In 2000 I wrote about “opacity holograms” — a way to encode a large number of two-dimensional input images into two images such that just by passing light through them both in different directions, you can reconstitute any of the original input images, using only geometrical optics (i.e. no wave mechanics.) The naïve approach to this involves a reduction of N× in both resolution and brightness for N input images: e.g. for 100 input images you take a hit of 99% of the original input light intensity. I think it’s possible to do better than that, maybe even as far as the √N that real interference holograms get, but I haven’t figured out how yet.
The naïve approach is something like this: on one sheet of film, leave one transparent pixel in the center of each 10×10 pixel square; now lay this atop another sheet of film on a lightbox. The upper “grille” will leave visible one out of every 100 pixels in the lower sheet, and by sliding it one pixel up, down, left, or right, you can select one of 100 different “pages” of information. It’s probably more practical, as I wrote in 2000, to permanently mount the “grille” and the interleaved image on opposite sides of a sheet of glass.
One possible use of this is for archival information storage. One of the problems confronted by the design of artifacts like the Rosetta Project’s Rosetta Disk is how to make the archived information retrievable without advanced technology like a computer. (Presumably if computers survive, then so will computerized archives of our current information.) The unhappy compromise adopted by the Rosetta Project is to require the reader to have a 650× microscope.
If your film is printed on a 1200dpi laser printer, then each of the 100 interleaved pages of information has 120dpi available to it — more than enough for crisp, readable text. In the roughly 3½×6 pixel font I designed for laser-printed microfilm and shown in http://canonical.org/~kragen/bible-columns, you’ll have 20 lines of text per vertical inch (rather than the usual 6: effectively, a 3.6-point font), moderately readable to the naked eye; roughly ten thousand words on a page, a dozen times the usual areal density. The 100 pages together are roughly a million words, or a bit longer than the Bible — on a single page. And since each page is potentially full color, you can do better still by encoding separate monochrome images in red, green, and blue color channels: 3600 pages of text, readable with the naked eye and a color filter, printable on a single pair of pages with a regular laser printer. With a high-resolution printer, you might be able to get more.
I suspect that you can do better than this naïve approach by jointly optimizing the two opacity images of the “grille” and “interleaved image”, but I don’t know how much better.
How much separation can you get? Ideally you’d like to spread out the 100 pages (or however many you can get) over as much solid angle as you can, so that, for example, you don’t have to be a precise distance from the page to see a single image, you don't switch images when your eye saccades (moving your pupil a few millimeters), and you see the same image from both eyes. Let's figure that the maximum angle you want to have to turn the page from looking at it straight on is 60°, because at that point you've visually squished it by a factor of 2, and more than that will impede readability. So you have 120° of angle that you need to divide into 10 increments, thus 12° each. So you want a single-pixel displacement between the two sheets (1/1200 inch, or 21 microns) to correspond to 12°, which means you want the distance between the sheets to be effectively about 1/sin⁻¹(12°) ≈ 5× that 21 microns: 105 microns, about a tenth of a millimeter. This is assuming no refraction; the refractive index reduces the necessary thickness, and also linearizes the displacement a bit, so that the nonlinearity of arcsin becomes less significant.
You need to make sure your pixels are big enough that geometrical optics is a good approximation, which is to say that the pixels need to be a lot bigger than the wavelength of light. 21 microns is sufficiently bigger than 0.7-micron red light, and there's room for another factor of 2 or 4 in there, which would be a factor of 4 or 16 in information density. But 2400dpi printers are a specialty item, and 4800dpi printers are only used for transferring CGI imagery onto movie film, so they are much less accessible.
Alternatively, you could accept lower resolution per encoded page (and lower light levels) in exchange for more encoded pages by making the grille holes sparser. This won't increase the number of words encoded, because the font size has to be bigger, but it may make the text easier to read by making it larger. Perhaps a factor of 2 is available here.
Amazon has 100 sheets of laser-printable transparency film at half an inch thick, or about 130 microns thick, which is in the right ballpark. The extra thickness (and refractive index) reduces the viewing angle correspondingly, perhaps to 8° or so. At a reading distance of half a meter, that’s about 7 cm; so your two eyes will see different pages, but each eye will comfortably see a single image regardless of where it saccades to.
Amazon’s current price on this is US$19.32, or US$0.19 per roughly-A4-size sheet. The material is probably cellulose acetate, which is not archival-quality and will degrade within a century under most conditions, through a process known as the “vinegar syndrome”, which poses major problems for current archival collections. It also has a refractive index of about 1.5.
The archival-quality substitute seems to be the now-discontinued Type D Mylar film or Melinex 516 or other equivalent PET film, which you can apparently etch with carbon tetrachloride to get it to take inkjet ink. Amazon has what appears to be inkjet-printable Mylar at 36" × 125' at 4 mil thick (216μm) for US$175, but I don’t know if it’s archival. Archival (but possibly not easily printable) Melinex 516 is available from Talas at US$290 for a 2-mil (51μm) 60" × 250' roll, which is 116m² or 1862 A4-page equivalents, or US$0.16 per A4 page — comparable to the acetate. Mylar’s refractive index is about 1.65.
The Rosetta Disk is currently slated to hold 13 000 pages of language documentation, according to the project's home page at the moment, out of the 100 000 they have gathered. These 13 000 pages could be encoded on about two to six A4-sized transparency films. On 2-mil film, this would occupy about 3–9 milliliters.
The whole 100 000 page collection is available for download from the Internet Archive. This would be eight times as large: 25 to 75 milliliters, 16 to 50 sheets.
The first edition of the Oxford English Dictionary is slightly larger; the English Wikipedia’s selection of 1000 “Vital Articles” is similar in size.