are applicable to various tasks in teaching physics in schools, colleges and universities. ... cheapest, because it provides stereo vision with ordinary displays.
Stereo 3D Vision in Teaching Physics Stereo 3D vision is a technology used to present images on a flat surface (screen, paper, etc.) and at the same time to create the notion of three dimensional spatial perception of the viewed scene. Observing scenes and settings of studied physical phenomena in stereo 3D vision is a helpful tool when teaching physics. Stereoscopic 3D photographs, figures, plots and interactive simulations substitute to certain extent the laboratory setting, where the latter may be inapplicable, expensive or dangerous to build and present to students. On the other hand, showing 3D visual materials to students enhances their involvement in the educational process as young people are very attracted nowadays to modern 3D motion pictures and hi-tech visual effects. A great number of physical processes are much better understood when viewed in 3-dimensional graphical interface in stereo 3D vision compared to standard flat 2D presentation. The current paper describes the modern stereo 3D technologies that are applicable to various tasks in teaching physics in schools, colleges and universities. Examples of stereo 3D simulations developed by the author can be observed on the Internet1. Why stereoscopy? When simulating a physics phenomenon, e.g. waves interference, particle system, pendulum, rotating rigid body, etc, one needs a three dimensional visualization of the process, because when studying such problems the perception of spatial location of the participating particles or bodies helps considerably understanding what is going on in the setting. An appropriate example of where spatial perception is crucial is the vector cross product which students often have difficulties in understanding and visualizing. The 3D-depth perception becomes even more worth while presenting dynamic phenomena like simulation of motion and rotation of pendulums and gyroscopes under the action of external forces. In such cases the stereo 3D vision comes to help. Stereoscopic technologies The stereoscopy imaging is the technique, which creates an illusion of depth into a flat (two dimensional) image. The first stereoscopic experiments in modern times started around 1850. The human perception of depth is built upon several sources of depth information such as focus, linear perspective, occlusion of one object over another, etc. But the clue with determining impact on the depth perception is the stereopsis – the difference in the projection of the same scene in each eye2,3,4. This factor is not present in standard flat images like the one on computer screens. Stereoscopy is the technology that presents a different image to each eye, namely a different and appropriate projection of the observed scene in accordance to eye position in space. There is still one source of depth information not presented through stereoscopy – the focus source, because the two images are still flat. To realize stereoscopy, the utilized technology needs to separate the viewed image into two different images – one for each eye. There are three principle approaches to achieving this task: 1. Use of stereoscopic spectacles 2. Use of stereoscopic displays 3. A combination of both
Fig. 1. Anaglyph stereoscopic 3D glasses 1. Use of stereoscopic spectacles When implementing the first approach, the mission to separate the light source coming from the display into two images (left and right) is carried out solely by the glasses the viewer wears. This technology is the cheapest, because it provides stereo vision with ordinary displays. Such a technology is applicable even to paper sources like printed magazines, printed images, plots, etc. The spectacles consist of two glasses – left and right glass and each one letting only the light information inherent to the respected image (left or right one). But how
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light could be separated? By studying the light phenomenon one reaches three possible modes of separation that are therefore utilized in the following three stereo glasses technologies: • Glasses that separate light by polarization • Glasses that separate light in time • Glasses that separate light by color (wavelength)
Fig. 2. Liquid crystal display (LCD) shutter 3D glasses The light separation by polarization is impossible without the aid of a special stereoscopic polarized display or projector, hence this method is discussed later. Separating light in time may be done using ordinary cathode ray tube (CRT) monitors while the glasses should transmit light alternatively through the left or right glass thus passing one frame to one eye and the next frame to the other eye. Figure 2 shows liquid crystal display (LCD) shutter glasses which accomplish the described task. The process of alternative light passing is done quickly in synchronization with the vertical blank of the CRT display (vertical reverse scan). In the period when the CRT ray is preparing for the next frame the special stereoscopic glasses should switch the light transparency from one eye to the other. As this process of switching is performed at least fifty times per second the observer could not notice the time separation of incoming light, but may notice an annoying effect called flicker under lower refresh rates. The final effect of this technology is that both images, left and right, seem simultaneous and noninterrupted, thus providing a stereoscopic experience. When higher monitor refresh rates are used the effect is smoother and less saddling to the viewer. It should be mentioned that except CRT displays several other more modern display types are applicable to this technology such as Light Emitting Diode (LED) displays. On the other hand, older LCD displays have lower frame to frame separation and the effect of stereo vision would be diminished when an ordinary LCD display is used. Furthermore, observing light in time separated stereo images from paper sources is impossible. The glasses used normally implement fast liquid crystal shutters controlled from the display video card in order to synchronize the shutters with the vertical reverse scan of the monitor. This implies a cable connecting the glasses to the computer, which may be cumbersome. There are glasses models with wireless synchronization and battery power (consumption around 7mW) yielding more comfort while viewing. Such glasses involve a considerable amount of electronics that makes them comparatively expensive – around $50 or more. The third mode of light separation using solely glasses is also the simplest. Visible light has wavelengths approximately from 750nm to 390nm (see Figure 3). If the left glass of the stereoscopic spectacles passes through only one portion of the visible spectrum, while the right glass passes through another portion, and if these two portions do not overlap, we have color separation. Such glasses are called anaglyph glasses. In order this separation be useful the light source (monitor or printed paper) should also separate the two images in accordance with the used anaglyph glasses.
