The Key to Light and Shadow
As a common story setting, a hero goes through a lot of hardships and dangers and fights to the death against countless bad guys in order to snatch several keys scattered around the place, and only by collecting them all at the same time can he open a mysterious magic box and get what he needs: priceless treasures, a codebook to prevent the destruction of the earth, and control the world's AI source code......
Each key is indispensable, which means that the opening of the magic box requires a high level of security authority, which is actually reflected in the ancient use of the mainland talisman (or tiger talisman): the talisman is composed of two halves of the left and right, just like two keys, which are kept by the king and the army generals, and when the army is mobilized, the envoys sent by the monarch will match the two halves of the soldiers into one, and the order can take effect. In the post-80s nostalgic anime "Dragon Ball", collect seven dragon balls hidden around the world and recite a spell to summon a divine dragon to fulfill any wish for the wisher.
In the optical world, there are many different ways to create such keys, and each key alone does not display useful information, and only when they are "combined" at the same time will the hidden secret text or pattern be revealed.
The magic effect of image visualization encryption
It's a common knowledge that light can be blocked by opaque obstacles, and when used smartly, a simple visual cryptography effect can be achieved. For a simple black and white image to be hidden, each pixel is either black or white, if the pattern is printed on transparencies, the black pixels indicate that point is opaque, the white pixels indicate that point is transparent, if the pattern is displayed through a perforated card, the black pixels indicate that point is not perforated, and the white pixels indicate that point is perforated and translucent.
Either way, the hidden pattern can be broken down into two or more seemingly random black and white patterns, each sub-pattern is called a visual key, like each key used to open a magic box, corresponding to a patterned film or punched card. When these films or cards are aligned and stacked together, whether it is a two-layer "double skin milk", a three-layer "sandwich", or a "Napoleon mille-feuille", the hidden pattern can be easily restored and directly into view.
Figure 1: Visual Encryption of Images: When two seemingly chaotic patterns (a) and (b) are printed on film, the hidden number 1 pattern can be revealed, as shown in (c) [1]
Figure 2: Dynamic demonstration of visual encryption of images Source: Wikipedia
The key point is that when two or more visual keys are superimposed, as long as at least one of them is black (opaque), it is equivalent to occluding the pixels of the other layers, and the result of the superposition will also be black. Conversely, only a pixel corresponding to all visual keys is transparent, and that pixel will be transparent when stacked. When designing a visual key, you need to follow this rule with the appropriate black (opaque) or white (transparent) encoding for each pixel.
There is a magic prop that contains four punched cards, which look irregular and do not have any meaningful patterns on the cards, but as long as the audience says any number from 1 to 9, the magician will stack the four cards in an appropriate way, and the number requested by the audience can be displayed immediately, which will amaze the onlookers.
Figure 3: The top four cards contain a lot of "random" holes, and if you name any number between 1 and 9, the four cards will overlap to show the number. Source: Photographed by the author
Visual keys can hide not only simple letters and numbers, but also more complex images, as shown in Figure 4.
Figure 4: Hiding a complex image (right) with two visual key images (left and center) [2]
In another magic trick, two different playing cards can be transformed back and forth, which also uses a technique similar to image visual encryption, and the details will not be revealed here, so you can think for yourself.
Video 1: Why do the playing cards in the deck change back and forth between the 5 of spades and the 6 of hearts?
Random dot stereogram: The eyes are the natural unlocking key
Our left and right eyes are not only windows to the soul, but also serve as two natural keys to protect secrets. The left and right eyes are separated by a few centimeters, resulting in slightly different viewing angles, and there will be a certain "parallax" between the left and right eyes of the same object, which is to a large extent the source of the three-dimensional sense of "different heights and heights from far and near". If two images with slight parallax are forcibly displayed in front of the left and right eyes, the viewer will involuntarily create a virtual three-dimensional feeling. When you wear glasses to watch a 3D movie in a theater, the left and right lenses allow only polarized light from different directions to pass through, in order to achieve this binocular three-dimensional display effect. Apple's Vision Pro virtual reality headset can create a three-dimensional effect, playing "spatial videos" shot by the new Apple phone, relying on two LED displays in front of the left and right eyes to display different content.
The two images below look like a jumble of black and white snowflakes, but instead of being printed on transparencies and overlapped, the two images are seen separately by the left and right eyes, as in a 3D movie.
