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From: jh@tuna.MIT.EDU (John Underkoffler)
Newsgroups: comp.graphics
Subject: Re: 3d Computer Generated Holography
Message-ID: <612@mit-amt.MEDIA.MIT.EDU>
Date: 27 Aug 89 04:30:49 GMT
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In-reply-to: ingoldsb@ctycal.COM's message of 25 Aug 89 18:31:45 GMT


	Wavefronts And You: The Holographic Scoop
	-----------------------------------------

	In response to Terry Ingoldsby's holo-worthy posting, it is
not necessarily the case that 3-D holography is reliant on a
three-dimensional film emulsion for its operation. The simplest kind
of transmission holograms employ diffraction (which, as we know, is a
phenomenon whereby waves of light are `perturbed' or `annoyed' after
propagation through some region of spatially varying opacities)
through a photographically recorded fringe pattern in a
high-resolution but otherwise workaday emulsion. As far is the imaging
properties of the beast are concerned, the film emulsion is merely a
two-dimensional mask of opaque fringes in a transparent field. A
theoretically infinitely thin [2-D, then] emulsion can contain a
complete record of the moving wavefronts which represent a fully
three-dimensional scene; no information is lost, unlike many
transatlantic telephone conversations. Of course, certain kinds of
holograms do depend on an emulsion of finite thickness, so I can't be
entirely trusted to tell the truth. An example is any kind of
reflection hologram (a hologram for which the illumination is on the
same side of the film as the viewer), which is similar to an
interference filter in its use of many nested, gently curved fringes,
roughly parallel to the plane of the film.

	A few notes on "real" Computer Generated Holograms (as we call
the fringe-calculated variety, as contrasted with Holographic
Stereograms, which may or may not employ a computer to generate the
myriad perspective views which become optically assembled in a fairly
non-thrilling manner) seem in order. First off, the preponderance of
CGHs made using FFTs is the result of a lucky coincindence in nature:
if you allow a certain distribution of light to propagate a long
way, what you get looks mathematically something like the Fourier
Transform of the distribution you started with. This made a lot of
people who wore white lab jackets and used terms like "Mach-Zender
Interferometer" and "apodization" very happy when they realized it.
Basically, it meant that if they wanted to compute what the fringes
in a holographic recording of an dismayingly distant two-dimensional
transparency would be, they wouldn't have to use the dreadful
ray-tracing method mentioned by Terry. Of course, that meant that
the only kind of holograms that they could make were ones which
featured images of dismayingly distant two-dimensional transparencies.
Such images became quite popular, of course. In short, then, FFTs
can be used to generate fringe patterns for a very highly constrained
class of holographic images, because a 2-D spatial Fourier Transform
happens to be a really good approximation to the actual thing for
that sadly flat class.

	But we want CGHs which display non-flat objects! It is therefore
not feasible to use the Fourier Transform shortcut. Instead,
you have to go ahead and play Momma Nature and use the ray-tracing
method; that is, you do what nature does when it makes a hologram
[er...], which is that light from each infinitesimal object in the
scene you're depicting propagates to each location on the holographic
film, unless it's precluded from reaching certain locations because
of occlusion by other objects. Thus, the contribution from each
little spot of light in your scene has to be communicated to each
little location in the holo-film. The number of each of these is
`a lot', as we say in the business. Example-numbers and statistics
are boring, so I won't give any, but think of something staggering
and then square it a few times to get a rough estimate of the number
of propagation-computations that're necessary.

	However, the problem is luckily not so computationally
intractable as Ms./Mr./Dr. Ingoldsby fears. There are many ways
to cheat. One of these is that we can dispense quickly with
vertical parallax: because your eyes are situated horizontally
(in order to fill out your face, as my colleague Mr. Halle noted),
most people don't notice if they cannot look over or under objects.
Therefore, you can get away with propagating light from each
scene-point only to hologram-points which are at the same vertical
level with them. Already, the problem is reduced by a few orders
of magnitude. For homework, think of other ways to make computation
of holograms easier. Tommy Mouser's estimate of 6 Cray2-days for
the computation of a one-inch-square hologram is consequently
slightly misfounded. Using, among other computation reduction
techniques, elimination of vertical parallax, we routinely compute
two-by-two-inch holograms in a few minutes on an HP 835 workstation.

	You and your friends can have fun making CGHs in your spare
time!

					John Underkoffler
					Pasteurizer,
					Spatial Imaging Group
					MIT Media Lab
					jh@media-lab.media.mit.edu