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Fig. 3. Spectral light separation using anaglyph glasses. The visible light spectrum is presented with corresponding wavelengths. The top-most plot shows normalized eye sensitivity to the three basic colors (red, green and blue). The middle plot describes the average monitor emission spectrum. The third plot (lowest) demonstrates the transmission of ordinary pair of paper frame red-cyan anaglyph glasses. Monitors emit light in three separate color spectral regions: red, green and blue (Figure 3 – middle plot). Hence, anaglyph glasses have only a few combinations possible of these three colors (red, green and blue) to form the left and right glass transmission spectra. The following table discusses the most used variants: Red-cyan anaglyphs. This variant is most common. The left glass transmits only red light, while the right glass transmits green and blue light. These anaglyphs provide good color perception (Figure 3 – lowest plot).
Yellow-blue anaglyphs. In this type of spectacles the left glass transmits red and green light, while the right glass transmits only blue light. The right eye is restricted to observe only blue light thus the detail comprehension of the right eye is decreased to a certain extend. The visibility of color is good.
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Red-green anaglyphs. This variant of stereo glasses is old and was used in early cinema stereoscopic movies and comics books of the 50-ies. The left glass transmits red light and the right glass transmits green light. The blue light is not utilized and thus color perception is diminished.
Magenta-green anaglyphs. These glasses transmit red and blue light through the left glass and green light through the right glass. They provide good color sensitivity.
Red-blue anaglyphs. This variant is new and is used where the green color of the monitor or printed material has wide spectrum and leaks into both images - passes through both glasses of anaglyph spectacles of the above types. Because red and blue colors are well separated, this variant of anaglyphs provides the best color separation but lacks the good perception of colors. Table 1. Different variants of anaglyph glasses. There are two major drawbacks when using anaglyph glasses. Firstly, the color perception is not perfect, because in order to regenerate the right color, the viewer has to combine color information from both eyes, while also comparing light intensity. Thus the most used red-cyan glasses loose color sense for the red color to some extent. The other drawback is that some monitors or printed media may have wide spectra of their basic colors thus, for example, the green could penetrate through the red glass and create the so called ghost image or image leaking. This negative effect presents the right image to the left eye (or vice versa) with lowered, but still visible luminance, ending with double vision and loss of stereo detail. To fight ghosting, software color filtering is applied and the leaking light from the opposite image into the prime image is neutralized by applying background intensity subtraction in the prime image. Color anaglyph image of physics simulation of a pendulum is shown on Figure 4. When the viewer looks at Figure 4 through red-cyan anaglyph glasses they would observe the presented scene in volume. The origin of the coordinate system has zero depth so it will appear on screen level. The pendulum would be seen coming out of the screen closer to the observer, while the back of the screen’s floor would appear as if it is behind screen level farther from the viewer. Thus the observer may easily distinguish the directions of the coordinate axes (white vectors X, Y and Z), all shown vectors and also comprehend the shape of the pendulums trajectory – something hardly feasible when looking at a flat image.
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Fig. 4. Simulation of a pendulum with trajectory drawn (stereoscopic 3D anaglyph image). Use red-cyan . anaglyph glasses To demonstrate further the visual effect of presenting physics scenes in stereo 3D anaglyph graphics, two simulations screenshots are shown on Figure 5. Again, when Figure 5 is observed using stereo anaglyph glasses, a perception of mutual disposition of the shown elements is obtained. On the left it is seen a complex rigid body construction called the Poinsot construction. The invariable plane is perceived in space and viewers may identify its orientation and normal vector. On the right side of Figure 5 a precession and nutation of rigid body motion is shown. Using red-cyan anaglyphs, the reader would acquire volumetric visualization of the force arm trajectory thus understanding precession and nutation basic characteristics. Stereoscopic simulations on a personal computer are useful for both teaching simpler physics settings (like planar pendulum) and also complex settings of phenomena and mathematical constructions taught in analytical and theoretical mechanics in the universities – a wide range of applications.
