RE:Re: RE: That encoder stuff.

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

Another interesting effect is caused by partial spatial coherence. A source
of light is said to be spatially coherent if it can be focused to a point.
A laser is a good example. Light focused through a small pinhole can be
made nearly spatially coherent.
This is important because the projection of an object grating onto the
analyzing grating changes in phase with different points on the source
perpendicular to the grating lines. Thus (in general) a broad source cannot
be used. If the source has a grating of the correct frequency directly on
it, then the phases of all the projected grating lines will be the same.
This can give a tremendous increase in brightness over a single slit, and
allows the use of very high frequency gratings.

These grating systems at high frequencies are best analyzed as
interferometers, as indicated above. This will clear up lots of the
confusion, if you feel like wading through an optics textbook. Another step
forward in understanding them requires a more rigorous diffraction theory,
which is a bit beyond the charter of this list.

Elliot Burke


Message: 10
Date: Thu, 23 Sep 1999 19:55:06 +0100
From: "Ian Wright" <Ian@...>
Subject: Re: RE: That encoder stuff.

Hi Elliot,

I haven't come across the term 'Talbot distance' before - is it a calculable
figure or only arrivable at by experiment? Presumably such a factor would
vary depending on the wavelength of the light source??

Ian
--
Ian W. Wright
Sheffield UK

> From: "Elliot Burke" <elliot@...>
>
>
> I'll give it a try.
> The light transmission through two contacted 50% duty gratings is a

triangle

> wave. Separate them and it approaches a sine wave, if you have a

non-point

> source (LED rather than laser). If spacing is increased to the Talbot
> distance, and you have a LED (extended) source, you'll get the triangle
> wave. Operating at half Talbot spacing gives close to sine wave.