Observations of the Talbot Effect.
Allison Schmitz, Austin College; John No�, Harold Metcalf, The 
Laser Teaching Center, Stony Brook University.

In 1836, Henry Fox Talbot, one of the inventors of photography,
observed sharp colored bands in the light from a white-light point
source which had passed through a periodic grating. Remarkably the
sharp bands persisted, with periodically varying colors, even at a
great distance from the grating. The phenomenon he observed, which is
now referred to as self-imaging or the Talbot effect, was explained by
Lord Rayleigh in the 1880's as a natural consequence of Fresnel
diffraction.  The imaging from the Talbot effect is similar to that of
a lens except there are multiple focal planes behind the grating at
which an image appears.  The distances from the grating where these
focal planes occur can be found using an equation similar to the
well-known thin lens equation.

In order to observe and better understand the Talbot effect, I
performed an experiment using a helium neon laser, a Ronchi grating
with 250 lines/inch, an Electrim 1000N CCD camera, and a Gaertner 1.2
meter optical carriage.  The laser was coupled through a single-mode
optical fiber and directed through the Ronchi grating placed 13 cm
away.  I recorded images in a computer at 1 mm intervals over the
length of the carriage. Some of these were later converted to
intensity profile plots.  I observed the sharp Talbot images at four
image distances, whose values were in good agreement with my
predictions.  It was also interesting to observe the complex and
rapidly-varying patterns in between the image. Magnification values
for the images can be determined from my data; this analysis is in
progress.  I later determined the image positions for several other
object distances, including infinity (parallel incident light), in
which case the images are equally spaced at the Talbot distance Z_t =
2a^2/lambda, where a is the grating period and lambda is the wavelength
of the light.

The Talbot effect is intimately related to diverse topics in
mathematics and physics, including number theory, fractal patterns,
and wave mechanics.  It also has many useful applications in imaging,
interferometry and atom optics.  In the future, I plan to continue my
research by creating a computer simulation of the Talbot effect to
better understand why the effect occurs.

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