Content uploaded by Kaveh Bazargan
Author content
All content in this area was uploaded by Kaveh Bazargan on Feb 29, 2016
Content may be subject to copyright.
12
Holographic Display
of
3D
Data
Kaveh Bazargan
1.
Introduction
to
3D Perception
.......................................
257
1.1.
Physiological Depth Cues
......................................
,
258
1.2.
Psychological Cues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
..
259
2.
Introduction to Holography
.........................................
260
2.1.
Laser Transmission Holography
.................................
260
2.2.
White-Light Transmission Holography
............................
262
2.3.
Reflection Holography
..........................................
266
2.4.
Multicolor Holography
.........................................
267
3.
Methods of Producing Holographic Display from 3D
Data
..............
267
3.1.
Fringe Writing
................................................
268
3.2.
Holographic Stereograms
.......................................
268
3.3.
Volumetric Multiplexing
........................................
272
4.
Concluding Remarks
...............................................
276
References
........................................................
276
1.
INTRODUCTION
TO
3D
PERCEPTION
Holography
is
a powerful optical technique for recording
and
displaying 3D infor-
mation.
In
this chapter
we
discuss the application of holography in the display of
tomographic data. It helps to have a good understanding
of
3D perception in order
to determine whether holography can be used beneficially in the display of scientific
and
medical data.
For
this reason, this chapter begins with an overview of the
mechanisms which help
us
perceive the world in three dimensions. Later,
we
shall
refer to these mechanisms to evaluate the various holographic techniques available.
The brain and eye work together to decipher the huge amount of optical infor-
mation received by the eye. The information contributing to 3D perception,
or
depth perception, can be divided into many "depth cues." These depth cues can
be
Kaveh Bazargan • Focal Image Limited, London
Wll
3QR, England
Electron Tomography: Three-Dimensional Imaging with the Transmission Electron Microscope, edited by
Joachim Frank, Plenum Press, New York,
1992.
257
258 KAVEH
BAZARGAN
further divided into physiological, and psychological ones, although some cues fall
into a gray area in between.
As
a rule, physiological depth cues are those derived
from the physical motion of (or other physical changes in) the eyes, and psycho-
logical depth cues are those derived by the brain after processing the retinal images
of the eye(
s).
1.1.
Physiological Depth Cues
Physiological depth cues are generally considered to be the most important
ones for depth perception. The strongest such cues are listed below.
Accommodation Accommodation
is
the reshaping of the lens in the eye by the
ciliary muscles in order to bring the image of a scene into sharp focus on the retina.
The state of the lens
at
any given time
is
a cue for depth perception. In the normal
eye, when the muscles are in a relaxed state, objects
at
infinity are in focus.
To
focus
closer objects, the lens
is
made more convex by the ciliary muscles, thus shortening
its focal length (Fig.
1).
This physiological transformation
is
a cue to the brain
about the distance of
an
object.
On
its own, accommodation
is
a weak cue, and is
more effective when combined with other cues.
It
is
a short-range cue, as changes
in the focal length of the lens are minimal when objects are more than a
few
feet
away.
Convergence When the brain concentrates on viewing a scene, the eyes are
arranged such that the point of interest in the scene
is
focused onto the most sensitive
spot in both eyes,
i.e.,
the fovea.
For
objects
at
infinity, the axes of the two eyes are
parallel.
For
objects at closer distances, the eyes converge such that there
is
an
angle between the two axes (Fig. 2). This angle
is
another physiological depth cue
called convergence.
As
in the case of accommodation, this cue
is
more effective
at
closer distances, because the variation of angle with distance diminishes
at
long
distances. Accommodation and convergence are both weak depth cues
on
their
own, but are significant when working together. (In fact, there
is
some interaction
FIGURE 1. Accommodation of the eye. For nearer objects the lens
is
made more convex.
HOLOGRAPHIC DISPLAY OF 3D DATA 259
FIGURE
2.
Convergence.
between the two, so that, for example, a variation in the focal length of the lens in
one eye causes
an
involuntary convergence of the eyes, and
vice
versa.)
Binocular Disparity
As
mentioned in the case of convergence, concentration
of the brain
on
a point in a scene causes the angle between the eyes to be such that
the point of interest
is
focused onto the fovea in each
eye.
Points that lie approx-
imately the same distance away from the eye, and are near the point of interest, are
focused onto corresponding positions on the retina in
both
eyes. However, points
that
are nearer to
or
further from the eye than the point of interest are not focused
onto corresponding positions in each eye, and are perceived as blurred double
images. The angular separation of the two images gives rise to a cue called binocular
disparity. This cue has a longer range than the first two,
and
is
considered to be the
most important for general depth perception.
Motion Parallax When an observer moves while viewing a scene, objects in
the scene seem to move relative to one another. Closer objects seem to move faster
than distant ones, thus constituting a depth cue. This effect
is
called motion
parallax. It is present even when the observer
is
stationary~as
the eyes are moved
from side to side, the position of the lens of the eye changes, thus the scene
is
viewed from slightly differing positions.
1.2.
Psychological
Cues
While physiological depth cues are derived directly from the eyes, psycho-
logical ones are "higher-level" cues that are the result of the processing of retinal
image by the brain. There are a multitude of different cues picked up by the brain
in this way, and many of them are difficult to categorize. Listed below are some of
the most important.
260
KAVEH
BAZARGAN
Hidden Surfaces A simple but powerful depth cue
is
the overlapping of
objects in a scene. When the fields of view of several objects overlap, the nearer
objects totally
or
partially hide the further ones. The simulation of this effect in
computer graphics
is
called hidden-surface removal. This
is
a strong depth cue.
