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The answer is random phase approximation (RPA), and this is based on a handful of key ideas.
First, waves are considered “in phase” when their peaks and troughs line up. Waves that are not in phase interfere with each other, thus distorting the image.
Second, each part of a system oscillates at its own frequency, but all of these frequencies average out, creating a system-wide frequency.
Third, when the system-wide frequency of two systems are randomized, there is an extremely high likelihood that they’ll be orthogonal, meaning they’ll be in phase with each other.
The researchers were able to sufficiently randomize the phases of each plate, eliminating any cross-talk between them. Therefore, the light emitting from one plate did not interfere with the light from other plates, creating a crisp, detailed 3D image.
“We demonstrate Fresnel holograms that form on-axis with full depth control without any cross-talk, producing large-volume, high-density, dynamic 3D projections with 1,000 image planes simultaneously,” they said in the paper.
Although it may still be a few years away, once this groundbreaking technique becomes commercially available, it will certainly be a turning point, similar to how x-rays revolutionized medicine.
Although our proof-of-principle experiments use spatial light modulators, our solution is applicable to all types of holographic media.
Source: Abstract, nature.com
However, in order to reach their goal, the researchers had to introduce another critical ingredient. The 3-D projection would suffer from interference between the constituent layers, which had to be efficiently suppressed. "A technological breakthrough can rarely be traced to a fundamental mathematical result," says Prof. Fatih Ömer Ilday, the other lead author of the paper. "Realistic 3-D projections could not be formed before, mainly because it requires back-to-back projection of a very large number of 2-D images to look realistic, with potential crosstalk between images. We use a corollary of the celebrated central limit theorem and the law of large numbers to successfully eliminate this fundamental limitation."