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How to see shadows in 3DGea O F Parikesit

Faculty of Engineering, Department of Engineering Physics, Gadjah Mada University,Jalan Grafika 2, Yogyakarta 55281, Indonesia

E-mail: geaofp@yahoo.com

AbstractShadows can be found easily everywhere around us, so that we rarely find itinteresting to reflect on how they work. In order to raise curiosity amongstudents on the optics of shadows, we can display the shadows in 3D,particularly using a stereoscopic set-up. In this paper we describe the optics ofstereoscopic shadows using simple schematic drawings. We also describe howto build a very simple demonstration set-up for casting and displayingstereoscopic shadows. Moreover, we also describe a list of student activitiesthat can be used to further raise their curiosity.

IntroductionShadows can be found easily everywhere aroundus [1], so that we rarely reflect on the physicsbehind the phenomenon. In order to raise curiosityabout the optics of shadows, we can display theshadows in three dimensions using a stereoscopicset-up. In this set-up, each of our two eyes getsa different view of the same shadow and ourbrain merges the two views to create a three-dimensional image. Stereoscopic shadows can berealized experimentally using two pairs of colourfilters, with one pair positioned in front of the lightsources and another pair placed in viewing glasses.

In The optics of stereoscopic shadows, wewill first describe the optics of stereoscopic shad-ows using simple schematic drawings. Then, wewill describe how to build a very simple set-upof stereoscopic shadows. Moreover, we will alsodescribe a list of student activities that can be usedto further raise their curiosity.

The optics of stereoscopic shadowsThe history of people playing with shadows datesback to at least the second century BCE [2]. Inorder to play with shadows, we only need three

components: a light source, an object and a screen.The object can be made from various materialsaround us, even including our own hands. TheUNESCO-listed Indonesian art of Wayang Kulitusually uses a set-up that consists of a light sourceusing a halogen lamp or a coconut-oil lamp, anobject crafted from buffalo skin and a screen thatis made from a white cotton sheet [3].

Stereoscopic displays have become increas-ingly popular, both in consumer electronic marketsand in technological applications [4]. A shadowcan also be displayed stereoscopically, as has beenperformed by the artist and TED fellow Chris-tine Marie, by using coloured shadows [5]. Thephenomenon of coloured shadows was first docu-mented by Goethe in 1810 [6], where he describedhow multiple shadows with various colours can becast by using several coloured light sources simul-taneously, such that different areas on the screendisplay shadows with different colours dependingon how the object blocks light from the colouredlight sources.

Figure 1(a) shows how a pair of colouredshadows can be cast on a screen. In this example,two light sources, L1 and L2, are equipped with redand cyan filters, respectively. An object is shown

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How to see shadows in 3D

Figure 1. A schematic illustration of (a) how a pair ofcoloured shadows can be cast on a screen and (b) howthese coloured shadows can be displayed as stereoscopicshadows. See the text for details.

by its two edges, i.e. A and B. A shadow with threedifferent colours will be cast on the screen S: a redshadow (in regions where the object blocks thecyan light), a black shadow (in regions where theobject blocks both the red and cyan light) and acyan shadow (in regions where the object blocksthe red light).

Figure 1(b) illustrates how these colouredshadows can be displayed as stereoscopic shad-ows. In this example, the viewers eyes E1 and E2are filtered with red and cyan filters, respectively.Due to the red filter, the eye E1 will only perceivethe black and cyan shadows, spanning betweenthe points AL1 and BL1; it sees the red shadowsimply as bright as the screen surface (i.e. noshadow). Meanwhile, due to the cyan filter, the eyeE2 will only perceive the black and red shadows,spanning between the points AL2 and BL2; it seesthe cyan shadow simply as bright as the screensurface (i.e. no shadow). This occurs such that theviewer will cross their eyes: the left eye will lookat the right-hand side of the screen while the righteye will look at the left-hand side of the screen.The brain of the viewer then uses the informationfrom the muscles that move the crossing eyes tocreate a three-dimensional image of the shadow:some parts of the shadow which result in moreeye-crossing will be perceived as shallow (i.e.closer to the viewer) and other parts of the shadow

which result in less eye-crossing will be perceivedas deep (i.e. further away from the viewer) [7].It should be noted that this stereoscopic three-dimensional display can only work properly underthe condition that there is no cross-talk betweenthe optical information received by the two eyes.A pair of red and cyan filters should work for thispurpose because the spectral properties of thesefilters complement each other, i.e. no light comingthrough the red filter can pass the cyan filter andno light coming through the cyan filter can passthe red filter.

It should be noted that the viewer can stillsee a proper three-dimensional shadow even whenthey move around. A curious student can verifythis, both experimentally by using a real set-up andtheoretically using simple schematic drawings.

A simple set-up for stereoscopic shadowsIn this section we describe how to build a very sim-ple set-up for stereoscopic shadows. Figures 2(a)and (b) show how we used a coloured light sourcemade using a Panasonic BF-977 LED Lamp(Panasonic, Japan), which has three lamps init, with the addition of red and cyan filtersmade from low-cost plastic sheets. Figure 2(c)shows an object, along with the resulting colouredshadows, cast on the wall behind the object. Thecharacters on the right side (I, R, 1 and 0)are positioned closer to the wall relative to thecharacters on the left side (A, J, S, and 2).Hence, when a red filter is positioned in front ofthe viewers left eye and a cyan filter is positionedin front of the viewers right eye, the colouredshadows of the characters on the left side and theright side result in higher and lower degrees ofeye-crossing, respectively. This, in turn, results inthe shadow of the characters on the left side beingperceived as closer to the viewer relative to theshadow of the characters on the right side.

