Re: X ray microscopy (was camera obscura)

["John S. Denker" <jsd@AV8N.COM>]

On 08/17/2003 10:31 AM, Ludwik Kowalski wrote:
> Does somebody understand how a parallel beam of
> X-rays is focused by a structure similar to that described
> on the web page provided by Bernard?

I assume the question refers to the page
http://www.esrf.fr/UsersAndScience/Publications/Highlights/2002/Methods/MET3/

> "Multilayer" for light usually refers to layers of materials
> whose index of refraction is different. But for X-rays n is
> practically one in any material.

Close to one, yes.  "Practically one", no.
There are differences that can be exploited
in practice.

> How can extremely small
> differences in n (like 0.001 or less ?) be used to focus?

A small index-difference just means you need a
thick lens.  The optical path in the lenses in
question is very long, because of the glancing
incidence.

> Perhaps the term "multilayer" means something else
> in this context.

I think it means just what it always means.  In
this case they describe Si layered on Mo.  It's
not clear whether "200 layers" means 100 Si +
100 Mo, or whether it means 200 pairs.

In any case, the physics in the X direction is
the same as the  quarter-wave AR (anti-reflective)
coating you see on camera lenses, except that in
this case it's half-wave R instead of quarter-wave
AR.

The physics in the Y direction is Fresnel.

Remember that the name Fresnel can be attached to
various bits of physics that are neither entirely
the same nor entirely distinct:
 a) lens (as in a lighthouse)
 b) absorptive zone plate
 c) phase-shifty zone plate

Ideas (b,c) blend together if you consider the full
complex index.  Idea (a) blends with the others if
you consider it an extreme form of blazing a grating,
i.e. a nontrivial profile *within* each zone.