How can Fourier Transforms help explain the process of holography?

[zimbabwe]

I'm really having trouble understanding how holograms work in a good enough way to explain it. I know it captures an interefernce pattern of two incoming waves in the form of a complicated diffraction grating. When the reference beam shines on to the plate the original object is created. But that really isn't clear.
So using 2 coherent beams of light with a ration of 1:4 and an angle of incidence 30 degrees different apart onto a holographic plate, is like adding 2 sin waves onto the plate. When I play the plate back using a laser I get three points. One in the center and two on either side. I was told this is a Fourier transform, can someone show me how do it with maths so it makes some sense, or explain what exactly is going on.

Thank a lot

 

[NateD]

. Holography is a complex and fascinating topic, so it can be difficult to explain it in a concise way. The basic idea is that two coherent light beams, with a 1:4 ratio and an angle of incidence of 30 degrees apart, interact with each other when they are incident on a holographic plate. This interaction creates an interference pattern which is recorded on the plate. When you then shine a reference beam of light on the plate, the original object is recreated as a three-dimensional image (the three points you mention). One way to understand this process mathematically is by using Fourier Transforms. A Fourier Transform is a mathematical tool that is used to break down a complex waveform into its component sinusoidal waves of different frequencies. In the case of holography, this means that the complex waveform created by the interference between the two coherent light beams can be broken down into its individual sinusoidal components. When the reference beam is shone onto the plate, each of these sinusoidal components is re-created, thus producing the three-dimensional image. Hope this helps!