Image Size In everyday experience
we
learn the physical sizes of common
objects. This information, combined with the
size
of the retinal image
of
the object
gives a direct clue to the distance of the object from the eye.
Of
course this cue only
applies to familiar objects.
Linear Perspective
As
objects move further from the
eye,
the size of the image
of the object decreases. This effect
is
called linear perspective.
It
is most apparent
in a photographs of familiar scenes with, for example, regular arrays of buildings.
Farther buildings of similar
size
get smaller and smaller in the photograph.
Aerial Perspective A more subtle effect
is
the gradual reduction of contrast in
distant objects due to atmospheric scattering (e.g., mist or dust).
Lighting We generally
see
objects by their reflection of light from sources in
one
or
more positions. The gradual change of surface color, and the appearance of
shadows on objects are strong depth cues.
2.
INTRODUCTION
TO
HOLOGRAPHY
Having reviewed depth perception,
we
now take a look at different types of
holograms and how they are made.
For
a deeper insight into various techniques in
holography the reader
is
referred to textbooks on the subject, such as Hariharan
(1984) and Syms (1989).
2.1. Laser Transmission
Holography
A transmission hologram
is
one in which the light used to reconstruct the
recorded image
is
on the opposite side of the hologram as the observer, and there-
fore passes through the plate in the reconstruction process. Transmission holograms
are generally considered to be the easiest to record. The simplest hologram, both
theoretically and practically,
is
probably the laser transmission hologram (Leith
and Upatnieks, 1964), so called because a laser
or
other coherent light source
is
needed to view the recorded image.
Figure 3 shows the basic arrangement for recording a laser transmission
hologram. The coherent beam from a laser source
is
split into two using a beam
splitter. (The simplest beam splitter is a piece of high-quality thick float glass.) The
beams are directed around the recording setup using a series of small mirrors. One
of the beams, usually the more powerful one,
is
used to illuminate the object.
As
the laser beam
is
small in diameter, typically 3 mm, it has to
be
expanded before
falling onto the object. This
is
done using a lens system.
The second beam emanating from the beam splitter
is
used
as
the reference
HOLOGRAPHIC DISPLAY
OF
3D DATA
Laser
~
Beamspl itter
collimating
lens
Reference beam
t:@F
Object
FIGURE
3.
Recordmg arrangement
for
a laser transmission hologram.
261
beam. This time it
is
directed toward the recording plate.
As
before, it
is
expanded
using a lens system. In this case, the beam
is
also
collimated-made
parallel-by
introducing a large lens. (This
is
not essential to recording,
but
usually simplifies
proceedings, especially if two-step procedures described later are employed.) The
recording plate (or film) consists of a photosensitive material coated
onto
a base
such as glass
or
polyester. The most common photosensitive material
is
the
photographic (silver halide) emulsion which has the advantage
of
relatively high
sensitivity.
What
distinguishes it from normal photographic material used in
photography
is
the very high resolution it needs to have.
Other
suitable recording
media include dichromated gelatin
(DCG;
Lin, 1969; Shankoff, 1968) and photo-
polymer.
According to the above description there are two beams falling onto the
recording plate: One
is
the reference beam,
and
the other
is
the light scattered from
the object, or the object beam.
It
is
the optical interference of these two beams
that
is
recorded
on
the photosensitive emulsion. The recorded interference patterns take
the form of microscopic, meandering lines
and
contain, in
an
encoded form, all the
optical information relating to the object. We can now see why the reference beam
is
so named.
It
is,
in effect, the yardstick against which each portion of the complex
scattered beam from the object
is
measured.
One way of looking at the recording process
is
to consider the light emanating
from the object as consisting of a large number of rays of light, each with a different
direction
and
intensity. They are scattered quasirandomly, and with no apparent
order. The reference beam,
on
the other hand, consists of a set of rays, all with
approximately the same strength, and all diverging from the same point. In the
recording process,
we
use the reference beam to record the direction
and
intensity
of each and every ray in the object beam.
Having recorded the interference fringes in the photosensitive material, the
material usually has to be processed so
that
the fringes can be used in the
reconstruction stage.
If
the material
is
of the silver halide variety, then the
262 KAVEH
BAZARGAN
processing
is
similar to that in conventional photography,
i.e.,
developing and fixing.
In fact the material
is
usually bleached to improve the brightness. The processing
of silver halide materials for holography
is
a vast
field
of theoretical and empirical
research, the goal being the production of the brightest and cleanest holograms.
After processing, the complex interference fringes are transformed into regions
of different optical density
or
different refractive index.
In order to reconstruct the recorded image, the processed plate
is
replaced in
its original position, the object beam
is
eliminated (e.g., by blocking its path), and
the plate
is
illuminated by a replica of the reference beam (now called the
reconstruction beam) (Fig. 4). The optical phenomenon that now occurs
is
called
diffraction and
is,
in a way, the opposite of interference: The reconstruction beam
falls on the numerous fringes recorded on the plate and
is
diffracted. In other words,
instead of continuing its path through the plate, some of the light
is
deflected into
other directions. In particular, a major part of the diffracted light leaves the plate
in the same direction
as
the original object beam. In fact, the rays making up this
part of the diffracted light are exact replicas
of
the original rays that were scattered
by the object during the recording stage. Following our ray model discussed above
the hologram
is,
in effect, reconstructing all the rays incident on it from the original
object beam, both in direction and in intensity.
It
follows, then, that if an observer
looks in the direction of the original object,
he
or
she will not be able to distinguish
the reconstructed image from the original object,
as
the rays are identical in both
cases. Clearly, all depth cues are present in the image.
