Are they really "holograms?"                          W. Beaty 1997





Here's why I call these images "holograms" 

In conventional "white light" or "Benton Rainbow" holograms, each point on
the photographed object generates a particular interference pattern on the
film.  This interference pattern is the basic "pixel" of the hologram.  A 
Rainbow Hologram of a single-point object looks roughly like this:

    ||||||//////====----====\\\\\\||||||

In reality the little lines are thousandths of a mm apart, and are
smoothly curved.  However, the entire "swatch" of interference fringes on
the film plane might be several mm wide and a fraction of a mm tall.  
It's similar to a small slice of the bullseye pattern in a Gabor zoneplate
lens.  The many points on the object become little horizontal swatches of
interference fringes on the film.  The long rectangular profile of the
"swatch" is produced by the slit aperature used in the one-step rainbow
hologram process.

Imagine that a Rainbow hologram is made up of thousands of these "pixels"  
layed atop each other.  The X,Y position of each "pixel" corresponds to
the X,Y position of each object point.  For example, if you could stamp
the above interference pattern in many places on your film, you'd have a
rainbow hologram of a field of stars (but each star having the same depth
virtual depth within the film plane.)

The depth information for each image point is encoded as the overall size
of the "single pixel" interference pattern:  an image-point which
reconstructs as being deep within the hologram will have a "pixel" with a
large width and with long-radius, slightly-curved fringes, while a shallow
point will have a tiny "pixel" and small-radius fringes.  So a Rainbow
hologram is very similar to a standard 2D photograph in structure, but
instead of pointlike pixels, it has various sizes of swatches of
interference fringes which store the depth info for each recorded point.

The above crude figure implies something interesting: depth information is
only stored in the ANGLES OF THE SMALL FRINGES, and not in their spacing.  
If we observe a Rainbow hologram under laser light and under sunlight, we
find that both types of light will reproduce the holographic image, but
the sunlight creates rainbows.  The fringes cause the diffracted image of
the sun to be spread into a stripe of rainbow colors which will be seen as
a virtual image within the horizontal "slot" comprising each
"single-pixel" fringe pattern.  Other than this rainbow-colored artifact,
the holographic image is not affected by changes in illumination
frequency.  A rainbow hologram, within limits, is a frequency independent
hologram.

Frequency independence implies size independence (size being the spacing
between interference fringes on the film plane.) In other words, if the
Rainbow Hologram operates correctly with a wide variety of illumination
frequencies, then the Rainbow Hologram should still operate correctly even
if the fringes were spaced MUCH more widely than the wavelength of the
illuminator.  Huh?  Really?  Yes.  If we double, or triple, or quadruple
the fringe spacing of the interference pattern, THE HOLOGRAM STILL WORKS.  
Very strange.  And it leads to something wonderful.  If the following
pattern was scratched by hand into a sheet of plastic:

    ||||||//////====----====\\\\\\||||||

...it would create a little glowing dot which floats inside the plastic as
a virtual image. It would be a Rainbow Hologram "single pixel", but with
absolutely gigantic interference fringes.  They wouldn't even be
interference fringes anymore, and optical interference would no longer
apply.  Yet the hologram would still function.  Holography without
interference.  (Pretty easy to generate with a computer, eh?  Hint hint!)

To recap, here is what we do: we take the "single pixel" stripes of a
Benton Rainbow hologram, square off the sinusoidal fringe pattern,
increase the distance between the fringes by several orders of magnitude,
and lower their duty cycle so they appear as single thin lines with wide
spaces between them.  In terms of interference, we would find that the
"rainbow" artifact would acquire numerou overlapping copies of itself
(higher-order beams produced by the square, nonsinusoidal fringes), and as
the fringe spacing was enlarged, the multiple copies of the rainbow stripe
would compress together into a glowing stripe of white light.  The
"rainbow" would be gone, it would have turned white, yet the rest of the
hologram still functions as it originally did, it still creates the same
3D scene.

Another person points out that "scratch holograms" cannot reconstruct 
opaque objects, therefore they are not true holograms.  Wrong!  Scratch-
holograms have no trouble with opaque objects.  I've drawn images of black 
objects against deeper objects, and images of transparent apertures in 
opaque plates which reveal larger, deeper images seen through the "hole."

The particular geometry of Benton's Rainbow holograms allows anyone to
draw the fringe patterns by hand with a needle, and to thereby create
"holographic" images without lasers and even without interference.  This
can be taken to ridiculous lengths: giant "holograms" composed of curved,
polished metal rods become practical.  The metal rods are the interference
fringes!