Figure 5: Two key images that rely on stereo vision of the left and right eyes to unlock the secret [3]
After doing so, you will be amazed by the results you see in front of you, the hidden letter pattern will be concave or protruding like a relief, this is because the above two keymaps are not completely random, there are hidden letter patterns with left and right eye parallax respectively, and the binocular three-dimensional display is used for the restoration of secret images.
Figure 6: Restore the effect of hidden text [3]
In ophthalmology, this snowflake dot picture is called a "random dot stereogram" and can be used to detect stereoscopic vision.
Figure 7: The random dot stereogram and red and blue glasses used by the ophthalmologist are printed in red and blue colors respectively, and the left and right lenses of different colors can filter and separate the corresponding patterns, and those with normal stereo vision can see the three-dimensional object image (such as a suspended triangle or a protruding letter) Source: Taken by the author
Hologram Key: Nothing is impossible, only unthinkable
Using a variety of optical principles, it is also possible to design more elaborate "optical keys". The two small glass pieces below do not look special, they are just painted with panda or lady patterns, but there is actually a mystery hidden under the camouflage of the exterior[4].
Figure 8: Two outwardly disguised hologram glass keys [4]
They are not ordinary glass sheets, but two "holograms", the thickness of different positions of the glass surface is optimized and coded design, slightly different, and processed by photolithography, so that when a laser beam is irradiated on the glass sheet, the phase of the light field at different positions will change, and after diffraction propagation through the glass sheet for a certain distance, a reconstructed image can finally be formed. Interestingly, this reconstructed image can be completely independent of the surface smeared pattern, and the hologram is only a carrier of the light field information of the reconstructed image, but does not directly display the image on it.
As an example, the images reconstructed from the hologram of the panda and the lady glass are the two checkerboard grids in the picture below, and the two checkerboard grid patterns can also be overlapped together through prisms, and the last thing you see is the text pattern of "OK", which is the real hidden information in the two glass pieces, and this light key unlocking method is hidden enough, right?
Figure 9: The images reconstructed by two hologram glass fragments under laser irradiation (left and center) and the final decryption result after the overlap of the two (right) [5]
Using holograms as "light keys", the following different design also buries the secret image in the deepest depths [5]. The two holograms, each illuminated by a light beam, can be reconstructed into a different image, but this is only a superficial camouflage, not the magic box that the two keys are really going to open. The correct way to unlock is to cascade two holograms together like a sugar gourd, and keep a pre-set separation distance, so that after the beam passes through the first hologram and is modulated, and then passes through the second hologram, and then goes through the same process, and finally the real hidden image can be reconstructed, and the "mystery" that is revealed is not the same as the image reconstructed separately from each hologram. In order to achieve this effect, these two special holograms need to be coded and designed using specialized optimization algorithms.
Figure 10: A scheme for protecting secret image information by cascading two holograms [5]
Of course, the number of hologram keys mentioned above is not limited to two, but also three, four or even more keys can be designed to "work together" to restore an upgraded version of the hidden image, in which each hologram "must not be missing".
By breaking down a secret image to be hidden into the keys in the hands of each unlocker, Light can provide a variety of safe and convenient solutions, each ingenious design that is both unexpected and optical in principle.
bibliography
[1] S. Jiao, J. Feng, Y. Gao, T. Lei, and X. Yuan, "Visual cryptography in single-pixel imaging," Opt. Express 28(5), 7301-7313 (2020).
[2] C. C. Lin and W. H. Tsai, “Visual cryptography for gray-level images by dithering techniques,” Pattern Recogn. Lett. 24(1-3), 349–358 (2003).
[3] K.-H. Lee and P.-L. Chiu, "Sharing Visual Secrets in Single Image Random Dot Stereograms," IEEE Transactions on Image Processing 23(10), 4336-4347 (2014).
[4] Y. Shi and X. Yang, “Optical hiding with visual cryptography,” J. Opt. 19(11), 115703 (2017).
[5] P. Georgi, Q. Wei, B. Sain, C. Schlickriede, Y. Wang, L. Huang, and T. Zentgraf, “Optical secret sharing with cascaded metasurface holography,” Sci. Adv. 7(16), eabf9718 (2021).
Written by: Jiao Shuming
Reviewer: Cao Liangcai
Source: China Optics
Edit: Eleven