William Beaty’s scratch holograms can be extended using dithering and noncircular scratch paths to support arbitrary movement and brightness change, with artistic and archival applications.
A piecewise-linear interpolation of scratch direction and density over a surface will give rise to nonlinear and, in general, noncircular scratch paths; this may be feasible to fabricate using disorganized abrasive embedded in a soft matrix, such as a piece of felt or rubber, which is moved in several passes over the surface to scratch. Due to the elasticity of the matrix, displacements of the matrix parallel to the surface vary the amount of pressure transmitted through the abrasive to the surface, and this varies the scratch density (number of scratches and average scratch width). Spatially varying this perpendicular displacement throughout the matrix, which is to say holding it slightly nonparallel to the surface, will result in a spatial scratch density gradient on the surface; temporally varying the displacement will also result in a spatial scratch gradient, but along the direction of movement. Both techniques can be used in concert to maximize scratch density gradient sharpness by moving the matrix parallel to the matrix. Nonparallel movement will blur the gradient, which may be desirable to prevent the faithful reproduction of mechanical errors such as unwanted vibration. Moving the matrix along an in-general-nonlinear path without rotating it will result in the scratches from a given point in time all being parallel, like the parking-lot floating polishing glove image mentioned in Beaty’s original notes, but rotating it around an axis more or less parallel to the surface will cause the scratch paths from one side of the matrix to the other to vary in both direction and radius of curvature.
By combining these gradient effects, it should be possible to rapidly fabricate scratch holograms that reproduce an arbitrary continuously-varying set of monochrome images to fairly high precision when viewed or illuminated from different angles; this goes beyond merely fabricating a hologram of a single physical object viewed from different angles and includes, for example, arbitrary animations, though animations with only a single (possibly cyclic) temporal dimension.
If the matrix is not soft, being for example steel or pitch, the perpendicular displacement directly controls scratch depth and density, rather than indirectly through pressure. This requires more precise positional control.
Randomly positioned abrasive is not the only thing that could be used this way. A single-point cutting or forming tool could also be moved over the workpiece in a controllably curved path by an analogous mechanism: mounted on a wheel whose rotation angle is precisely controlled as a gantry or other two-degree-of-freedom mechanism moves the wheel’s center over the work. (A hardened-steel glass-cutting wheel might make an adequate tool for forming lines in the surface of a softer metal, or cutting them in glass.) A series of regularly spaced points would also work; for example, you could use the edge of a saw blade held nearly parallel to the workpiece surface, controlling the angle and curvature of the blade as you drag it over the surface to scratch it, using a six- or seven-degree-of-freedom control mechanism. And you might be able to use a rotary brush of aluminum-oxide-particle-impregnated nylon — either rotating around an axis parallel to the surface to make straight scratches at a given angle, or even rotating non-parallel to the surface to make elliptical scratch arcs.
More highly reflective surfaces, such as metals, are of course more desirable. Grinding copper flat, then electropolishing it, then engraving the hologram with abrasive, then plating it in silver, chrome, or nickel, should enable very high contrast ratios. Aluminum might be easier to form. Glass is in some ways the optimal material, having no grain size or work-hardening to worry about, but getting it to be highly reflective requires some kind of silvering process, nowadays typically by vacuum sputtering. If this is not done, objects on the other side of the glass may be clearly visible, and for some applications — such as superimposing a sort of hardcopy alternate reality view on an object, for example for measurement purposes — this could be desirable.
Metallic media can perhaps be mass-duplicated by electrotyping, but molding, as is done for vinyl phonorecords or diffraction gratings from the Grating Lab, is probably a better process. The molded reproductions can then be silvered through sputtering, as gratings are.
By adding color filters over the surface, ideally after scratching, some color should be possible, although it means that scratch density needs to vary in phase with the color-filter variation to get color, which requires much higher spatial frequencies than would otherwise be needed, thus substantially increasing fabrication time. The R-G-B-G checkerboard used in modern digital cameras might be ideal in some sense, but using parallel strips (either R-G-B-G, R-G-B, or R-G-B-W as in some modern LCDs) would reduce the scratching problem. If the surface is titanium, chrome, or stainless steel, iridescent oxide layers may be an adequate way to apply color filters.
At the extreme of soft materials, it should be possible to produce most of these effects in a film of oil or grease on a smooth surface, such as glass or PMMA, without using abrasives or cutting tools at all; a soft rubber squeegee is adequate. Such a temporary hologram might serve as a frame of an animated display or as a temporary hardcopy. In time the minimal surface tension of oil will erase the images.
It should be possible to apply these effects to more than one side of a polished metal polyhedron or convex curve to produce parallax-correct views of a three-dimensional object within, though with only a single dimension of parallax. The illusion will be that of seeing a luminous object within the polyhedron through the metal surface, as if it were merely a wire frame enclosing the object.
Of course the usual archival applications exist; by virtue of scattering light directionally, a scratch that is only half a micron in width and a few microns long becomes brilliantly visible from a certain angle. Under ordinary sunlight viewing conditions, a single sheet of material can encode some 300 different images at illumination angles differing by half a degree (180 degrees / ½ degree minus a safety factor), or perhaps more if the contrast-enhancement techniques in Analemma sundial are applied. Art-gallery viewing conditions, with a more directional light source than the sun and a background that is much darker than the blue sky, could permit many more images to be encoded.
10-micron household aluminum foil, shiny on one side, with 300 images encoded at 300 dpi and one bit per pixel, would provide archival bit density of 42 gigabits per square meter and 4.2 petabits per cubic meter with this approach; scaled down to the size of Paul Atreides’ Orange Catholic Bible, that’s 4.2 gigabits per cubic centimeter. But such a delicate medium as 10-μm annealed aluminum is difficult to handle without creasing it, and the electrostatic page-selection mechanism described in Dune is unfortunately probably not feasible outside of fiction.
The 100-μm forged aluminum used for drink cans can withstand rough handling, but it is surely overkill for this application. 30-μm aluminum flashing is probably adequate and can be polished on both sides. This would provide 2.8 gigabits per cubic centimeter.
By this method you could produce a book, readable with the naked eye in direct sunlight, safe to handle with bare hands, using inexpensive materials (but very expensive fabrication techniques), that will last millennia under reasonable archival conditions, which at 130 mm × 80 mm × 10 mm contains 290 gigabits of data, 36 gigabytes. If we want it to use normal lettering, we probably need about 3×6 pixels per letter at least, so that would be only 16 billion letters of text, about 3 billion words. This is about a third the size of English Wikipedia.
More aggressive specifications might use 600 dpi and 1200 images rather than 300, thus requiring a light four times more directional than the sun, such as a sunbeam entering an otherwise dark room through a peephole or vertical slit. This would enable sixteen times greater information density but would probably require a magnifying glass to read.
For mass production of such holographic archival devices, perhaps a plastic film could first be molded (as described above) out of an archival-safe thermoplastic such as PET, then silvered with aluminum in a vacuum.