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BRIEF VERSION: Benton's white-light 'rainbow' holograms employ size-independent fringe spacing. They employ no diffraction in reconstructing images, and they will still function if enlarged or reduced. A scratch hologram is essentially a Benton hologram greatly enlarged and with fringe count reduced. So, if scratch holograms aren't true holograms, then to be honest and consistent, Rainbow holograms aren't true holograms either. If the security holograms on your credit card are "holograms," then abrasion holograms are also "holograms." Heh, we can even say that: holograms don't require lasers; after all, D. Gabor's original discovery of holography occurred years before Lasers, and was based on monochromatic sodium or mercury light passed through a pinhole. (Conventional off-axis holograms require coherent light for image reconstruction, not lasers.)
First of all, be aware that diffraction gratings do not function
exclusively by optical interference. In addition to acting as
diffractors, all diffraction gratings are also mirrors: they are arrays
of parallel
line-scatterers. Because these line-scatterers (the fringes)
are spaced equally, only light scattered from certain angles is reinforced
while light from other angles is extinguished. But because the
fringes behave as
line-scatters, their orientation determines the angle of deflection of
the diffracted beams. If each long fringe did not behave as a coherent
mirror, then gratings couldn't aim the beam, and they'd diffract light
into a cone rather than into a pair of 1st-order beams. (This of course
is obvious, but it's so obvious that we might overlook it!)
Here's another way to say it. A diffraction grating can bend light with
TWO angles, both X and also Y deflection. One angle depends on
diffraction; controlled by fringe-spacing. The other angle depends
on grating rotation: it depends only on the angle of the ruled lines in
the grating with respect to the incoming light.
If we change the spacing of the grating's fringes, we can change the path
of the diffracted light, but if instead we ROTATE the entire grating
without
otherwise modifying it, we also change the path of the diffracted light,
but moved in a roughly perpendicular direction. The fringe spacing
controls the
"X-deflection," while the fringe angle controls the "Y."
This concept is important, since off-axis holography is not based only on
diffraction-bent light. In fact it
relies on BOTH effects: the angle produced by diffraction, and also the
angle of the deflection-vector which is perpendicular to the diffraction.
Some types of holograms (Rainbow holograms) don't employ diffraction at
all, but instead rely only on the fringe rotation angle; on the optics of
line-scatterers for producing 3D depth effects. They rely ONLY on the
angle of the gratings in the recorded zoneplates, and the spacing of the
fringes plays no role in forming their 3D images. The fringe spacing
could be totally random, and the holographic image would still appear.
(The rainbow-colored artifact would disappear, of course.)
And that's why Rainbow holograms can still create images even when illuminated by white light. Benton holograms are very different from conventional or "off-axis" holograms. The zoneplates of conventional holograms harness both the diffraction and the "line-scatterer" effects in order to create images. For this reason a monochromatic light source is critically important for conventional holograms. Or said another way: when reconstructing images, off-axis holograms are diffractive, while Benton Rainbow holograms are not. Here's why I call these images "holograms"
In reality the little lines are thousandths of a mm apart. For an illuminator at infinity, the lines are smooth parabolas with a sinusoidal density profile.
The lines are microscopic. 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. During production of a Rainbow hologram, the many
individual
points on the recorded object become little horizontal swatches of
interference fringes on the film. The long rectangular profile of the
above "swatch" is produced by the slit aperture used in the one-step
Rainbow hologram process.
Imagine that a Rainbow hologram is made up of thousands of these "pixels"
laid 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
hologram of a field of stars (but where each star has the same
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 hologram's 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 "stripe-window" comprising each
"single-pixel" fringe pattern. Other than this rainbow-colored artifact,
the holographic image is not strongly 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
wavelengths, then the Rainbow Hologram should also operate correctly with
a wide variety of fringe spacings. We could give the fringes random
spacing ...and the hologram would still work! We could increase the
fringe
spacing,
so higher order diffraction invaded the images... and the hologram would
still work. Changes to the fringe spacing only affect the rainbow-colored
artifact. The depth information and horizontal location of the
image is stored entirely in the orientation of the fringes.
