{'fraction_non_alphanumeric': 0.02135054617676266, 'fraction_numerical': 0.006355511420059583, 'mean_word_length': 4.865463016889924, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Alternative Approach to 3D Displaying

A method for displaying volumetric images, which exploits our binocular vision and does not require eyewear, is discussed. The display can be rendered as a matrix of pivoting micromirrors irradiated by a light beam; each micromirror focuses its pixel beams to the same point of displayed volumetric image. 3D perception of image can be achieved by scanning the point of beams intersection over a virtual surface of displayed image in space.


Introduction
The dream about a device generating optical volumetric replicas of real objects, just as we see them by eyes, persisted over centuries and recently found its second wind after invention of video imagers and image processors. Image processing has already become a huge scientific area where thousand researchers are actively working. The engineering efforts are mostly concentrated on the 'old good' two-dimensional imaging however a growing team of engineers in three-dimensional (3D) vision area is also working actively. The current "demand for 3D stems more from whim then necessity, which makes it difficult to gauge exactly what kind of image is sought" 1 to be preferable for a potential customer, however the likewise whim seemed to drive, in its time, the engineers toward the prominent progress in automobile industry and, recently, toward the boom in the cellular phones with cameras. A variety of 3D stereo-displays and quasi-volumetric imagers has been proposed and some have already appeared on the market. Nonetheless, the common vision is a display round with people, each seeing what they would see if they were looking at a solid object instead of an image.
Virtually all the tricks for achieving 3D-perception of images, from paintings to modern stereo movies and displays, are based on optical illusion. 2D-images on a flat surface are either distorted in accordance with the rules of perspective to produce the perception of depth, or consist of two images separately for right and left eyes to create a stereo effect.
While visual art such as photography and cinematography uses perspective 2 together with light and shade play, interposition, aerial perspective (blurring of distant objects as if they were in haze), textual gradient, and motion parallax, 3 leaving the rest to our imagination in perceiving the depth, stereoscopy mimics, in addition to all the tricks above, our binocular vision to actually see the depth by forcing our brain to arrange the objects of a flat image as if they were hovering in 3D space. However, despite the prominent eye-catching effect of stereoscopy and the persistent efforts to promote the stereoscopic systems, they have not found a proper recognition in mass production so far. There are two reasons for this slow advance: firstly, the stereoscopic systems are costly in comparison with the conventional 2D systems and secondly, they need a kind of eyewear to watch stereoscopic images: on a colormultimplexed (anaglyph) display that creates images of different colors for left and right eyes, on a polarization-multiplexed display producing images of mutually perpendicular polarization, or on a time-multiplexed display where the left and right views are sequentially shown. The recently appeared autostereoscopic displays 1,4 require no eyewear; the views are spatially multiplexed on a pixel-addressable screen and then separated by an optical layer which sends the left view and the right view at different angles to be perceived by left and right eyes separately. All stereoscopic methods are suffering from two drawbacks: firstly, the angle of viewing is limited (as well as the distance to the screen in the case of autostereoscopy) and secondly, at any angle of viewing a viewer sees the same image, i.e. the image does not rotate with the change of angle of view because the viewer sees actually through the viewpoints of the cameras.
One of the first truly volumetric imagers was developed by NASA. 5 The image capabilities of the system stem from the technique that uses a laser-light projection apparatus and a rotating "vortex" screen to create a "viewing box." The system displays nearly 34 million "voxels" (i.e., x, y, and z points corresponding to the pixels of a 2-D image) of data, enabling a user to view a 3-D shape from multiple perspectives without the need for special viewing aids or goggles. The information about another system generating the real spatial image with 360º view angle was published in 2002 6 and 2004. 7 The system is based on a rotating screen, where a sequence of 5940 2-D images from a XGA-resolution light modulator is projected. This combination of hardware and software generates 3D volumetric images inside a vacuumed transparent spherical dome, which can be seen from a full 360 degrees without goggles. Nevertheless, this masterpiece of optomechanics is far from mass production and out of reach of ordinary consumers.
Our dream is about something like communication devices shown in sci-fi movies, where a 3D image is hovering in air without screens or scattering media being observed from any direction without goggles or other eyewear. A possible approach to displaying the volumetric images which can be seen as hovering in space without reflecting screens or light scattering fog and which can be observed without eyewear is outlined below.