We used the image processing softwareImageJ1 to split the digital RGB image into thered, green and blue channels (see figures 2(d)(f)),simulating how the shadows will be perceivedwhen a viewer uses a red, a green or a bluefilter, respectively. Because the cyan filter doesnot perfectly balance the weighting factors of thegreen and blue filters, the simulated shadow for thegreen filter does not perfectly match the simulated

1 www.rsbweb.nih.gov/ij/.

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Figure 2. A coloured light source made from three lamps and two colour filters, (a) before and (b) after thefilters were added. The resulting coloured shadows (c) of an object were cast on the wall, along with the simulatedshadows seen with (d) a red filter, (e) a green filter and (f) a blue filter.

shadow for the blue filter. However, the simulatedshadow for the red filter is significantly differentfrom the simulated shadows for the green and bluefilters, indicating that we have minimal cross-talkbetween the red and cyan filters in our light source.

In order to better display the shadows stereo-scopically, we need to engineer the light sourceso that we will only obtain two coloured shadows(and no more than that). We therefore performedfurther experiments using two Lightspro LEDLamps (Lightspro, Indonesia) which had beenequipped with light absorbers (to block unwantedparts in the light sources) as well as red andcyan filters. As shown in figure 3, this experimentresults in only two shadows, which can then beviewed stereoscopically using a pair of glassesequipped with the corresponding colour filters.

Student activitiesThe casting of coloured shadows and stereoscopicdisplay of them can be a good way to raisestudents curiosity on the optics of shadows.However, we can further raise their curiosityby engaging them in more activities. Here, wedescribe two types of activities: mathematicalanalysis and conceptual investigations.

Mathematical analysis of stereoscopic shad-ows can be performed by using the followingquestions.

Casting of coloured shadows: given thecoordinates of L1, L2, A and B, can youdetermine the coordinates of the colouredshadows edges AL1, AL2, BL1 and BL2?(Hint: because light rays travel in straight

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Figure 3. A better coloured light source, made using appropriate (a) light absorbers and (b) colour filters, resultsin (c) a pair of coloured shadows that can be viewed stereoscopically using glasses equipped with red and cyanfilters positioned in front of the left and right eyes, respectively, such that the viewer crosses their eyes.

lines, the line that connects A and L1 willarrive at AL1; the same holds for AL2, BL1and BL2.)

Display of stereoscopic shadows: given thecoordinates E1, E2, AL1, AL2, BL1 and BL2,can you determine the coordinates of the

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stereoscopic shadows edges A and B?(Hint: due to the viewers eye-crossing, thepoint A is formed by the intersectionbetween the line that connects AL2 to E2 andthe line that connects AL1 to E1; a similarmethod holds for finding the point B.)

Conceptual investigations can be performedusing the following questions.

Why do we find it more difficult to obtainstereoscopic shadows when we usenon-point-like light sources? Can we still obtain stereoscopic shadows

when we swap the colours of the filterspositioned in front of the two eyes? What happens if the objects dimensions are

smaller than the distance between the twolight sources? Can we use filters of different colours (i.e.

other than red and cyan)?

While the first type of activity, which allowsstudents to deepen their understanding on theobserved stereoscopic shadows, is more suitablefor high-school students, the second type of activ-ity, which can be useful to foster critical thinkingabilities among students, is probably more suitablefor first-year undergraduate students. The concep-tual investigations can be performed either theoret-ically using schematic drawings and mathematicalanalysis or experimentally using a real set-up ofstereoscopic shadows.

ConclusionsWe have described a method to raise studentscuriosity on how shadows work, particularly bycasting coloured shadows and displaying themin 3D using a stereoscopic set-up. We have alsosuggested a way to build a very simple set-up ofstereoscopic shadows, which is suitable for class-room demonstrations. Aiming to further raise thestudents curiosity, we have also included a list of

student activities, which comprise a mathematicalanalysis and a conceptual investigation. We fore-see that our method will be able to attract morestudents to learn about how light works in generaland how shadows work in particular.

Received 12 February 2014, revised 12 March 2014, acceptedfor publication 14 March 2014doi:10.1088/0031-9120/49/3/314

References[1] Lynch D K and Livingston W 2001 Color and

Light in Nature (Cambridge: CambridgeUniversity Press)

[2] Chen F P 2003 Shadow theaters of the worldAsian Folklore Studies vol 62 (Nagoya: NanzanUniversity) pp 2564

[3] Foley K 2010 Dancing shadows, epic tales:wayang kulit of Indonesia (review) AsianTheatre J. 27 3949

[4] McIntire J P, Havig P R and Geiselman E E 2014Stereoscopic 3D displays and humanperformance: a comprehensive review Displays35 1826

[5] http://cimimarie.com/christinemarie/Christine Marie.html, (accessed on 15 February2014)

[6] von Goethe J W 1810 Theory of Colors (London:John Murray)

[7] Gregory R L 1964 Stereoscopic shadow-imagesNature 203 14078

Gea O F Parikesit joined theDepartment of Engineering Physics atthe Gadjah Mada University in Indonesiain 2009, following two years ofpost-doctoral research work onnano-particle image velocimetry at theDelft University of Technology. Heobtained his degrees from the DelftUniversity of Technology in TheNetherlands (PhD in Applied Physicswith research work in the QuantitativeImaging research group; MSc in AppliedPhysics with research work in the Opticsresearch group) and the BandungInstitute of Technology in Indonesia (STin Engineering Physics with researchwork in the Optics laboratory). Hiscurrent research activities are centred onthe field of optics education.

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