Lens as a Fourier tranform

Lens as a Fourier tranform

Post by fj » Sun, 06 Jul 2003 22:39:16



Hi,
I'm looking for a good explanation (mathematical and intutive) for the
action of a lens as an optical fourier transform. could somebody point me to
a good resource for this?
Thanks,
-fj
 
 
 

Lens as a Fourier tranform

Post by Dmytry Lavro » Mon, 07 Jul 2003 02:26:10



> Hi,
> I'm looking for a good explanation (mathematical and intutive) for the
> action of a lens as an optical fourier transform. could somebody point me to
> a good resource for this?
> Thanks,
> -fj

You're mean optical prisme? Or bad chromatical lense? Or something with
interference?

 
 
 

Lens as a Fourier tranform

Post by Just d' FAQ » Mon, 07 Jul 2003 13:51:38



>I'm looking for a good explanation (mathematical and intutive) for the
>action of a lens as an optical fourier transform. could somebody point me to
>a good resource for this?

If you're getting this seriously into optics, you might want some free
software to experiment.

  <http://www.sinopt.com/>

Here's an online optics tutorial, with interactive 3D graphics.

  <http://www.erc.msstate.edu/~foley/newtop/>

However, Fourier transforms are used more to analyze the effects of
Fraunhofer (far field) diffraction. For example, suppose you have a
telescope with a 200mm circular aperture; the Fourier transform of the
aperture, an Airy function, is like a circularly symmetric sinc, with
a central bright disk that limits the resolving power by convolving
with the ideal point images of stars. As you increase the aperture,
the Airy disk shrinks, increasing the amount of detail that can be
resolved (as well as gathering more light). A Newtonian telescope has
a small secondary mirror and supports, and these obstructions further
spread the point images; again the diffraction effects are captured by
a Fourier transform.

 
 
 

Lens as a Fourier tranform

Post by fj » Mon, 07 Jul 2003 17:00:50





> If you're getting this seriously into optics, you might want some free
> software to experiment.

>   <http://www.sinopt.com/>

> Here's an online optics tutorial, with interactive 3D graphics.

>   <http://www.erc.msstate.edu/~foley/newtop/>

Thanks a lot.

Quote:

> However, Fourier transforms are used more to analyze the effects of
> Fraunhofer (far field) diffraction.

Do you mean Fresnel diffraction - isnt Fresnel diffraction the one with a
sinc pattern ?

-fj

 
 
 

Lens as a Fourier tranform

Post by Just d' FAQ » Mon, 07 Jul 2003 18:00:13



>Do you mean Fresnel diffraction - isnt Fresnel diffraction the one with a
>sinc pattern ?

<http://scienceworld.wolfram.com/physics/FraunhoferDiffractionCircular...>