These magical stripes have ruined countless photos, but they can also be so beautiful!

This magical stripe has ruined countless photos, but it can also be so beautiful

Jiao Shuming Greater Bay Area University

(Originally published on the "Guokr.com" public account)

Many people born in the 1990s have a set of books called "The Adventures of Little Tigers" and a mysterious "decryption card" in their childhood memories. Whenever the gripping story of the novel reaches its climax, the next paragraph on the page suddenly has no text, but a bunch of chaotic stripes appear, "Want to know what happens next? Please take out the decryption card."

This mysterious little card brought joy to many people's childhood

Cover the special card with the puzzle, and the answer will emerge from the disordered pattern. What is going on? In fact, you may encounter the same phenomenon every day in your life - when you take out your mobile phone to take a picture of the screen.

This phenomenon is the Moiré Pattern effect.

In life, we often encounter moiré in this annoying way.

Where does moiré come from?

What exactly is "moiré"? Let's start with simple stripes.

In the image below, we see two vertical stripe patterns, A and B, which look similar, but have slightly different frequencies of the stripes - here, frequency is used to describe the density in the spatial dimension.

Next, we stack A and B together. The result C will not make you have trypophobia, but you can find that the thin fences in the pattern seem to form some huge pillars.

When two high-frequency patterns meet, they will "degenerate" and produce a low-frequency pattern effect, which is the moiré effect. Mathematically speaking, when two cosine periodic functions with similar but different frequencies are multiplied, a low-frequency periodic signal with the frequency difference between them will appear in the result.

Of course, these high-frequency patterns do not necessarily have to be stripes. They can be dense dot patterns or dense rings, and both can create a moiré effect.

The stripes on the pages of "The Adventurers" and the stripes on the decryption card are equivalent to A and B above. In fact, the original pattern printed on the page also contains hidden text, but just like a soldier wearing camouflage uniforms hiding in the bushes, the text is submerged in the dense stripes and difficult for the human eye to detect. After the decryption card is used, the originally hidden text is exposed under the low-frequency moiré pattern.

Magical patterns in photos

In fact, all kinds of digital devices that shoot and display images generally have pixel array structures. Whether it is the screen of a TV or computer, a scanner or projector, or the sensors in a mobile phone or digital camera, they are all composed of periodic pixel units, which can be regarded as high-frequency array patterns.

When these "high-frequency array patterns" are combined with each other, or encounter other densely detailed images, all kinds of magical moiré effects appear.

Magical moiré in photos

The most annoying thing in life is the moiré pattern when taking pictures of mobile phone/computer screens. Not only are the patterns magical, but they are also colorful.

What's going on with this strange color? To explain it, we first need to understand the composition of color pixels on digital devices. Each pixel on the display is actually composed of three adjacent red, green, and blue pixels, which display colors through different combinations of light and dark.

Zoomed in, this is what the pixels on the display look like | extremetech.com

These pixels are so small in size and spacing that the human eye cannot distinguish them. However, the three-color pixels arranged separately mean that there are three different high-frequency arrays. This makes the moiré pattern more complex.

Moiré is also art

Moiré patterns are not always ugly, obtrusive streaks; in the hands of artists and designers, they can actually be very beautiful.

Japanese graphic designer Takahiro Kurashima created a book called "Poemotion". There are no fully formed pictures in the book, but as long as you cover it with striped film and slide it up, down, left, and right, you can see the magical effect produced by the moiré pattern, just like a playground on paper.

Designer John Leung used moiré patterns to transform a still image into a school of swimming carp. As long as you move your perspective and look down through the striped glass coffee table, you will see the fish wagging their tails.

"Magic carp-pet", johnleungdesign

Italian designer Andrea Minini also had a lot of creative ideas. He used curves similar to moiré to draw a series of abstract portraits of different animals, "Animals in Moiré", showing a delicate and exquisite beauty.

The pictures show an owl, a cobra, a bat and a peacock | Andrea Minini

Through it, you can also see details that break through limitations

Not just a "decryption card" or a "magic carp", moiré patterns also have more advanced applications - for example, they can be used to see very tiny details under a microscope.

Inspired by moiré, scientists invented a technology called "structured illumination microscopy" (SIM). It can go beyond the limitations of ordinary optical microscopes and see smaller details. The method of using this microscope is: each time a different high-frequency stripe light pattern is projected onto a sample (such as a tiny cell), the high-frequency detail texture of the sample and the projected light pattern work together to produce low-frequency moiré. The former originally exceeds the magnification of the microscope and cannot be seen clearly, but the low-frequency moiré produced is within the magnification of the microscope. Therefore, various moiré patterns can indirectly restore the details of the object, making the microscope magnify many times more than the original magnification limit.

Superimpose high-frequency streak light with the difficult-to-distinguish "high-frequency details" to obtain a more easily distinguishable low-frequency pattern.

This method can help researchers see tiny details indirectly

The principle of moiré is also often used in the anti-counterfeiting identification of coins. In the 2018 movie "The King's Avatar", the counterfeit money manufacturing gang played by Chow Yun-fat and Aaron Kwok encountered considerable trouble: even if a high-definition printer was used to copy the counterfeit money, moiré defects would appear on the banknotes, making them easy to detect. This is the result of the superposition of the fine stripe pattern on the banknote and the printed pixel matrix.

Moiré patterns mentioned in the movie "Wushuang"

Not only that, even the ugly stripes on the screen of a mobile phone can actually be turned into treasure. Recently, some researchers have cleverly used this moiré pattern to design a QR code that can prevent "scanning". When we use one mobile phone to take a picture of another mobile phone screen, moiré patterns often appear, and they are related to the distance and angle of the two mobile phones when taking pictures. In the scheme designed by the researchers, only when shooting from a specific distance and angle can the correct QR code pattern be extracted from the moiré patterns, otherwise the protected QR code cannot be seen.

References

[1] L. Junfei, Z. Youqi, W. Jianglong, X. Yang, W. Zhipei, M. Qinwei, and M. Shaopeng, (2014). Formation mechanism and a universal period formula for the CCD moiré. Optics Express, 22(17), 20914-20923.

[2] M. Saxena, G. Eluru, and SS Gorthi, (2015). Structured illumination microscopy. Advances in Optics and Photonics, 7(2), 241-275.

[3] H. Pan, YC Chen, L. Yang, G. Xue, CW You, and X. Ji, (2019, October). mQRCode: Secure QR Code Using Nonlinearity of Spatial Frequency in Light. In The 25th Annual International Conference on Mobile Computing and Networking (pp. 1-18).

[4] http://mt.sohu.com/20170628/n498989826.shtml

[5] https://www.sohu.com/a/195950561_224832

[6] http://art.ifeng.com/2018/0720/3431657.shtml

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[8] https://news.artron.net/20180608/n1006101.html