What if the fringes were spaced MUCH more widely than the
wavelength of the illuminator? If we double, or triple, or quadruple the
fringe spacing of the interference pattern, the hologram still works If
we convert each fringe into an independent macroscopic line scatterer, 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 "single pixel" Rainbow Hologram, 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, it would still reconstruct a 3D scene. 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 we see in these holograms would acquire numerous overlapping copies of itself (each caused by higher-order beams produced by the square, nonsinusoidal fringes.) As the fringe spacing was enlarged, the multiple copies of the rainbow stripe would compress together into a single glowing stripe of apparently 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 employ the same geometry as genuine Rainbow holograms and they
have no trouble with opaque objects. Opacity is created by removing
certain portions of the zoneplate interference patterns (or portions of
the curved scratch.) I've drawn images of black opaque objects against
deeper objects, and images of transparent apertures in opaque plates which
reveal larger, deeper images seen through the "hole." Note the upper
hologram in the following photo, where an opaque black square floats above
a deep plane of glowing dots. There's a trick to it, but Benton's
holograms employ exactly the same trick.
In addition, a scratch-hologram can produce conjugate or "pseudoscopic"
images. Rather than lighting your scratch-hologram from above, light it
from below. The image will appear... but it will be inside out! If your
image was designed to float deep inside the plastic plate, now it will be
hovering in the air in front of the plate. A conjugate illumination beam
will convert a virtual image into a real image whether you're working with
conventional holograms or "scratch-holos."
Also, a scratch-hologram can function in transmission mode as well as
reflection mode, just like a conventional hologram. If you use clear
plastic rather than black plastic, you
can place your hologram between your eyes and a distant light source, then
find the holographic image.
The particular geometry of 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! Or imagine huge sheets of vacu-formed silvered plastic; like
greatly enlarged foil holograms taken from your credit card.
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. If some vertical and depth
distortions can be tolerated, then a circular scratch drawn with a compass
makes a dandy "hologram diffraction grating."
I've been drawing holograms of numerous 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 a nearby extended source
these
"holograms" appear as sets of fine curved scratches, somewhat like several
superposed LP record albums. When illuminated by a distant 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!
Other writers point out that "scratch holograms" are like conventional
photographs in that the film-plate itself does not preserve the phase
of the illuminating light source, and therefore they are not holograms.
This is simply wrong: the polished scratches do preserve horizontal
phase information. If they weren't specular, then the hologram wouldn't
function.
Remember that mirrors preserve the phase of reflected light. So
do the interference patterns of conventional Rainbow holograms. So also
do
cylinder lenses and shiny fibers. And so do the polished scratches of
"scratch
holograms". Eliminate the phase by painting the scratches white, and
you also eliminate the 3D depth effect.
True, "Scratch holograms" are
astigmatic, preserving only 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 produce 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 formed by
the curved mirror, and since
the illuminator is a point source, we see a glowing dot which floats
either behind or before the plastic surface.
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 destroy one
another.) In true holography the light waves add linearly, and one wave
does not block the effects of another. "Stamping" of complete zoneplate
patterns onto the plastic is not an additive process as it would be with
light-exposed emulsion. However there is a cure: divide the film-plane
itself into pixels, then move any overlapping scratches within each pixel
so they no longer overlap, but so they do not alter the 3D image by moving
outside their pixel boundaries. This allows the "scratch-holo" technique
to reproduce arbitrary scenes, rather than only being used for glowing
white lines on a dark background.
BUT ARE THEY HOLOGRAMS? The answer is a matter of opinion. Some people
don't regard Rainbow holograms as true holograms either. These "scratch
holograms" are even further away from the original off-axis holographic
technique of the 1960s. Yet they do include the arrays of line-scatterers
which all
holograms exhibit. And they do rely on coherent reflection of an
illumination beam, and so they absolutely require point-source
illumination, and cannot be used with extended light sources. Use of
extended-source illuminators causes severe depth-blurring in every sort of
holographic recording. Simply because "scratch-holos" suffer from the
same unique limitations as conventional holograms, that alone is enough to
declare them to be truly holographic.
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