This article is produced by "Light Science Workshop".
Written by: Jiao Shuming (Guangdong-Hong Kong-Macao Greater Bay Area Quantum Science Centre)
Reviewer: Zhang Xinzheng (Nankai University)
Figure 1: Corner reflector
Source: Mathematical Etude Project (Sczelov Institute of Mathematics, Russian Academy of Sciences)
Corner reflectors: from basic principles to innovative applications
The corner reflector, this seemingly simple optical device, is revolutionizing our interactive experience in a new form.
In recent years, an innovative technology known as "interactive aerial imaging" has attracted a lot of attention. This technology cleverly takes the basic principle of the corner reflector and develops it into a new type of display device. The user can see a virtual screen suspended in the air and can even interact with it by touching the 'air'. Behind this stunning effect is a clever application of the corner reflector principle.
Figure 2: "Interactive Aerial Imaging" technology
Source: Drawn by the author/VEER
Micromirror Array Plates: A New Form of Corner Reflectors
At the heart of this innovative technology is a device known as a "micro-mirror array plate". It is equivalent to an upgrade and extension of the traditional corner reflector principle. This particular slab consists of two tiny mirrored arrays, each of which resembles a delicate shutter, with the two layers perpendicular to each other. This structure allows the light to be double-reflected precisely to form a virtual image in the air. The working principle of the micro-mirror array plate is similar to that of traditional corner reflectors, both of which use multiple reflections to change the path of light, but with innovation in form and application.
Figure 3: The micromirror array is structurally divided into two layers, a row of parallel micromirrors, the two sets of micromirrors are orthogonal and perpendicular to each other, and the light incident on one side of the mirror is reflected by the mirrors in the two-layer array and then emits from the other side¹
The basic principle of corner reflectors
To understand this innovative technology in depth, we need to go back to the fundamentals of corner reflectors. In fact, the working principle of the corner reflector is simple and elegant, and it shows how the behavior of light can be precisely controlled through clever geometric design.
The most basic angular reflector principle can be understood by two mirrors that intersect perpendicularly at 90 degrees, a structure known as a "two-dimensional corner reflector", like a laptop that opens and closes 90 degrees (Figure 4). This structure has an interesting effect: in a two-dimensional plane, when light is incident at an angle, it returns in a parallel but opposite direction to the direction of incidence after being reflected by two mirrors that intersect perpendicularly. This is known as the "go back where you come from" effect.
Figure 4: Two-dimensional corner reflector
Source: Internet
It is important to note that this two-dimensional structure can only achieve full reflection in one plane. A complete corner reflector usually refers to a three-dimensional structure composed of three mirrors perpendicular to each other, which can achieve all-round reflection in three-dimensional space.
Encyclopedia 1: How does a corner reflector work?
The more common corner reflector is a three-dimensional structure consisting of mirrors perpendicular to each other on three sides (Figure 5). This design further enhances the effect of the corner reflector, allowing light from any direction to be precisely reflected back to its original path. Mathematically, this process can be described in terms of vectors: assuming that the direction of the incident ray is represented by the vectors (a, b, c), then after reflection from the xOy plane, its direction vector becomes (a, b, −c), and after reflection from the yOz and zOx planes, the direction vectors become (−a, b, −c) and (−a, −b, −c), respectively.
Figure 5: Principle of a three-dimensional corner reflector
Source: Internet
It is worth noting that this characteristic is unique to corner reflectors. A normal single-sided mirror can only reflect light back to its original path if it hits it vertically. And corner reflectors, whether two-dimensional or three-dimensional, allow light from all directions to "honestly return the way it came". This unique property makes corner reflectors play an important role in a variety of applications.
Figure 6: Demonstration of the principle of a corner reflector
Source: Internet
The application of corner reflectors in daily life
The seemingly simple optical device of the corner reflector, with its unique reflection characteristics, has been quietly integrated into our daily life. From road safety to precision measurements, the range of applications for corner reflectors is impressive. Let's start with an example that we may encounter every day, but is often overlooked: bicycle taillights. This inconspicuous little device is actually an ingenious application of the corner reflector principle, which provides an important guarantee for our daily travel safety.
I believe that for the old-fashioned tail lights of the bicycle, many people were quite puzzled when they were children, this kind of light does not need to install batteries, nor does it need to be plugged in, and the switch of the light can not be found before and after the whole bicycle. If the light is broken, it can't be broken on every bike, so what is it for?