Perception of image
Our binocular vision is based on the separate perception of light beams emitted by an object at different angles. We see an illuminated object when it scatters light emitted from natural or artificial sources and every point on the object's surface radiates the scattered light more or less isotropically. An eye catches a fraction of scattered light from a particular point on the surface within a solid angle of vision-by-D 2 , where A is the area of pupil and D is the distance to the object (Fig. 1). The object is seen slightly different by left and right eyes, because our eyes see the object from different angles: the closer is the object, the lager is the stereo-angle = 2arctg(d/2D), where d is the distance between the eyes, and the larger is disparity between the images on the retinas of left and right eyes.
To obtain a volumetric replica of a real object, which can be perceived as a real object, an optical system and/or a multiplexing display is supposed to   Fig.4. Diffraction spot d s p = 100 (bottom line). Solid circles on the lines indicate the distance R eq at which the diffraction spot diameter is equal to pixel size. Additional focusing of pixel beams is advantageous for better resolution if R < R eq and useless otherwise.
Divergence. In addition to diffraction, the pixel beams will be more or less divergent by the nature of the real sources of electromagnetic waves (e.g., laser beams consisting of multiple angular modes or light beams formed by optical systems when emitters of finite size are used), so the wave-fronts of pixel beams will never be absolutely flat or precisely spherical.
If no focusing is implemented, the cross-sections d b of unfocused beams at a distance R will

Technical problems and perspectives
The "Mirage"-like method of volumetric imaging requires a display consisting of multiple Yet another approach to control the tilt is to implement thermomechanical actuators in combination with electrostatic actuators to control the dual-servo mirrors. 11 -15 As for intensity multiplexing, the use of Grating Light Valve (GLV) 16 technology with the beam intensity controlled by a grid of ribbons of controllable displacement could be also thinkable, when used in combination with the tilting mechanisms to allow both scanning and intensity multiplexing of each pixel. The drawback of GLV technology is that each pixel actually produces several beams (at least, one zero order and two first order beams) and parasitic images can be perceived at different angles of observation.
The high fill-factor arrays of micromirrors with electrostatically controlled and individually addressed 2D-tilt have been reported. 17  Displaying the fictional volumetric objects, such as cartoon characters, molecular structures, object of battlefield, etc., is mainly the task of corresponding software. Displaying the real objects would require shooting of a scene by a multi-camera system, for example, by the system described in 5 with the followed reconstruction of 3D images using the proper software to transform the multi-camera flat images to the stream of data analogous to the system described by Park and Inoue. 8 One of anticipated software problems will be, in particular, the "inverse occlusion", when a portion of volumetric surface visible from one position of a viewer must be made invisible from another direction of viewing (Fig. 5). A possible solution is to scan the corresponding pixel beams only over the farthest portions of surface from the given pixel in the case when two or more image surfaces intersect the line of sight between an eye and a given pixel, i.e.
to extinguish the beams from the pixels that 'see' more then one surface when the scanned point of the beams crossing is on a surface, which is supposed to be invisible for a given direction of displaying. On the other hand, for many applications all the surfaces could be made visible through each other including cavities and inclusions which could also be contrasted by artificial colors.

Conclusion
It seems viable to create true 3D-volumetric images with a display made of tilting micromechanical pixels that emit quasi-parallel or focused light beams of multiplexed intensity and color, so all the beams are crossed at a transient point that can be controllably scanned over the surface of virtual image. The optical blur due to diffraction, micro-beam divergence, and optical aberrations can be kept sufficiently small to obtain satisfactory resolution at of two-axis reflecting pixels with controllable tilt, however the technology of dual-servo micromirrors is developing rapidly and the manufacturability of such displays seems to be technically achievable.