Talbot

Elliotf wrote:

>The Talbot effect is easy to understand if you consider the many

diffraction orders of a square wave grating. Considering only a

>point source, each diffraction order will propogate an image of a

grating in the direction u, when a is the grating period, w is the

>wavelength, and m the order of diffraction:
>
>a sin u = m w
>
>(I wish there were theta's and lambda's on this keyboard)
>
>At the Talbot distance these orders coincide in phase,

reconstructing or imaging the grating.

>

This is giving me "arne-itis" again, - this is too difficult for
me !

I may be wrong, but what you have written here, looks like the the
condition for a "dark" fringe:

sin ( theta ) = n*(lambda)/ a, ( n= +-1,+-2,+-3,....)

? and this is for a single slit, - but we are talking about many,
hence interference with many. That is a diffraction grating.
But we have more: We have two separate diffraction gratings on top
of each other, we must also take into the account, the source of
light, and the sensor characteristics. Distances, and energy
distribution.

>This is a remarkable effect, and i recommend trying to view it.

Okay, could you dream up a simple way for us to see this. Why I
say "dream" - is that we would need an example with things we could
use, and not some lab equipment.

> Another step forward in understanding them requires a more

rigorous diffraction theory, which is a bit beyond the charter of
this > list.

Well, what ever you could tell us, is okay by me - if you could
put it in plain english :-)

Okay, let see...hmmmm Jon Elson could make a film, this could
be glued on top of an aluminum bar, you could shine a laser or
something down at this bar at say, 45 degree. Have a grating at -45
degree. You could interpolate the output, - giving much higher
resolution than he now has. And for rapid moves, you would skip the
interpolation. How about it ?

The thing is, - we need to understand some of the problems
involved, but the use of it would be to make some stuff.

//ARNE