remaining inf. on a cut hologram + FT

On: Sat, Dec 22, 01 01:14:39 PM

Thilo K. wrote:

I would like to know if anyone knows and can tell me the physical explanation for the information missing when you cut one hologram into two ones. Furthermore does anyone know what the Fourier transform looks like if the wavefront of a sphere is transformed ?


Colin Kaminski - Sun, Dec 23, 01 06:33:37 PM

I only can offer a simplistic explanation if you want a mathematical explanation I can't help. But I think of a hologram as being a window into the scene. When you cover a portion of the window you only get a small point of view. This makes sense because a piece of film can contain no information from the parts of the object that it can't see. As far as a FT of a sphere it is the same as the diffraction pattern of a plane wave front and a spherical wave front interfering. But you probably are looking for a more mathematical description. It would be fairly easy to make math cad generate diffraction patterns for simple objects. I also have a FFT written in C I could post if you want to write some of your own code.

Jonathan - Sun, Dec 23, 01 11:00:26 PM

Good question, Thilo. It's always been a source of amazement to me, that if you are so inclined, you can take a reflection hologram, hold it in the light at the right angle, cut it in two, and actually watch as two holograms of the same whole object emerge. On the first part of your question I believe you could say that there are two senses in which information is lost when you do such a thing. The lost viewpoint of the scene provided by that part of the hologram cut out, which Colin describes above. And the resolution lost by having that much less area diffracting and reflecting light in the process of creating the wavefront that you see. To better answer your question there's a very good introduction to the "wave" model in "The Complete Book of Holograms: How They Work and How to Make Them" by Kasper and Feller - a good but inexpensive book. And Saxby's book "Practical Holography" deals with Fourier transforms in its appendix (another book well worth owning).

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