It is not strictly necessary that the above horizontal swatch of
interference pattern be exactly duplicated in order to produce a hologram.  
When the fringes have been widely separated they stop interacting, so an
individual "fringe" can replace the multiple-fringe pattern.  A
conventional hologram's pattern of nested hyperbolic fringes can be
replaced with a single curved reflective fiber or surface scratch.  It
need not even have a hyperbolic shape, a circular scratch drawn with a
compass makes a dandy "hologram diffraction grating."

I've been drawing holograms of simple 3D objects by scratching a polished
plastic plate by hand with a compass.  The X,Y position of the scratches
determines the X,Y position of the reconstructed image points, and the
radius of each scratch determines the perceived depth of the image point.
It's akin to needlepoint knitting, since images must be built up from
hundreds of brightly glowing dots.  It takes quite a bit of labor to
produce a simple image such as a piece of holographic text, or a 3D
polyhedron.

So far I've drawn such things as polyhedra, starfields, text at various
depths, opaque planes which hide text behind them, boxes with walls
composed of random dots, etc.  When lit with an extended source these
"holograms" appear as sets of fine curved scratches, somewhat like several
superposed LP record albums.  When illuminated by a point-source, each
scratch produces a small "highlight," and the whole set of scratches
produces a 3D object composed of bright highlight points. 

See, scratch holograms ARE real holograms.  Nyaa-nyaa, tol ya so! <grin!>

BUT ARE THEY REALLY?

  I've received email which points out that conventional holograms store
  phase information as the spacing between diffraction fringes on the
  film plane, while "scratch holograms" do not.  This is correct. 
  The authors then use this fact to argue that "scratch holograms" are not
  holograms.  This is incorrect, because conventional Benton Rainbow
  Holograms don't use phase either.  That's why they can still operate
  under white light illumination. The spacing of their interference
  patterns is unimportant, it only affects the colors of the rainbow
  artifact.  If "scratch holograms" are not holograms because they do not
  record the phase of the light waves, THEN WE ARE FORCED TO SAY THAT THE
  RAINBOW HOLOGRAMS ON CREDIT CARDS AND ELSEWHERE ARE NOT HOLOGRAMS
  EITHER.  Such an assertion would be silly.  Therefore I jump on the
  coat-tails of Rainbow Holography and claim that if Rainbow Holograms are
  holograms, then so are "scratch holograms." 

  Other writers point out that "scratch holograms" are like conventional
  photographs in that the hologram itself does not preserve the phase 
  of the illuminating light source, and therefore they are not holograms.  
  This is wrong.   Mirrors preserve the phase of reflected light.  So 
  do the interference patterns of conventional Rainbow holograms.  So do 
  cylinder lenses and shiny fibers.  And so dd the scratches of "scratch 
  holograms".  They are astigmatic, preserving the horizontal phase 
  (and the horizontal parallax) while scrambling the vertical phase.  
  Each scratch in a "scratch hologram" acts as a tiny cylindrical mirror, 
  and it reflects light like a flat mirror in one dimension while 
  scattering light in the other.  As a result, both rainbow holograms and 
  "scratch holograms" only have horizontal parallax, and the 3D effect 
  will vanish if they are turned sideways.  Their horizontal parallax 
  depends upon their ability to preserve horizontal spatial phase of the 
  illuminating light source.  It's like looking into a curved, slit-shaped 
  mirror.  We see a virtual image of the illuminating source, and since 
  the illuminator is a point source, we see a glowing dot which floats 
  either behind or before the plastic surface.

WHY THESE ARE NOT TRUE HOLOGRAMS

So, can "scratch holograms" reconstruct any arbitrary scene?  They do go
with glowing points on a black background, but what about textured
surfaces?  GOOD QUESTION.  The "scratch holograms" cannot reconstruct an 
image shaped like a horizontal line.  A horizontal array of closely-spaced 
object points creates an array of scratches which interact with each other 
terribly, producing artifacts.  The resulting virtual image does not 
resemble a horizontal line, instead it becomes a fuzzy mess distributed at 
multiple depths.

The cause is simple:  if we "rubber stamp" some single-pixel holograms 
onto a recording medium, we do not create a hologram of a multi-pixel 
object.  The scratches interact (overlapped scratches destro one another.)  
In addition, there is phase information missing, information produced by 
light from closely-spaced object points.  Remember that "object light" 
does not just interfere with "reference light" during the holographic 
recording process.  "Object light" also interferes with itself.  In a 
Rainbow Hologram this effect is minimized when object points are oriented 
vertically from one another, but for object points oriented along a 
horizontal line, the self-interference of light coming from the object is 
crucial for holographic recording and reproduction.

The upshot: scratch holograms lack one big feature of true holograms, and
as a result they cannot reconstruct close-spaced horizontal arrays of
object points.  They do best with objects which resemble vertical or
diagonal lines against a dark background.


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William J. Beaty                                  SCIENCE HOBBYIST website
billbeskimo.com                                  amasci.com
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