Laser transmission holograms were the first type of display holograms to be
made, and still produce the most realistic images which amaze even the most
hardened of holographers. The main disadvantage
is
that a laser
or
another coherent
optical source
is
required for the reconstruction of the image.
2.2.
White-Light
Transmission
Holography
A major goal in the field of holography has been, and still
is,
the production
of high-quality images that can be viewed using noncoherent light sources (such as
Laser
Mirror
Reconstruction
beam
Observer
FIGURE 4. Reconstruction
of
a laser transmission hologram.
HOLOGRAPHIC DISPLAY
OF
3D
DATA
263
white light) for image reconstruction. Perhaps the most popular method
is
to use
the reflection hologram recording technique (see below). Several methods have been
devised to allow white light viewing of transmission holograms. Let us briefly look
at
these, starting with an explanation
of
why simple transmission holograms cannot
be viewed with white light.
2.2.1.
Why
Can't We
Use
White Light?
Let's assume that
we
have produced a laser transmission hologram according
to the above procedure. Why can
we
not
use an ordinary light source such as a
white spot lamp to
view
the image? Figure 5 illustrates the problem. White light
is
composed of a continuum of wavelengths from the blue end to the red end of the
spectrum.
An
undistorted image
is
only obtained when the wavelength of the
reconstructing beam
is
equal to that of the recording beam. The angle through
which a beam
is
diffracted is dependent on its wavelength, shorter wavelengths
being deviated less than longer ones. Consequently, each wavelength produces its
own image
at
a different position. This effect
is
called chromatic dispersion. The
result is a spectral blur of images, generally unacceptable for viewing.
2.2.2. Image- Plane Holography
As
can be appreciated by examining Fig.
5,
the magnitude of spectral blurring
is
proportional to the distance of the image from the hologram.
It
can therefore be
minimized by reducing this distance. In fact, the spectral blurring would be totally
eliminated if the image could appear
III
the plane of the hologram, resulting in a
sharp, achromatic (black and white) image. However, the simple recording geometry
of Fig. 3 does
not
allow this.
If
the object
is
placed too close to the recording plate,
it impedes the path of the reference beam. The answer
is
to use a more complex,
two-step technique for recording which allows the image to be positioned not only
near, but even cutting through the hologram plate (Rotz and Friesem, 1966).
The first stage in the two-step process involves making a "master" hologram
by
a process identical to that for the laser transmission hologram. The second stage
is
shown in Fig.
6.
The processed hologram
is
illuminated by a reconstruction beam
White
light
Blue Hologram
image .
..--.;~.-;?
fJ.~~~)
...
...
-.
Green
:":">;;;::"
.
;.t)
j
........................
tt--------"
Image
'>'--
.
./
(6':(------
Red
.:"--,)
Observer
image
FIGURE
5.
Chromatic dispersion in a hologram.
264
Recording
plate
Reconstruction
beam
.
---.~.
c?
:!::". Reference
Projected
.......
beam
image
FIGURE
6.
Recording
an
image-plane hologram.
KAVEH BAZARGAN
that
is
"conjugate" to the original reference beam.
In
other words, all the original
rays in the reference beam are reversed in direction.
If
the original reference beam
had been diverging, then the conjugate beam
is
converging.
As
we
have used a
collimated beam in the first step, the conjugate beam
is
also collimated. The image
from the hologram
is
now projected into space in front
of
the hologram. This image
suffers from the curious effect of "pseudoscopy"
or
depth reversal.
In
other words,
the shapes appear "inside out," with convex shapes becoming concave. However,
this
is
only an intermediate image and will be corrected in the second stage.
A second hologram can now be recorded by placing a recording plate near, or
even within, the projected image (something clearly impossible with a real object)
and adding a reference beam as before.
We
can reconstruct an orthoscopic (as
opposed to pseudoscopic) image from this hologram
by
using the conjugate
of
the
second reference beam to reconstruct the image (Fig.
7).
The image appears to
protrude from the holographic plate and to project partially. This
is
called an
image-plane hologram.
As
the image points are very close to the hologram plane,
the image can be viewed with minimal chromatic dispersion. Points in the image
plane will be absolutely sharp, and points in front and behind the plate
will
be
blurred proportionally to their distance from the plate. [By an optical technique the
plane of zero dispersion can be shifted (Bazargan and Forshaw, 1980).]
The disadvantage of the image-plane technique
is
that the depth of the image
is
severely limited, typically to some 20-30
mm.
Reconstruction
beam
FIGURE
7.
Viewing
an
image-plane hologram.
HOLOGRAPHIC DISPLAY
OF
3D
DATA
265
2.2.3.
"Rainbow"
Holography
The "rainbow"
or
"Benton" hologram (Benton, 1969)
is
an extension of the
image-plane technique
that
dramatically increases the usable image depth in white
light by sacrificing vertical parallax. The recording procedure
is
similar to that of
the image-plane hologram, except that in the second stage the height of the master
hologram is limited to a
few
millimeters. When the final image is viewed, it appears
in a range of spectral colors, depending on the position of the viewer.
As
the eyes
are moved in a vertical direction the color of the image changes from the blue end
of the spectrum to the red. The perspective of the image, however, does not change.
In
other words, one cannot look over
or
under foreground objects to
see
background
ones. The unorthodox recording geometry also means that there are distortions and
aberrations present unless the image
is
viewed from a specific position in space.