Fig. 5. Stereo 3D simulations of rigid body free motion (on the left) and gyroscopic effects (on the right). . Use red-cyan anaglyph glasses A comparison between the same image in stereoscopic anaglyph and non-stereoscopic view modes is observed on Figure 6 (a simulation of a rotating disc). When viewing Figure 6 using anaglyph glasses the reader would quite clearly understand the difference - the left image would position the disk’s center on screen level, while half of the disk would appear out of the screen and the other half sinking into the screen.
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Fig. 6. Comparison between stereoscopic anaglyph view mode (left) and non-stereoscopic view mode . (right). Use red-cyan anaglyph glasses 2. Use of stereoscopic displays The display of such kind separates the visual field in consecutive narrow angle sectors, where alternatively the left or the right image is visible. The perception of the correct images is dependant on the position of the viewer’s head in respect to the stereoscopic display and small readjustments would degrade the visual effect. 3. A combination of both: stereoscopic spectacles and a stereoscopic display The most common technology of this class is the polarized light displays and glasses. This is the preferred technology in stereo 3D cinematography. Light coming from the display is polarized in two opposite manners, e.g. circularly polarized in two opposite rotations or linearly polarized under 90 degrees difference. The latter model causes ghosting when viewers incline their heads to left or right and is generally unacceptable. Hence modern polarized glasses are usually circularly polarized (Figure 7). Such glasses cost around $3. The expensive part of the hardware is the display that emits light in two opposite circular polarizations. A common solution is a special polarized light projector (or a pair of projectors) along with a silver-plated projection screen (in order to keep the polarization unchanged under reflection). Such a system is presented in “The Physics Teacher” journal vol.46 of March 20085. As the author states, it offers good color perception and clear images. There are limitations of course. These limitations start with the high cost of several thousand dollars for the hardware required (special projectors and screen, dual monitor video card, etc.). Another drawback is the high weight and size of the system, uneasy to move from one room to another and the need to readjust the projectors so that their images match each other on the screen. Such a system yields perfect results, but is not very practical for use by everyone and everywhere, especially for a single user configuration, such as sitting at home and watching 3D stereoscopic simulations on your personal laptop. Applying this technology at movie cinemas is beneficial due to the large number of visitors.
Fig. 7. Polarized 3D glasses
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Another possible stereoscopic solution that combines 3D glasses and a special monitor is the headmounted display. It involves a separate miniature LCD or LED display in front of each eye with the appropriate set of inbuilt optics (Figure 8).
Fig. 8. Head mounted display This technology yields ideal results, but requires considerable investment. 3D Cinema In its dawn movie industry incorporated red-green anaglyph glasses for the first stereo movies in the 50ies. As technology advanced today 3D cinemas in most cases employ the polarized light technology. Such an approach yields perfect visual results and the great success of the recent 3D movies such as James Cameron’s ‘Avatar’ are the best proof of the effectiveness of this approach and the interest among cinema visitors in 3D visual effects and entertainment. For the movie industry, implementing the polarized light technology is justified – there are many viewers of one screen costing several hundred thousand dollars. Coming to personal 3D cinema the approach gives in to the anaglyph technology or to moderate cost methods such as shutter glasses of headmounted display. There were a total of 21,936 3D cinema screens installed worldwide at the end of 20106 and the number is still growing. It is clear that when viewed in 3D, scenes of physics settings are perceived better and understood by more students. But except this benefit, implementing 3D visual approaches in schools and universities would attract more students to physics classes just like cinemas do. Conclusion Presenting physics through stereoscopic 3D vision not only helps easy and quick understanding of the phenomena studied, but also gives students an enjoyable experience thus attracting them to the learning of physics. The problem solving is also benefited by stereo 3D presentations as the discussed physics settings are clarified. The illustrated technologies of stereo 3D vision are all applicable to this task, while each one has its limitations. Clearly, the cheapest and hence most accessible technology is the anaglyph glasses, to which this paper paid most attention.
References 1. Stereo 3D simulations: http://ialms.net/sim/ 2. Steinman, S., Steinman, B., and Garzia, R. (2000). Foundations of Binocular Vision: A Clinical perspective. McGraw-Hill Medical. ISBN 0-8385-2670-5 3. H. Richard Crane, “Uncommon uses of the stereoscope,” Phys. Teach. 25, 588 (Dec. 1987). 4. Curt Gabrielson, “One brain, two eyes, three-D,” Phys. Teach. 34, 10 (Jan. 1996). 5. Philip Dukes and Dan Bruton, “A GeoWall with Physics and Astronomy Applications,” Phys. Teach. 46, 180 (Mar. 2008). 6. David Hancock, “Digital Screen Numbers and Forecasts to 2015 are Finalised”, iSuppli (Jan. 2011), (http://www.isuppli.com/media-research/marketwatch/pages/digital-screen-numbers-and-forecasts-to2015-are-finalised.aspx)
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