Computer-generated holography

Computer Generated Holography

Computer Generated Holography (CGH) is the method of creating digital holographic interference patterns by computer program. This technique has wide ranging applications from futuristic "Holovideo" (MIT Media Lab) to digital 3-D modeling to holographic displays.

Overview

Holography, a technique originally invented by Hungarian physicist Dennis Gabor (1900-1979) to improve the resolving power on electron microscopes, has evolved over the years to represent an art form. "Traditional" holography is done with a laser (or other source of coherent, monochromatic light), but recent advances in computing technology has allowed computer modeling of the optical setup. In essence, CGHs made by ray-tracing (see below) recreate the interference pattern that would be captured optically and print the image to a medium for displaying.

Different Methods

Although there are many different methods for calculating the interference pattern for a CGH, the two that will be discussed here are Fourier Transform Holograms (FT holograms) and ray-tracing holography. (For a good tutorial on Fourier Transformations, see Complex To Real and click on Fourier Analysis Made Easy Part I and II).

Ray Tracing

Ray tracing is perhaps the simplest method of computer generated holography to visualize. Essentially, the path length difference between the distance a virtual "reference beam" and a virtual "object beam" have to travel is calculated using the three dimensional distance formula ($<SQRT>x^{2}+y^{2}+z^{2}</SQRT>$ ---WORK IN PROGRESS---

Fourier Transform Hologram

In a Fourier Transform hologram the reconstruction of the image occurs in the far field. This is usually achieved by using the Fourier transforming properties of a positive lens. The inverse Fourier transform of the hologram is calculated and is then represented on some holographic media. This is Fourier transformed by the lens to reproduce the original signal.

It is usually difficult in practice modulate both the phase and amplitude of light so typically only one of them is modulated. The phase component is normally the most important part of the signal so if amplitude is the only parameter that can be modulated the phase must be encoded by some other method such as phase detour.

If phase is the only parameter encoded the CGH is then also known as a kinoform or sometimes diffractive optical elements (DOE). Although technically a DOE is the super-class of kinoforms since the term can describe optical elements that are not strictly kinoforms. These are commonly designed using the iterative Fourier transform algorithm.