The changing colors can be distracting to the viewer, but fortunately there are
methods to achromatize the image (Benton, 1978), and the limitation
is
not a serious
one. The limited parallax, however,
is
a more fundamental limitation and renders
the method unsuitable for many scientific applications. The inherent distortions and
aberrations must also be taken into account. Notwithstanding these problems the
rainbow hologram has proved to extremely popular, especially in display and
artistic applications.
2.2.4. Dispersion-Compensated Holography
A simple but powerful white-light display method
is
the dispersion-compensated
technique. The idea
is
simply to cancel
out
the chromatic dispersion at the hologram
by predispersing the light in the opposite sense before it reaches the hologram. The
best way of achieving this predispersion
is
to use a diffraction grating with the
same fringe spacing as the average fringe spacing of the hologram (Burckhardt,
1966; De Bitetto, 1966; Paques, 1966). Such a diffraction grating can be made
by
recording the interference pattern between two collimated beams.
As
in the case
of the rainbow hologram, the method extends the effective depth of the image-
plane hologram. Figure 8 shows the reconstruction of the image in a dispersion-
compensated system. The collimated light from a white light source falls onto a
diffraction grating. Some of the light
is
diffracted and
is
chromatically dispersed.
White light
Chromatically
Diffra~tion,
dispersed light
grating
========
~'{
~
t>
~\!\~
'Venetian
blin~HOIOgram
~
Sharp .
structure
~chromatlc
Image
FIGURE
8.
A dispersion-compensated hologram.
266 KAVEH BAZARGAN
(The undiffracted light is blocked by a miniature venetian blind structure in order
that it does not reach the observer.) The diffracted light
is
used as the reconstruc-
tion beam for the hologram which produces an equal and opposite dispersion. The
resultant image
is
sharp and achromatic.
The distortions and aberrations in such a dispersion-compensated image are
very small, and the image
is
comfortable to
view.
Moreover, the image retains
full
parallax and is therefore better suited than the rainbow hologram for scientific
applications. The obvious disadvantage
is
the need for the diffraction grating and
the venetian blind structure. One solution
is
to incorporate these and the light
source into a desktop viewer (Bazargan, 1985). This has been tested and found to
work well, with the viewer being mass producible.
2.3.
Reflection
Holography
A different approach to producing white-light-viewable holograms
is
to use the
"reflection" recording technique (Denisyuk, 1962). The essential difference between
this technique and the transmission one
is
that in reflection holography the object
and the reference beams
fall
onto opposite sides of the recording plate. Figure 9
shows the basic arrangement. The recording medium in this case must be a
"volume" material;
i.e.,
the fringes must be recorded in the depth of the material
rather than on the surface. Figure
10
shows a schematic representation of fringes
recorded in a volume material. The fringes can now be regarded as 3D surfaces in
the volume of the emulsion rather than 2D lines
on
its surface.
The image from a reflection hologram
is
reconstructed
as
before by illuminating
it with a replica of the original reference beam. This time the viewer observes the
image from the same side of the hologram as the reconstruction beam. The basic
principles of interference and diffraction apply as before, with one qualification: the
fringes have, in this case, recorded not only the complete optical information about
the object, but also the wavelength used in recording. This means that, in general,
the hologram
will
only respond to a reconstruction wavelength near the recording
Laser
"-
Beamsplitter
collimating
lens
Reference
beam
Recording
plate
~
Object
FIGURE
9.
Recording a reflection hologram.
HOLOGRAPHIC DISPLAY
OF
3D DATA
Object
beam
Cross-section
through emulsion
Reference beam
FIG
U R E 10. Schematic representation
of
fringes in a reflection hologram.
267
one.
If
white light
is
used in the reconstruction, only a narrow band of wavelengths
near the recording one will take
part
in the reconstruction. This means that the
chromatic dispersion will be small and
that
an image of considerable depth can be
viewed in white light.
Reflection holography can, of course, be combined with image-plane holo-
graphy to produce sharp, low-dispersion holograms. Usually a transmission master
hologram
is
used, as described above.
One disadvantage of the reflection hologram
is
that if the observer gets too
close to the hologram to examine the image the reconstruction beam
is
impeded
and the image disappears.
2.4.
Mullicolor
Holography
The above techniques use a single wavelength to record the hologram. The
image produced
is
therefore in a single color. Even when multiple colors are
present, as in the rainbow hologram, the colors seen bear no relation to the colors
of the object.
In
order to record the color of the object, two
or
more laser wave-
lengths are required. They are a large number of techniques available to produce
color holograms (Bazargan, 1983, 1986; Hariharan, 1983), and a detailed description
of these methods
is
beyond the scope of this chapter.
3.
METHODS OF PRODUCING HOLOGRAPHIC
DISPLA Y
FROM
3D
DA
T A
In all the previous discussions
we
have assumed that a real object
is
available
at
the recording stage. With the tremendous computing power now available,
computers are used to store, manipulate, and display a wide range of 3D data.
Displaying the data presents a fundamental problem as the display medium--e.g.,
the computer screen, printer output,
etc.-is
invariably two dimensional. Ingenious
solutions have been found for displaying such data, especially in the field of 3D
268 KAVEH BAZARGAN
modeling and rendering, but the fact remains that an observer cannot
see
around
foreground objects
or
artifacts simply by moving his or her head. Holography has
the potential for displaying data in true 3D, and there are three
broad
approaches
to the problem, namely fringe writing, holographic stereography, and volumetric
multiplexing. These are discussed in detail below.
3.1. Fringe Writing
Let
us
take the most fundamental approach to creating a hologram artificially.
For
simplicity
we
can consider a laser transmission hologram. The information in
such a hologram
is
recorded in the minute fringes in the recording material. The
physics of the formation of such fringes is
well
known and, in principle, can be
computed for every point
on
a hologram. The fringes usually vary gradually between
totally light and totally dark.
