1. Monocular vs. Binocular View Monocular view: one eye only! Many optical instruments are designed from one eye view. Binocular view: two eyes with each seeing a separate picture of the world.  Increase the field of view: fish, rabbits can see 360.  Overlapping view: predators with two eyes in the front.

2. Human eyes Separated by ~ 6.5 cm. Have field of view ~ 208˚. Overlapping view ~ 130˚. Each eye sees a slightly different view. Your brain combines the two images into one view of the world! (mixing of signals in the optical chiasma and visional cortex)

3. 2-D vs. 3-D world A picture is a 2D reduction of the 3D world. How do we appreciate 3D? We use many different cues ( a feature indicating the nature of something perceived)  Accommodation  Convergence  parallax

5. Accommodation The amount of accommodation necessary to focus your eye on an object tells you the object’s distance.  See the object clearly with a relaxed eye: it is far away.  Tense your eye muscles to focus, it is close by.. It is only useful, however, to measure distances for close objects.

6. Angle of convergence The angle between two eyes’ directions of gaze.  For object close by, say 25cm. It is the biggest, about 15 degree.  It is 1 degree for an object 4m away. If the brain keeps track of the convergence of eyes, it can determine the distance to the object. ( help to distinguish a painting from a real scene !)

8. Parallax Your view is different from different positions.  Viewing something from two different perspectives causes it to seem to move between two positions, at least compared to its background Has been used by astronomers to determine the distances of the stars from us.

10. The first parallax shift of a star was detected in 1838 by an astronomer named F. W. Bessel, at the Konigsberg Observatory in Prussia. The star was actually a binary called 61 Cygni, a gravitationally bound pair of red dwarf stars. Bessel found that these stars were making annual loops with a radius of.29 arcseconds, corresponding to a distance of 10.3 lightyears (in other words, the distance light would travel in 10.3 years!). What's an arcsecond, It's a sixtieth of an arcminute, of course, which is a sixtieth of a degree. A degree is about the width of your thumbnail, held at arm's length. It's not surprising that earlier astronomers had such a hard time detecting such a tiny shift!)

11. Binocular Disparity Two eyes, at different positions at the same time, see slightly different views of the any object they look at. The binocular disparity provides a way of determining the distance of the object in sight.

13. Because the eye are fixated on the tree, the tree is imaged on corresponding points of the retina ( those points that would be identical if one retina was moved over to superimpose the other retina ) and thus there is no disparity. The policeman, who is closer to the observer, has its image falling on non- corresponding points of the retinas. That is to say its images are binocular disparate. This binocular disparity provides a cue to the distance of the policeman relative to the distance of the tree.

14. Where could it fail?  If the two eyes see the same image: Two examples horizontal power lines! objects that repeat themselves (bars in a cage)  Distant scenes.

15. Stereoscope

16. Create 3-D images!  Present two different pictures to the two eyes so that each eyes sees only the image intended for it. How to create them?  Two cameras side by side  Moving a camera slightly

18. Superimposed 2D pictures Use color filters:  Two similar pictures with different colors are superimposed (anaglyph). Viewers are given a different color filter for each eye. Use polarization  Two similar pictures are projected with light of different polarizations (horizontal or vertical)  Viewers are given a special pair of glasses with polarization filters. (3D movie) Stereogram