodicities in time or space?
• 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 it?
• 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 picture form?
• What things might have ONLY first-order spots in their diffraction patterns?
• How do Huygens, Rayleigh-Sommerfeld, & Fresnel Propagators differ?
• How may one reveal the anatomy of an optical system, as in...

Some local resources of possible interest:

• Try focussing a high-res electron microscope image on-line!
• deBroglie's electrons and some interesting TEM facts.
• Three abstracts for the Winter 1998 AAPT Conference.
• An applet for solving constant acceleration problems at any speed.
• Does making a hotdog require 50 nanoseconds of life's power stream?
• Start relativity with the metric equation instead of Lorentz transforms!.
• Is statistical physics a dead subject, or is there another paradigm change afoot?
• What other resources might help you? E-mail suggestions to pfraundorf@umsl.edu.
• At UM-StLouis see also: a1toc, cme, i-fzx, phys&astr, programs, stei-lab, & wuzzlers.
• Some current and previous courses: p111, p112, p231, p341, p400.
• Cite/Link: http://newton.umsl.edu/~philf/p111f97s.html
• This release dated 25 Aug 1997 (Copyright by Phil Fraundorf 1988-1997)

A few of the many web resources...

...on transforms

• Kevin Cowtan's Book of Fourier.
• Steffen Weber's web-interactive 2D Fourier transform applet.

...on circuit analysis

• The OrCAD circuit simulator with downloadable demo.

...on Fourier transform spectroscopy

• Photometric's notes on FTIR.
• Widener University notes on FTIR articles.
• Our downloadable visible FTIR simulator program for PC.

...on diffraction and contrast analysis

• The Bragg's Law applet by Konstantin Lukin.
• A web tutorial on x-ray and neutron diffraction.
• Steffen Weber's great stuff on transforms, (quasi)crystals, & diffraction.

...on lenses and wavefield optics

• Our web-based electron-phase-contrast focus/astigmatism simulator.

...on propagators

• Edwin Taylor's web-page on Many-Path Quantum Mechanics & Scouting Black Holes.

...on Bayesian inference

• Our web-based notes on computer imaginations.
• Our information-physics page and link collection.

...on other stuff

• SUNY-Buffalo Physics 107C Mech&Heat Lecture Notes by R. J. Gonsalves.
• Kenny Felder's Math and Physics Help pages.
• Univ. Oregon Student Physics Problems Page
• What is d^3x/dt^3? Check sci.physics' Frequently Asked Questions.
• Contemporary Physics Education Project's Particle Adventure.
• Other physics education links that may be of interest include those at: Yahoo, Quantum, c3p, McGill, ....