For
the purposes of this discussion, however,
we
can
assume them to be binary; i.e., each point on the hologram
is
either transparent
(light)
or
opaque (dark). The basic rule
is
that the state of the interference pattern
for each point on the hologram depends on the sum of the phases of all the rays
incident on it. The reference beam can be considered as contributing one ray to
each point, but the object contributes a tremendous number. In normal holographic
recording the fringes are effectively calculated by a hugely parallel optical computer.
When fringe writing, these calculations have to be made on conventional electronic
computers. With the high density of points on a typical hologram, the number of
calculations turns
out
to be prohibitively large. The fringe density in a typical
hologram
is
about 1 million points/mm2.
For
each of these points the contributions
of all points of interest in the object must be calculated (Brown and Lohman,
1966). Even with the most powerful parallel processors the time taken to calculate
the fringe structure for one hologram
is
impractically long.
There are ways of reducing the information content of the hologram (Barnard,
1988), but these invariably result in lower-quality holograms or limited fields of
VIew.
Even
if
the computing problems for fringe writing were overcome, only half the
problem
is
solved.
It
is
necessary to write the fringes onto a suitable material. The
only process currently available for writing such small
data
on a two-dimensional
surface
is
photolithography, normally used for producing integrated circuits.
Unfortunately, the hardware
is
designed specifically for producing shapes with
rectilinear geometry, and
is
not suited to the undulating shapes of typical holo-
graphic fringes.
Fringe writing
is
a useful method for producing holographic optical elements
used, for example, in optical testing.
For
the moment, however, it must be
considered impractical for producing realistic three-dimensional images.
If
the two
technological problems are resolved, then fringe writing has the potential advantage
of producing totally realistic holographic scenes, with all depth cues present.
3.2.
Holographic
Stereograms
We now examine in detail one of the two practical methods for producing
holographic images from 3D data. The most popular
is
the holographic stereogram
HOLOGRAPHIC DISPLAY
OF
3D DATA 269
(Benton, 1982; De Bitetto, 1969; McCrickerd and George, 1968). There are many
variations to this technique, but the general procedure is as follows: (1) The
computer
is
used to produce a large number of perspective views of the 3D data.
(2) With a laser beam, each image is projected onto a diffusing screen and a narrow-
strip hologram
is
made of each
view.
(3) The strip holograms are treated as a master
hologram, and all the views are simultaneously transferred onto a secondary
recording plate. (4) The secondary plate
is
illuminated, and the composite 3D
image
is
viewed.
Figure
11
shows the details of one geometry for recording the master
hologram. Different views of an object are computed, and recorded on a
film
strip.
Typically, the number of frames
is
200, and the first and last views are angularly
separated by some 90°.
In
a
film
recorder
is
not available as a computer peripheral,
then the computer monitor can
be
photographed with a pin-registered camera. The
film
strip
is
placed into an optical system which projects each frame onto a diffusing
screen, using a laser source. The diffusing screen
is
then treated as the object,
and
a hologram
is
recorded onto a narrow strip of the master plate. The position of the
strip corresponds to the perspective view recorded in the frame. A moving slit
controls the position
of
the strip.
It
starts
at
one extreme of the plate,
and
moves
to the other.
After the plate
is
processed as usual, the image
is
transferred onto a second
plate by a technique similar to the image-plane method. Figure
12
shows the
arrangement for this stage of the recording.
All
perspective views are simultaneously
recorded on the transfer plate, using a reference beam as before. The image can now
be viewed by illuminating the transfer hologram with the conjugate of the reference
beam used in the recording process (Fig.
13).
In
the reconstruction stage, all 2D
views recorded are reconstructed simultaneously, but each view
is
visible only if
viewed through the corresponding narrow slit which
is
now projected onto the
viewer space. When the observer places the eyes within these projected slits, each
eye sees a different perspective of the image. The depth cue in operation
is
clearly
that of binocular disparity. This
is
a strong cue, and the sensation of depth
is
Direction
of
movement
of
slit
Reference
beam
FIGURE 11. Recording
the
master
for
a
holographic
stereogram.
270
Reconstruction
beam
Projected
2D images
Recording
plate
KAVEH BAZARGAN
FIGURE 12. Recording a white-light-viewable holographic stereogram.
present. The convergence cue
is
also present
as
the observer concentrates on
different parts of the image.
As
the observer moves laterally, each
eye
looks through
a different slit, and a different view
is
therefore selected. This means that motion
parallax, another strong depth cue,
is
also present.
If
the recording procedures have
been carefully followed, then the transition from one
view
to
the next will be
smooth, and the depth sensation
is
further enhanced.
3.2.1. Advantages of Holographic Stereograms
Each image in the sequence
is
a 2D view of a 3D scene, calculated by a
computer. Consequently, all the powerful techniques currently available in 3D
modelling and rendering can be brought into play. This includes hidden surface
Observer's
eyes
3D
image
FIGURE 13. Viewing a holographic stereogram.
HOLOGRAPHIC DISPLAY
OF
3D DATA 271
removal, texture mapping, Phong shading, etc. The method
is
ideally suited to
computer-aided design (CAD) applications which use most of these techniques. The
idea of 3D hard copy
is
an
attractive proposition for the visualization of CAD-type
images.
A holographic stereogram of a wire-frame image,
i.e.,
one with no hidden-line
or
hidden-surface removal, can be perceived to have a perfectly understandable 3D
form, even though the individual frames may have ambiguities about
depth-the
3D depth cues present in the stereogram aid understanding of the data.
