Holographic archival

Kragen Javier Sitaker, 2014-04-24 (10 minutes)

I thought I'd written about this before, but I can't seem to find it in the archives.

The Rosetta Project wants to make an etched nickel-alloy disc with reduced-size images of some ten or twenty thousand pages, readable under a 650× optical microscope. They're using a process developed at Sandia based on microchip etching techniques — that is to say, microphotolithography.

This approach has a few significant drawbacks:

  1. It's extremely expensive. We're used to microchips being cheap, but in fact they cost several dollars each, and each of the Rosetta discs is like an entire wafer, not a single microchip. So we can expect the price per disc to stay in the hundreds to thousands of US dollars.

  2. You need a microscope to read it. It would be better if you could read it with no special equipment, or only very simple special equipment, such as could be easily improvised from rocks.

  3. The information capacity is limited by the wavelength of light. Pixels in the original image can't be more than about half a wavelength across for an optical microscope to resolve them: figure 250nm. That gives you a density of, at best, 16 terabits per square meter. With the 7.6-centimeter Rosetta disk, you only have 72 gigabits, not even enough for English Wikipedia in a readable font.

Suppose we could instead usefully encode archival information at a density substantially higher than a light wavelength, reproduce it cheaply, and read it without special equipment. That might produce a much more useful Rosetta disc.

I think that rainbow holography may provide this medium. Rainbow holograms have been inexpensively mass-produced since 1984; they can be viewed in sunlight; and their ability to encode many images in the same film is limited by the film resolution and the directionality of the light source.

Rainbow holograms can present a different image for each angle within an 180° viewing arc. The resolution of this image is degraded as more images from more angles are recorded, and the angle of the illumination and viewer are limiting factors in the number of angles. The degradation of the image is vaguely related in a way I don't understand to the square root of the number of images.

The illumination angle from the sun is the first problem: the sun subtends some 32 arcminutes, and without further work, this limits you to about 330 distinct images. This is about 1½ to 2 orders of magnitude worse than our objective. Fortunately, direct sunlight is excessive; it amounts to about 100klx, while people can read comfortably at 100lx, three orders of magnitude dimmer. If you go into a camera obscura with the holographic archival disc, illuminated by the sun shining through a vertical slit, you can obtain illumination that is much more directional and therefore allows you much more precision in imaging. You simply set the disc in the beam of light stretching across the floor from the slit in the wall.

The slit should, ideally, reduce the illumination by about three orders of magnitude from direct sunlight; but the illumination will vary across the beam, since the sides of the beam can only see the edges of the sun's disc, and will therefore be dimmer. If we try for a factor of 2 between the brightest and dimmest parts of the disc, then we want the points on the edge of the sun's disc at 30° above and below the horizontal, since sin 30° = ½. cos 30° ≈ 0.87, so we only lose about 13% of the sun's width this way, leaving us with a usable sun-disk width of about 28 arcminutes horizontally.

For a beam spreading out from a thin slit with a divergence of 28 arcminutes to illuminate a whole 7.6-centimeter-wide disc, the disc needs to be some 9.4 meters away from the slit, which makes for a pretty big camera obscura. Now, how wide is the slit? We want to see about a thousandth of the roughly 28-arcminute-wide sun through it. To see the entire 28-arcminute-wide chunk of the sun through it, it would be about 7.6 centimeters across; instead, it needs to be about a thousandth of that, or about 76 microns. That is, it would need to be about the width of a human hair, and at least some 10 centimeters tall, although ideally many meters tall. It doesn't need to be perfectly straight, but it can't deviate from the vertical by more than its width within the 10-centimeter-tall chunk illuminating the disk at any moment.

So that's probably a bit too stringent; it might allow us to put 330 000 naked-eye-viewable images on the disk, but only at the cost of the solar illumination mechanism being unreasonably finicky.

Suppose instead that we allow the slit to be a millimeter wide, which will also boost our light level from 100 lux to 1300 lux, which is quite comfortable. Now, at 9.4 meters, it subtends a 9400th of a radian, which means that the light can illuminate the disc from about 30 000 distinct angles. By rotating the edge of the disc 4 microns to the left or right, we can switch to the "next" or "previous" "page".

How about our eyes? If our pupils are too big, we may need to wear pinhole goggles, or peek through a finger pinhole, to see a single page instead of a mixture of several. If we're trying to read at a distance of one meter, so that we can reach the disc with our hands, then a 9400th of a radian is about 0.1 millimeters. Pupils only shrink down to about 3 to 5 millimeters, so such dense encoding would indeed require something like pinhole goggles; but rather than pure pinhole goggles, they can be vertical-slit goggles, which can probably be improvised adequately from rocks, sticks, etc.

Can we really interfere 30 000 distinct wavefronts and get an image of reasonable resolution and contrast? Supposing the "grain size" of the "film" is 50 nanometers and we're shooting for 100 dpi resolution, each of our 0.01" pixels contains about 5000×5000 grains. I'm vague on exactly how holography scales, but I'm pretty sure it can manage to encode a pixel each of 30 000 different images in 2.5 million grains.

So suppose we can get 30 000 frames at 100dpi on a disc in the form of rainbow holograms. How many pixels is that in total? 30000×π×(½7.6cm)² is an effective area of 136m², or 2 gigapixels. That works out to 465 gigabits per square meter. This is not nearly as good as the current Rosetta disc's microscopy approach, although it would still make the disc quite a bit denser than a book.

(Is there a limit in angular resolution resulting from the light itself? There must be: the light path length from the source to the hologram to the eye needs to differ by at least half a wavelength for a pixel to go from light to dark, right? At (half of) 500nm over a hundredth of an inch, we have an angle of about 1 milliradian, which is actually a much more stringent limit than the slit width thing: it would limit you to about 3100 frames.)

Non-rainbow holograms could get some three orders of magnitude higher storage density by using both dimensions, but as far as I know, can only be read under laser illumination. Perhaps you could get 500 terabits per square meter that way.

As for manufacturing, the common approach to manufacturing rainbow holograms is embossing: you nickel-plate the master hologram, then squish molten plastic against it, then take the now-shaped plastic off and plate it with something — typically aluminum, but nickel would work too, and probably last longer. (Remember, we're talking about millennia here.) Ideally you'd use entirely amorphous materials (glasses) to avoid noise due to crystal grain boundaries, entirely covalently bonded materials like SiO₂ for chemical stability and hardness, and thoroughly oxidized materials like SiO₂ for chemical stability and resistance to combustion. But producing a sufficiently shiny surface on glass (whether pure fused silica, borosilicate, soda-lime glass, or something else) might prove too difficult.

If your manufacturing cost is low enough and your material flexible and robust enough, then instead of a single disc, you could produce a codex. If you're storing some 500 gigabits per square meter, a hardback book consisting of 400 A5-sized pages could store 6 terabits in human-readable form.

For the case of holographic archival discs, you probably want to compute the original image, if possible, rather than attempting to produce it with thousands of interfering optical wavefronts. Bill Beaty's scratch holograms provide a practical way of doing this that wouldn't require computing trillions of grains in order to store billions of pixels. They also, like rainbow holograms, limit you to one direction of parallax motion.

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