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I have just finished watching the new Star Wars movie (The Force Awakens), and during the end credits, text is shown upon a background of stars. Wearing the 3D glasses, I noticed that the text appears in the foreground, and the stars appear in the background. On removing the glasses, I then noticed that the text is crisp, clear and drawn only once on the screen, whereas the stars are all drawn twice, with a constant distance (from left to right) between the two instances of each star.

However, from my understand of how 3D glasses work, objects whose two instances are further apart should appear closer to the eyes, and objects whose two instances are close together (or at the same location, as with the text), should appear further away from the eyes. So why did I experience the opposite effect when I watched the credits?

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up vote 22 down vote accepted

The others have already provided good explanations, but since it sounded like an interesting question and I already sketched up a diagram, I thought I would show it, too. As already mentioned, if you have an object that is to be shown as the exact same distance as the distance between you and the screen, it's very easy to represent that: It's just a single object on the screen that looks the same to both eyes. If, on the other hand, you want to show an object which is far away, then you need to 'trick' your eyes by showing two separate images on the screen, one for the left eye and another for the right eye. That's indicated by the two hollow green dots on the screen on the diagram below. And if you want to show an object which is closer to you than the actual screen distance, then to trick your eyes two images at the locations of the hollow blue dots need to be presented on screen. Note that for objects that are to appear closer than the screen distance that the placement of the images is reversed: The image for the left eye is to the right of the image for the right eye, and the image for the right eye is to the left of the image for the left eye.

It's interesting to note that the apparent distances of the objects are all scaled to the actual distance of the observer to the screen, so audience members will have somewhat different impressions of the distances to the on-screen objects depending on how far from the screen they are seated. Perhaps something to take into account the next time you go to see a 3D movie.

(P.S.: On the diagram the actual observer-to-screen distance is assumed to be 30 feet. Hence, an object to be presented at an apparent distance of 30 feet is represented by a single dot on the screen.)

Diagram

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Some followup: As seen from the sketch, the green dots should never be further apart than the viewer's eys (6.6 cm for me, possibly less for kids). But what if a movie with (nearly) infinitely far objects is shown in different cinemas with different screen sizes? Wouldn't either small screen cinemas bring those objects into finite distance, or super-large screen cinemas produce "impossible" images (the two copies more than 6.6cm apart)? – Hagen von Eitzen Jan 12 at 16:13
    
@HagenvonEitzen - An interesting point. How would one perceive an object that is apparently flying off into the far distance if the separation between its two images for the left and right eyes became greater than the distance between one's eyes? Would the illusion of depth be suddenly shattered and your brain suddenly perceive two separate images? Or would your sense of depth "fail gracefully" and your brain interpret the object as still being at infinity because it refuses to let the illusion of depth be shattered? That answer lies outside of physics and in the physiology of human vision. – Samuel Weir Jan 12 at 19:37
    
@HagenvonEitzen: I hope you're asking this as a followup! – Charles Jan 12 at 20:17
    
@SamuelWeir Make your hand flat, and place it against your nose as a divider between your eyes. You notice that you "half-see" your hand, and "half-see" what the other eye is looking at. You also notice that you can choose to focus on one image over the other. A similar test is done when I go to the optometrist (I assume it tests whether there is a difference between each eye's sight in comparison to each other) where a word is "split" up for one eye, and down for the other. Your vision attempts to correct it to a point , but when it can't, it appears the same as your hand, "half visible". – DoubleDouble Jan 12 at 20:41
    
..but with two copies. That is because each eye is only looking at one image which doesn't match the other eye. If both eyes are looking at two stars, it probably just appears as two separate stars once it gets out of that "correction" threshold, which is different for each person. – DoubleDouble Jan 12 at 20:42

That's a very good observation! The screen is at a finite distance. If you want to show something at the distance of the screen, then, obviously (?) the two images would be in the exact same location on the plane of the screen. That's the text. Now imagine something way, way behind the screen (stars are at infinity). Draw an imaginary line from each star to your eyes. Where do these lines intersect the plane of the screen? At two different points, right? That's where the cgi algorithm places the left/right star images to make them appear at infinity.

enter image description here

Test question for max. points: Where would the stereo images be for something that should appear in front of the screen?

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If the text appeared to be at about the position/distance of the actual screen in the theater and if the stars appeared to be much further behind the screen, then what you observed with the glasses off was exactly correct. To focus on the screen, which is not at "infinity", your eyes have to cross slightly. In that case, the stars that are intended to be much further away will have to have a different position on the retina of each of the eyes relative to the position of the text on each retina.

To make it clearer, if the movie makers intention was to have the stars look like they were at the screen distance and if they wanted the text to appear closer than the screen; then the stars would only appear once on the screen, but the text would be doubled with each eye seeing the text at a slightly different position on the retina relative to the stars. This would cause you to have to cross your eyes a little more to make the text images coincide at the brain to make the text appear closer than the screen.

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As others have noted, the stereopsis cues to depth would indicate that objects appearing on the same point on the screen for both eyes would be perceived as being at the screen. While points being farther appart in the direction of the eye(left eye image moved further to the left, right eye image further to the right) appear to be further away than the screen. So the stereoptic effect of the image would be as you experienced.

However note that stereopsis is only part of what we use to constuct a depth field for our perceptions. The fact that the stars are occluded by the text is sufficient that our mental image would perceive the text as being in front of the stars.

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