3.2.2. Drawbacks
of
Holographic Stereograms
It
is
important to realize that although holographic stereography
is
a powerful
technique, it lacks the accommodation cue which
is
important for images near
the observer. Also, the basic ingredient of a holographic stereogram
is
a set of
perspective
views.
There are many types of data which cannot unambiguously
be
produced in this format. Tomographic data
is
a good example. In order to produce
perspective views of such data,
we
have a choice of simply stacking the data
together and adding the contributions from all slices, or
we
can attempt to extract
3D shapes from the data, and perform rendering operations on a computer. In the
former case, the amount
of
data could be such that the overall picture for each
view
becomes almost a single shade of gray.
In
the second case, it may be very difficult
to extract the shapes unambiguously. Indeed, many forms of data are "cloudy" in
nature, and any attempt
at
shape extraction may destroy the data. In the case of
medical tomography, the added dangers of manipulating the data are obvious.
3.2.3. Lack of Vertical Parallax
A major disadvantage of holographic stereography
is
the lack of vertical
parallax in the image. With the recording system described, the perspective in each
strip hologram
is
fixed.
In other words, the observer cannot look over
or
under
foreground objects. This can be a serious limitation for the display of scientific data.
It
is
possible to extend the technique to produce full parallax, but the number
of frames required becomes tremendous, and the technique becomes impractical.
For
example if 200
views
are used for a single parallax stereogram, then 40,000
will
be required for the corresponding
full
parallax recording.
Because the normal holographic stereogram
is
single parallax, it
is
ideally
suited
to
white-light display in a rainbow format.
3.2.4. Using a Spatial Light Modulator
(SLM)
In the above procedure the perspective images are first recorded onto a
photographic material which has
to
be
processed and then placed in the master
recording rig. Apart from the lengthy process, the
film
transport for recording and
displaying the images must be pin registered, because the smallest misregistration
will
be visible in the final hologram. Furthermore, it
is
impractical to automate
the above procedure because of the many mechanical steps involved. A great
improvement would
be
to have a system in which the images are projected directly
272 KAVEH
BAZARGAN
from the computer. There are different ways of achieving this,
but
in general what
is
needed
is
a spatial light modulator (SLM). This
is
a 2D screen that changes in
transparency in response to an external signal (usually electrical). An example of
an
SLM in common use
is
the liquid crystal screen display on some portable
computers. Most such SLMs do
not
have the required resolution and contrast ratio
for use in recording stereograms, but, fortunately, SLM research and development
field
is
currently very active, and some of the high-end products can produce very
high quality images.
3.2.5.
Multicolor
Images
Most computer systems designed for serious 3D modeling and rendering work
in several colors.
It
is obviously desirable to use these colors in the stereogram.
Most techniques of color holography can readily be extended to stereograms.
Again, there are many different techniques available (Bazargan, 1983; Hariharan,
1983; Walker and Benton, 1989),
and
the detailed explanation
is
beyond the scope
of this chapter.
3.3. Volumetric
Multiplexing
We now come to the technique which
is
perhaps the most suitable for tomo-
graphic data. Like holographic stereography, this technique relies on combining
a number of 2D
data
sets to produce a composite 3D holographic image. The
difference
is
that in the case of volumetric multiplexing the 2D
data
sets are not
views of the whole object, but slices through it
(Hart
and Dalton, 1990; Johnson
et a/., 1982; Keane, 1983). These slices may be tomographic data. Let
us
first look
at
the problem of image understanding in 3D tomographic data:
3.3.1. Image Understanding in 3D Tomographic Data
When a set of tomographic slices are placed side by side, the brain finds it
difficult to deduce shapes
or
3D patterns except for the very simplest of data sets.
The obvious solution
is
to reorder the slices into the original 3D shape. This could
be done, for example, by forming a transparency from each slice and physically
mounting them in correct relation to one another. Apart from the inconvenience of
building a cumbersome structure, the opaque areas on the front slices tend to
obscure the back slices, and only a
few
slices can be accommodated usefully. This
is because such a physical structure
is
a "subtractive" system.
In
other words the
dark areas absorb ambient light, and the light areas transmit.
In
a volumetrically
multiplexed hologram, the dark areas are "voids," and the light areas are analogues
to sources of light, so there
is
no "hiding" of the back slices by the front ones, and
all the information
is
visible simultaneously.
The tomographic data are in no way altered, and all the original data are
recorded in the hologram. This
is
especially important in the case of medical data.
Other 3D display techniques, including most computer rendering techniques and
stereography, have to make a priori assumptions about the
data
in order to create
different perspective views. Usually this involves looking for 3D surfaces in the data
HOLOGRAPHIC DISPLAY OF
3D
DATA
273
and removing hidden surfaces. The problem
is
that much tomographic
data
cannot
be reduced to a set of surfaces, and any attempt to treat the
data
as such may
distort it.
3.3.2. Recording a Volumetrically Multiplexed Hologram
Figure
14
shows the basic arrangement for recording a volumetrically multi-
plexed hologram. The projection system
is
identical to the case of holographic
stereograms, with the different "frames" recorded on a
film
strip. The moving part
in this arrangement
is
not a narrow slit, but the projection assembly.
As
each slice
of the image
is
projected onto the screen, the screen and the projection system are
moved towards
or
away from the hologram to a position corresponding to that slice.
(If
a collimating lens, such as a large Fresnel lens,
is
placed just before the projection
screen, then it
is
possible to move only the screen and keep the projecting assembly
fixed.)
All
the component holograms are recorded onto the same area of the plate,
so each area of the plate has many different fringe patterns superimposed.
