A "frequency-doubling" crystal is able to absorb some of a particular wavelength of light, two photons at a time, and emit single photons that contain twice the energy and half the wavelength. A wide variety of such crystals exist.
We don't want those here, though. What we want is a slightly different type of crystal, called a "frequency summing" crystal. This crystal absorbs photons of two different wavelengths and adds their different energies together in emitting new photons. See the link on frequency tripling for an example of a frequency- summing crystal.
Here I will assume that an appropriately wide variety of frequency-summing crystals also exist. We are going to want three different types of them (all of them reasonably transparent to infrared and visible light).
Next, according to the linked Wikipedia article, the human eye responds to wavelengths of light from 390 nanometers (violet) to 700 nanometers (deep red). The article also shows some pretty good representations of the three the primary colors --blue, green and red-- as having wavelengths of 445, 532, and 635 nanometers, respectively.
So, with those colors as a good-enough starting point for what follows here, let us assume that our three different frequency-summing crystals can output light at one of those three wavelengths.
The visual fanatic may now consider the following construction: We assemble billions of tiny crystals into a significant-sized cube. Each tiny crystal is one "voxel" (a "volume pixel") of our 3D display; its size will be perhaps a quarter of a millimeter. So, if we want the display to have a resolution of 2048x2048x2048, then that is 8,589,934,592 voxel crystals, and the overall size of the display will be 1/4 of 2048 millimeters, or 512 millimeters, about half-a-meter on each side.
However, the preceding description left something rather important out. Normally one pixel of a regular 2D display can display any color; the above only outputs 1 color at each voxel. That means the actual resolution, in terms of full color, would be about 682x682x682 --we'd need to decrease the voxel size by 1/3, and use 3x3x3=27 times as many voxels as those more-than-8- billion above, to actually obtain 2048-cubed full-color resolution, in a half-meter overall cube.
So, let us consider a simpler way. Some 2D displays (Sony "Trinitron", mostly) used stripes of phosphor, not individual phosphor dots. Instead of 1 full-color pixel being made from 3 different-colored phosphor dots, 1 full-color pixel is produced when the horizontally- scanning electron beam crosses 3 adjacent different- colored vertical stripes. So, the equivalent for a 3D display would start by using thin "plates" of frequency- summing crystal. Each plate could be 512 millimeters square, and 1/12mm thick, and there would be 2048x3=6144 plates in the full-color stack, half-a-meter high.
Now we get to talk about the lasers. We want at least 4 and perhaps 6 of them; it depends on the exact properties of the chosen frequency-summing crystals in the stack just described above. Suppose that one laser outputs in the infrared at 710 nanometers; if all three types of frequency-summing crystals can use that as a "base" wavelength, then we need 3 more infrared lasers, such that one crystals adds one wavelength with base-of- 710 to produce 635 nanometers (red), another crystal adds the base-of-710 to the second wavelength to produce 532 nanometers (green), and the third crystal adds the base-of-710 to the third wavelength to produce 445 nanometers (blue).
If the crystals add all-different-wavelengths, then we will need 6 different infrared lasers, two-at-a-time, for producing each color of light.
Perhaps you can now see where this Idea is headed. Since infrared light is invisible, each laser beam can INDIVIDUALLY be invisibly passed through any part of the 3D crystal-stack with no effect. But if two beams intersect at an appropriate frequency-summing crystal plate, then that SPOT of the plate, where the beams intersect, will start absorbing and adding those photons, and glow with one color of visible light. Nowhere else will glow except that single monochrome voxel.
(Note this means you can't illuminate the whole crystal with, say 710-nanometer infrared light, and pass any other infrared laser through it, because you will get a visible line of light as the laser beam is summed with the background light, in its whole path through the crystal.)
Adjacent spots, in the neighboring crystal layers, can be illuminated by other pairs of lasers, to get a full-color voxel. And since the intensities of laser beams can be adjusted, so can we have different intensities of the different colors of the full-color voxel (allowing the same full-spectrum illusion as ordinary 2D color-monitor systems).
The 4 or 5 or 6 laser beams all need to be fully steerable, so that any spot in the overall crystal cube can be excited into glowing by absorbing light from an appropriate pair of infrared laser beams. You can now construct a true 3D image of glowing voxels. And since the glow stops as soon as the beams stop intersecting, you can also do full-motion video, provided the lasers can scan the whole crystal cube fast enough. (Or use even more lasers, and dedicate groups of them to different portions of the crystal block.)
The final factor to take into account is "refraction". As light passes through different substances at an angle, its path gets bent. We will need full information about to what degree these layers of frequency-summing crystals affect the path of the infrared laser light, as they scan through the crystal block at different angles. Signficant computer power is likely needed, to ensure that, at each voxel-location that we want to cause to glow, we actually get laser beams intersecting at that location.