Figure 7: A bicycle tail light that doesn't need to be plugged in: it's actually an array of optical corner reflectors
图源：Light科普坊/VEER
Take a closer look at this kind of tail light, the surface is a red lampshade that only allows red light to pass through, and there are several important reasons to use red: First, in traffic safety rules, red is often used to indicate a warning or stop, so red tail lights can effectively alert rear vehicles to the presence of a bicycle ahead. Second, the sensitivity of the human eye to red light is relatively high in low-light conditions, which makes red taillights easier to notice at night. In addition, red light has a longer wavelength and is more penetrating than other colors of light in foggy or other conditions with low visibility. Finally, the use of a single red color can avoid confusion with other traffic lights, improving recognition and safety. Under the cover of the lampshade, many small corner reflectors form an array, reflecting the red light into the eyes of the car driver behind the car.
This reflective principle using corner reflectors is not limited to bicycle taillights, similar applications can be seen in many places in our daily lives. For example, on the road, we can often see various reflective signs and markings, which work in the same way as bicycle taillights, all utilizing corner reflectors to enhance visibility and safety.
Figure 8: Reflective signs on the road (same principle as bicycle tail lights)
Source: Photographed by the author
Application of corner reflector in precision optical instruments
Corner reflectors are not only widely used in daily life, but also play an important role in precision optical instruments. For example, in the laser ranging system, the distance is calculated by measuring the time from the emission to the return of the laser, but if the target distance is very far away, after a trip back and forth "switchback and run", the laser signal strength has been almost exhausted, and the corner reflector as a "heart booster", the use of efficient reflection characteristics can ensure the return of the light signal of sufficient intensity, thereby greatly improving the accuracy of ranging. One specific application is in satellite laser ranging, where the ground station emits laser pulses to a satellite equipped with a corner reflector, and accurately calculates the satellite orbit by measuring the round-trip time, and the error can be controlled at the centimeter level.
Corner reflectors are also indispensable tools in optical alignment and alignment. They are used to establish precise optical datums and help adjust the position of components in complex optical systems. For example, during the assembly of large telescopes, corner reflectors can be used to ensure that the individual optical components are tightly aligned, guaranteeing the image quality of the entire system.
In interferometry, corner reflectors can be used as moving mirrors to produce high-precision optical path differences. A typical application is the Michelson interferometer, where a corner reflector is used as a moving mirror that allows precise control of the optical path difference to achieve precise measurements at the wavelength level. This technique is widely used in precision length measurement, spectral analysis, and other fields.
Encyclopedia 2: What is "optical path difference"?
Optical path difference refers to the difference in the distance traveled by light waves to travel in different paths. In interferometry, this concept is particularly important. Imagine two beams of light starting from the same light source, propagating along different paths and reconverging. If the lengths of these two paths are different, an optical path difference will occur. This difference causes a change in the phase of the light waves, which in turn affects the interference effect when they reconverge. By precisely controlling the optical path difference, scientists can take advantage of interference effects to make high-precision measurements. For example, in Michelson interferometers, precise measurements at the wavelength level are achieved by adjusting a moving mirror (commonly used corner reflector) to change the optical path difference. These applications make full use of the high-precision reflective properties of corner reflectors and make an important contribution to the development of modern precision measurement and optical instruments. From the microscopic world at the nanoscale to the macroscopic scale of astronomical observations, corner reflectors play an irreplaceable role.
Looking to the future: challenges and opportunities
The principle of the corner reflector is deceptively simple, but it contains profound physical intelligence, reminding us that the most elegant solutions often stem from the most basic principles. From everyday life to cutting-edge technology, it not only inspires us to think about the nature and potential of light, but also faces its own challenges: angle of incidence limitations, high-precision manufacturing requirements, temperature sensitivity, and dimensional weight constraints. These limitations are driving the development of new materials and designs, such as high-angle reflective materials and lighter structures.
With the rapid development of science and technology, corner reflectors have found more innovative applications in emerging fields, showing their strong adaptability and potential. In autonomous driving technology, corner reflectors are used to enhance the visibility of road signs and improve the performance of LiDAR systems in a variety of weather conditions, thereby improving the safety and reliability of autonomous vehicles. In the field of augmented reality (AR) technology, miniature corner reflectors serve as precisely positioned markers, helping AR devices accurately determine the user's position and orientation in large indoor spaces, providing a more immersive experience.
In addition, corner reflectors also play an important role in communication technology. In 5G and 6G high-frequency mmWave communications, it is used to enhance signal strength and improve coverage. In the field of quantum communication, corner reflectors improve the efficiency of photon collection, which is essential for establishing secure quantum key distribution (QKD) systems. Finally, in smart city planning, corner reflectors are integrated into the infrastructure to provide precise positioning and situational awareness capabilities for a variety of sensors and automation systems. These diverse applications are a testament to the continued importance of corner reflectors in modern technology and indicate that they will continue to play a key role in future technological developments.
Resources
1. [1] Makoto Otsubo, “Aerial imaging principle and its commercialization and future developments,” Proceedings of the International Display Workshops, Vol. 28: 227-230, 2021
Note: The images from the Internet used in this article are all public domain images.
Producer: Zhao Yang
Editor: Zhao Wei
Source: China Optics
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