When the composite hologram
is
illuminated by a reconstruction beam, all
component holographic images are simultaneously reconstructed, each slice of data
in its correct relative position in space. The effect
is
that the brain reconstructs the
original 3D object using the depth cues present.
It
is
clear that this method
is
ideally suited to the display of tomographic data, as such
data
can be used almost
without modification.
As
in previous cases, it
is
convenient to produce a white-light-viewable version
of the composite hologram. This can be done by following the procedure for
recording image-plane holograms as described above. Figure
15
shows the setup for
transferring the image.
3.3.3. Using Photographic Transparencies
The simplest way to project the 2D images onto the screen
is
to photograph
the images consecutively, directly from the monitor. The
film
used should be a
Reference
beam
'Slice'
of
image
FI
G U R E 14. Recording a volumetrically multiplexed hologram.
274
Composite
image
KAVEH
BAZARGAN
FIGURE 15. Recording a white-light-viewable volumetrically multiplexed hologram.
positive transparency, either color
or
monochrome. One problem that must be
addressed carefully
is
that of registration. It
is
essential that the 2D images be
recorded in correct registration to one another. The best way to achieve this
is
to
ensure
that
in all the steps involved in the recording and projection of the images
the frames are registered. The monitor displaying the images must be fixed with
relation to the camera. Furthermore, the camera must have a pin-registration
mechanism
so
that each frame
is
in register with the sprockets
or
with some other
physical mark
on
the
film.
(There are commercially available
35
mm cameras with
pin-registered backs.)
When recording the composite hologram, two approaches can be taken to
projecting the images onto the diffusing screen: the transparencies can either
be
mounted in conventional slide mounts
or
they can be left in the form of a
film
strip.
In either case, it
is
essential that the frames are projected in registration to one
another.
If
the slides are mounted, then a slide projector can be adapted so
that
a
laser
is
used to project the images rather than the normal projection lamp. Only a
few
commercially available projectors can be used for this purpose, as most cannot
project with repeatable positional accuracy. It
is
also an advantage to choose a
projector that can
be
interfaced to a computer so that the whole procedure can
be
automated.
The contrast of the holographic image
is
invariably reduced because of
unwanted noise in the recording and reconstruction stages, so it
is
important that
the quality of the original transparencies be high. It
is
usually best to increase the
contrast in the transparencies in order to offset the noise in the final hologram. This
can
be
achieved
by
adjusting the monitor
or
using a high-contrast film-processor
combination.
3.3.4. Using a Spatial Light
Modulator
As
in the case of holographic stereography, the photographic stage can be
eliminated
by
using a suitable SLM to produce the 2D sections directly from the
HOLOGRAPHIC DISPLAY
OF
3D DATA 275
computer. At present, transmitting
LCD
panels are the best types of SLMs
available for this purpose. The most important parameter
is
the contrast ratio of
the LCD panel (the ratio of the transmittance of the transmitting to the opaque
pixels.)
3.3.5. Other Practical Considerations
The importance of positional stability in any form of optical holography
cannot be overemphasized.
It
is
essential that specialized vibration isolation units
be used. Homemade tables can also be used for such vibration isolation. The details
of such devices
is
beyond the scope of this book, and the reader
is
referred to any
standard practical book on holography.
For
practical reasons, it
is
best to control the whole process of recording by
interfacing the laser (or shutter),
film
projection unit, and the moving platform to
a microcomputer.
3.3.6. Depth Cues Available
Each recording in a volumetrically multiplexed hologram
is
a conventional
laser transmission one, with the whole of the recording plate exposed.
All
the depth
cues are therefore present, including accommodation which
is
absent in holographic
stereography. When the composite image
is
viewed, the brain can therefore perceive
the 3D data and extract shape information even with complex, irregular data. The
limitation of single parallax
is
not present, and the observer can freely look around
and over foreground objects.
3.3.7. Limitations
of
Volumetric Multiplexing
Let
us
look at some of the inherent drawbacks in using this technique.
An
important consideration
is
the absence of hidden-surface removal. In other words,
nearer slices cannot obscure back ones.
As
the slices are recorded sequentially
and independently, there
is
no mechanism for effecting hidden-surface removal.
Although this can be a distinct advantage for medical data, it
is
a serious drawback
for CAD applications.
The number of exposures that can be made on a single recording plate
is
not limitless. In general,
as
the number increases, the brightness of the composite
image (diffraction efficiency) decreases, and the unwanted background intensity
(noise) increases. The maximum number that can be combined depends on the
characteristics of the recording medium, the maximum noise tolerable, and, to some
extent, on the type
of
data.
It
is
certainly possible to obtain useful images with
100
exposures (Hart and Dalton, 1990). One simple method of increasing the effective
number of exposures
is
to distribute them among several holograms and then
to
use
these holograms to record the final composite one (Johnson
et
al., 1985).
For
example, if
500
data
slices have to
be
recorded, exposures 1 to
50
could
be
made
on the first plate,
51
to
100
on the second, and so on. The images from the
10
multiply exposed holograms could then be transferred to the final hologram. The
276 KAVEH BAZARGAN
clarity of the final image would be better than if 500 exposures were made onto the
sample plate. This process
is,
of course, rather tedious and
is
difficult to automate.
Another problem
is
that equal exposure times given to all slices does not result
in equal brightness. The earlier exposures tend to come out brighter (Bazargan
et
a/.,
1988; Johnson et al., 1985; Kostuk,
1989;
Kostuk et
a/.,
1986). This can be
corrected
by
gradually increasing the exposure through the series of recordings.
4.