(This effect could possibly be minimized by the appropriate selection of materials, but just in case we can't get 3 different frequency-summing crystals that all have exactly the same index of refraction for different frequencies of infrared light --the ideal case-- we need to be prepared to computationally compensate for different refraction indexes.)
======================== Added March 13, 2013 ========================
In the main text above I neglected to mention that the lasers probably should be located under the crystal cube. In theory this means the image created inside the cube would be visible from all sides, and from above the cube.
And since writing the main text, it has occurred to me that the index-of-refraction problem could be minimized with one simple and one not-so-simple change.
First, while a stack of crystal plates was described, it is not essential that that stack be oriented like a typical stack of pancakes. Four faces of the crystal cube will be associated with the edges of the crystal plates. One of those faces could be oriented downward. Now consider this ASCII sketch: _________ o | | | | o________
The sketch represents the mouths of two laser-aimers located at each end of the edge of one crystal plate (turned sideways, with body of plate at right). These two lasers would create beams that are no wider than that plate (about 1/12 mm, per the main text), and they are directed into that plate from that edge.
The aimers, of course, direct the beams into the edge of plate at a range of angles, such that with two aimers, the two beams can be caused to intersect anywhere in that plate.
This pair of lasers/aimers is dedicated to JUST this single plate in the stack. That would completely eliminate any index-of-refraction problem with respect to aiming a laser across multiple plates with different refraction indexes. So, only at this one place do we have to worry about how much the beams are refracted, as they first enter this plate.
With 6144 plates, we would like for there to be 6144 pairs of lasers, each pair associated with just one plate in the overall stack. That's the not-so-simple thing, of course. Each laser needs an aimer, see?
============ Added Sept 7, 2015 ============ In the annotations to this Idea is mention of the Law of Conservation of Momentum, and how it could cause the photons created inside this display to be visible in only one direction, relative to the display. I'm writing this to suggest a fix for that problem.
The fix begins by changing the construction of the display to include phosphors that are transparent to visible light (if any such thing exists). The different types of frequency-adding crystals can be changed to a single type. The output of the new crystals will be UV light. The phosphors will not be transparent to UV; they will absorb the UV, and emit regular light (different phosphors for red, green, and blue). The phosphors will be located inside the crystal at places specifically intended to receive monodirectional photons generated by nearby spots of the frequency-adding crystal. The main fact here is that phosphors radiate in all directions, thus solving the problem specified.
However, a new problem arises, in that two beams of infrared light-photons cannot be added to produce UV photons (two infrared photons simply don't have enough energy for their sum to equal UV energy). At least one of the lasers, interacting at some specific location inside a frequency-adding crystal, will have to be a visible-light laser.
So, this means the lasers can still be located at the bottom of the display, but the top of the display must be covered with a light-absorbing material, and viewers won't be allowed to see the images generated inside the display from above the display (can't risk harming their eyes with laser light).
Anyway, since the overall substance of the display is transparent, beams of light passing through it should be invisible (nothing in there would scatter the light toward the viewers, see?). It simply comes up from the bottom of the display and gets absorbed either by the frequency-adding crystal, or by the material at the top of the display.-- Vernon, Mar 08 2013 Frequency Tripling http://www.rp-photo...uency_tripling.htmlAs mentioned in the main text. [Vernon, Mar 08 2013] Visible light wavelengths http://en.wikipedia...ki/Visible_spectrumAs mentioned in the main text. [Vernon, Mar 08 2013] Trinitron phosphor stripes http://en.wikipedia.org/wiki/TrinitronAs mentioned in the main text. [Vernon, Mar 08 2013] DLP micromirrors http://www.ti.com/l.../how-dlp-works.pageSuitably small and fast-acting aimers, manufactured in quantity, do exist. [Vernon, Aug 27 2014] US 5684621 https://www.google....u/patents/US5684621Method and system for three-dimensional display of information based on two-photon upconversion [xaviergisz, Sep 04 2014] Note to all: This is an Idea I've been mulling over for a number of years. I didn't know about frequency-summing crystals until today, and the Idea can't really work without them....-- Vernon, Mar 08 2013 rather dependent on the slew time of the crystals. Each 3d-shell frame might require many subframes to avoid "crossing the streams" as it were. [+]-- FlyingToaster, Mar 08 2013 That could simply be another reason to use lots of lasers, as mentioned, with each group only operating on a portion of the overall crystal block.-- Vernon, Mar 08 2013 So I get about two paragraphs in before I scroll down to the bottom--yep, it's a Vernon. So nice to find one in such pristine condition, hardly any corners knocked off yet. Then I scroll back up to keep reading and I my eyes saccade to this line:
// Now we get to talk about the lasers. //
Immediate [marked-for-tagline] Immediate bun. Now returning to read the rest of it.-- Alterother, Mar 08 2013 I don't think you'll get a great 3D effect with this system. If the voxels are transparent and are point sources of light then you'll get 'bleed-through', i.e. you won't be able to selectively transmit light to each eye of the viewer.
