Why can a small grating card allow people to experience a rich three-dimensional world?

A small card can show different pictures as you swing it at different angles, and even make the image "jump" out of the card. You must be familiar with this magical visual experience. You can see it in shopping mall windows, billboards, and even in anime peripheral products. This optical device called "grating card" has created a hot wave on major platforms with its amazing visual effects and has been widely used in various fields. Compared with its own magical visual effects, the optical principle behind it is even more worth exploring.

Before experiencing the 3D world, we must first understand that all visible objects in the world are three-dimensional. Human eyes are about 6 cm apart, which makes each eye observe objects at a slightly different angle and see slightly different images. This tiny difference in perspective is called binocular parallax, which is one of the key factors in producing 3D vision. As shown in the figure, a scene of a cube and a cone are shown in front of the observer. Due to the different positions of the two eyes, the images of the cube and cone seen by the left eye and the right eye are also different.

Figure 1 Binocular image perception

When you use your left or right eye alone, you see only a flat image. The image your left eye sees is slightly different in angle from the image your right eye sees because the distance between your eyes causes parallax. When both eyes see together, your brain combines the two images and, through parallax processing, creates a three-dimensional image with depth.

To further enhance 3D vision, the brain also needs to use other physical depth cues such as accommodation, convergence, and motion parallax. Accommodation is when the eye muscles adjust the shape of the lens to change the focal length, allowing us to clearly see objects at different distances. Convergence is the difference in the angle of inward rotation of the two eyes when looking at the same object, with closer objects requiring a larger convergence angle. Motion parallax is when close objects appear to move faster than distant objects when we move our head, which also provides us with a sense of depth.

The realization of grating cards utilizes these principles, mainly through two methods: slit grating and cylindrical grating. First, let us understand what a grating is and what is the difference between a cylindrical grating and a slit grating. Grating is a widely used and very important diffraction optical element, usually based on the Fraunhofer diffraction effect. The grating is composed of a large number of slits of equal width and equal spacing. It is an optical element that can periodically modulate the amplitude or phase of the incident light. The origin of the grating can be traced back to 1819, when a wire grid was made by Fraunhofer. Nowadays, gratings are generally made by engraving equal-width and equal-spaced grooves on flat glass or metal plates. With the development of theory and technology, grating diffraction units are not limited to slits, but also include new gratings such as crystal gratings, ultrasonic gratings, and crystal refractive index gratings.

Slit grating adds an array of slits in front of the image. When we look at the image through these slits, different image bands enter our left and right eyes respectively. Because these image bands are separated by the slits, the images seen by the left and right eyes are slightly different. The brain processes these differences and synthesizes a three-dimensional image. The principle of slit grating is simple and the production cost is low, but because of the opaque nature of the slits, part of the light is blocked, causing the brightness of the picture to decrease. The viewer needs to watch from a specific position to see the three-dimensional effect, otherwise the observation results will overlap or be distorted.

The lenticular grating adds an array of many small lenticular lenses in front of the image, and the image enters the left and right eyes respectively after being refracted through these lenticular lenses. According to their functions, lenticular gratings are divided into stereoscopic gratings and variable-image gratings: stereoscopic gratings are thicker and have a stronger sense of three-dimensionality. Variable-image gratings are thinner and are mainly used to present different images at different angles.

Figure 2 Principle of cylindrical grating stereo imaging

When making a lenticular card, multiple images taken from different angles are taken or generated. These images are cut into thin strips and arranged together in a specific order. The lenticular lens is overlaid on these images, and each tiny cylindrical lens disperses the light in different directions, so that the thin strips of each perspective image can be transmitted to the observer's eyes at the correct angle. Therefore, when we watch the lenticular stereogram from different angles, the left and right eyes see different perspective images, and the brain combines these images into a three-dimensional image, thus producing a stereoscopic visual effect.

After understanding the optical principle of grating card imaging, we can further explore the process of grating card production, which can be summarized into the following main steps.

First, in order to ensure that the final effect is more three-dimensional, images with rich layers and strong vertical depth of field need to be selected, and there are certain requirements for the size and accuracy of the images. After selecting the images, the images are layered in Photoshop, and the patterns are separated into separate layers according to the distance relationship and color brightness of the images, and each part is repaired to ensure a complete pattern.

After the image processing is completed, the pitch is calculated according to the number of lines of the lenticular grating to determine the image resolution. The depth of field value is set, and different depth of field values ​​are set for the near view, the middle view, and the far view. The selected layer is copied and moved according to the set depth of field value to form multiple images suitable for different positions of the lenticular grating. These images are rasterized and merged to finally form an image combination perpendicular to the lenticular grating.

With the continuous advancement of 3D display technology, the application field of grating cards as an optical device that can present stereoscopic images will become more extensive. The future 3D display technology will develop in the direction of holographic projection and volumetric display. These technologies can not only provide a more realistic and immersive visual experience, but also overcome the limitations faced by many current 3D display technologies, such as viewing angle and resolution limitations.

The grating card uses the unique characteristics of the cylindrical grating material, and through precise image processing and high-precision printing technology, it achieves a three-dimensional effect of a flat image. This process not only enriches the expressiveness of the printing process, but also brings a new visual experience to the fields of advertising, entertainment, education, etc. In the future, with the maturity of computer-generated hologram (CGH) technology, the development prospects of grating cards will be full of more and more possibilities.

References

Yang, Lin, et al. "See in 3D: state of the art of 3D display technologies." Multimedia Tools and Applications 75 (2016): 17121-17155.

Sun Guanguo, Bai Guomin. Research on the application of naked-eye 3D raster technology in map compilation[J]. Surveying and Mapping Geographic Information, 2021.

Peng Lixia, Liu Kunhong. Research on cylindrical mirror grating stereo imaging technology[J]. China New Technologies and New Products, 2022, (16): 21-23.

Tan Qirui, Lu Haiming, Lu Zengxiang. Design of large-format stereoscopic images with multiple viewpoints based on lenticular grating[J]. Journal of Tsinghua University(Science and Technology), 2019, 59(04): 249-255.

Author: Cai Wenchui, a postgraduate student at Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences

Reviewer: Li Ming, Researcher, Institute of High Energy Physics, Chinese Academy of Sciences

The article is produced by Science Popularization China-Creation Cultivation Program. Please indicate the source when reprinting.