CONCLUDING REMARKS
The technique of volumetric multiplexing
is
ideally suited to the reconstruction
of 3D images from a set of tomographic 2D images. The technique does not interfere
with the original data, and the 3D image produced contains the
full
set of depth
cues. This means that a large amount of information
is
available for the brain to
understand the data. The hologram produced
is
a kind of 3D hard copy
that
can
be viewed
at
leisure, without the need for sophisticated equipment.
It
can
be
kept
conveniently with the patient's notes and need not be handled with any special care.
Current improvements in laser and
LCD
technology
i&
making the technique
more readily available and more reliable.
REFERENCES
Barnard, E. (1988).
Optimal
error
diffusion for computer-generated holograms.
J.
Opt. Soc. Am. A
5:1803-1817.
Bazargan, K. (1983). Review of colour holography, in Proc.
SPIE
391
(S.
A.
Benton, ed.), pp. 11-18.
Los Angeles, CA.
Bazargan,
K.
(1985). A practical, portable system for white-light display of transmission holograms
using dispersion compensation, in Proc. SPJE 523 (L. Huff, ed.), pp. 24-25. Los Angeles, CA.
Bazargan, K. (1986). A new
method
of
colour holography, in Proc.
SPIE
673
(1.
Ke
and
R.
1.
Pryputniewicz, eds.), pp. 68-70. Beijing, China.
Bazargan, K., Chen,
X.
Y.,
Hart,
S.,
Mendes, G.,
and
Xu,
S.
(1988). Beam ratio in multiple-exposure
volume holograms.
J.
Phys. D: Appl. Phys. 21:S160-S163.
Bazargan, K.
and
Forshaw, M.
R.
B.
(1980). An image-plane hologram with non-image-plane motion
parallax. Opt. Comm. 32:45-47.
Benton,
S.
A.
(1969). Hologram reconstructions with extended incoherent sources.
J.
Opt. Soc. Am.
59:1545-1546.
Benton,
S.
A.
(1978). Achromatic images from white-light transmission holograms.
J.
Opt. Soc. Am.
68:1441.
Benton,
S.
A.
(1982). Survey of holographic stereograms, in Proc.
SPIE
367 (J.
J.
Pearson, ed.),
pp. 15-19.
Brown,
B.
R.
and
Lohman,
A.
W.
(1966). Complex spatial filtering with binary masks. Appl. Opt.
5:967-969.
Burckhardt,
C.
B.
(1966). Display of holograms in white light. Bell. Syst. Tech. J.45:1841-1844.
De
Bitetto, D. J. (1966). White-light viewing
of
surface holograms
by
simple dispersion compensation.
Appl. Phys. Lett. 9:417-418.
De Bitetto, D.
J.
(1969). Holographic panoramic stereograms synthesized from white light recordings.
Appl. Opt. 8:1740-1741.
Denisyuk,
Y.
N. (1962). Photographic reconstruction of the optical properties of an object in its own
scattered radiation field.
SOV.
Phys. Dokl. 7:543-545.
Hariharan, P. (1983). Colour holography, in Progress
in
Optics
20
(E. Wolf, ed.) North-Holland,
Amsterdam.
HOLOGRAPHIC
DISPLAY OF 3D DATA 277
Hariharan,
P. (1984). Optical Holography. Cambridge University Press, Cambridge.
Hart,
S.
J.
and
Dalton, M. N. (1990). Display holography for medical tomography, in Proc.
SPIE
1212
(S.
A.
Benton, ed.), pp. 116-135. Los Angeles, CA.
Johnson,
K.
M., Armstrong, M., Hesselink, L., and
Goodman,
J.
W.
(1985). Multiple multiple-exposure
hologram. Appl. Opt. 24:4467-4472.
Johnson, K. M., Hesselink, L.
and
Goodman,
J.
W.
(1982). MultIple exposure holographic display
of
CT
medical data, in Proc.
SPlE
367, pp. 149-154.
Keane,
B.
E.
(1983). Holographic three-dimensional
hard
copy for medical computer graphIcs, in Proc.
SPlE
361 (E. Herron, ed.), pp. 164-168.
Kostuk,
R.
K.
(1989).
Comparison
of
models for multiplexed holograms. Appl. Opt. 28:771-777.
Kostuk,
R.
K.,
Goodman,
J.
W.,
and
Hesselink,
L.
(1986). Volume reflection holograms with multiple
gratings: an experimental
and
theoretical evaluation. Appl. Opt. 25:4362-4369.
Leith,
E.
N.
and
Upatnieks, J. (1964). Wavefront reconstruction with diffuse illumination
and
three-
dimensional objects.
J.
Opt. Soc. Am. 54:1295-1301.
Lin, L.
H.
(1969). Hologram formation in hardened dichromated gelatin films. Appl. Opt. 8:963-966.
McCrickerd,
J.
T. and George, N. (1968). Holographic stereogram from sequential component
photographs. Appl. Phys. Lett. 12:10--12.
Paques, H. (1966). Achromatization
of
holograms. Proc.
IEEE
54:1195-1196.
Rotz, F.
B.
and
Friesem,
A. A.
(1966). Holograms with non-pseuedoscopic real images. Appl. Phys. Lett.
8:146-148.
Shankoff,
T.
A.
(1968). Phase holograms in dichromated gelatin. Appl. Opt. 7:2101-2105.
Syms,
R.
R.
A.
(1989). Practical Volume Holography. Oxford University Press, Oxford.
Walker, J. L.
and
Benton,
S.
A.
(1989). In-situ swelling for holographic color control, in Proc.
SPIE
1051
(S.
A.
Benton, ed.), pp. 192-199. Los Angeles, CA.