You could possibly fix this with 'parallax barriers' running vertically through the crystal display. Alternatively, interspersing the crystal display with elements that can be selectively switched between transparent and opaque could be used.-- xaviergisz, Mar 09 2013 Well, the frequency-tripling link shows something that implies the photons produced by the frequency-summing crystal travel in the same direction as the photons it absorbed. It may be a Conservation of Momentum thing.
To the extent that is true, and considering the fact that we want our laser beams to cross at various points, it may be possible to ensure most of the summation-created photons travel in one range of directions, toward the outer surface of the crystal cube, and not in all directions.-- Vernon, Mar 09 2013 Third reading, and now that I mostly understand the sciency stuff in this idea...my bun remains.-- Alterother, Mar 10 2013 This is quite impressive, [Vernon]. The main sticking point will be aiming the lasers accurately at high speed. Are there any substances that change their refractive index under electrical stimulation? (Much like liquid crystal changes its polarisation when zapped.) Because trying to move the lasers mechanically will be too difficult, I think. Unless you do a grid of little lasers on each face of the crystal block, each aimed precisely along a row/column/rank. Then there is no motion to worry about; but it might be difficult to fit enough lasers (4 frequencies) in. Laser diodes 1/4 the size of your voxels?-- neutrinos_shadow, Mar 12 2013 [bigsleep], since others have already done what you suggested, I couldn't have posted any such Idea here and gotten away with it. Originality is somewhat important.-- Vernon, Mar 13 2013 This was quite possibly a genius idea until I saw that for the addition and subtraction to take place _efficiently_ the light needs to be in phase (what a pity!). Quite how that is done with different frequencies is something I didn't see immediately. I followed some of the links from the frequency tripling link that you gave. Anyway, big +.-- Ling, Mar 13 2013 This is impressively close to being real engineering. (So what is it doing on the HB?) But there are complications: 1) the efficiency of converting laser light into the sum frequency is very small - tiny fraction of 1% - so most of the laser light is traveling out the other side of the crystal. 2) because of the "momentum conservation thing" mentioned, the sum-frequency light travels in a specific direction so each voxel does not act as a point source. These could be turned into features - create a right angle prism of voxels instead of a cube; send the laser beams into the two or three back sides of the prism and view the prism from the large flat side. The laser beams will not emerge from the large front side but the sum-frequency light will, if the design is right. It might even be possible to create a stereo vision effect by creating two outputs from each voxel traveling in slightly different directions (as someone above mentioned). The whole problem now is that the viewer must place her head in a very specific location to see anything. It kind of defeats the whole purpose of 3D.-- sqeaketh the wheel, Mar 13 2013 [squeaketh], the stereo vision effect comes from the simple fact that we can cause voxels to glow all through the DEPTH of the crystal cube. That is, the 3D is real, not an illusion.
I will agree that the bigger problem is the conservation-of-momentum thing, with respect to the direction that the created light travels. If all the voxels each only "glow in one direction", that would indeed make this Idea truly Half-Baked!-- Vernon, Mar 13 2013 Are you going to be able to refresh your voxels quickly enough and frequently enough to achieve any sort of persistence of vision? Unlike phosphors, these crystals will dim as soon as the laser moves off them.-- MechE, Aug 27 2014 [MechE], persistence of vision is an eye-related thing, not a phosphor-related thing. And DLP micromirrors are fast enough for existing 2D displays. The last part of the main text proposes using them in sort-of a 2D fashion. One thing not pointed out in the main text is a kind of shortcut that can save a lot of time. Most 3D objects have a surface, and in most videos we only need to activate voxels associated with the surface of the object, not voxels associated with its interior.-- Vernon, Aug 27 2014 // Most 3D objects have a surface //
Intriguing … can you provide a link to a description of any 3-dimensional objects that don't have a surface ? We ask merely for information.-- 8th of 7, Sep 04 2014 Fog does not have a well-defined surface. The Sun doesn't have one, either (just LOOKS like it does, from 93 million miles away). Then there are the gas-giant planets....-- Vernon, Sep 05 2014 [xaviergisz], that's an impressive link! Nevertheless, I thought of it independently, just didn't know for a long time, as mentioned in the first anno here, that it was possible to do.-- Vernon, Sep 05 2014 random, halfbakery