Using cellophane to convert a liquid crystal display screen into a three dimensional display

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5. Eye Fatigue

We now consider a modification to the configuration in order to ease the problem of eye fatigue. We begin by reviewing factors that contribute to eye fatigue. The eye ball itself rotates when viewing an object. The inside muscle (medial rectus muscle) contracts and the outside muscle (lateral rectus muscle) expands to turn the eyeball inward. The macula (yellow spot) near the optical axis is the area where the sharpest image is formed in our retina, but it is tiny and is within 4 degrees of the optical axis. The eye ball is continuously working to place the image onto this spot. This eyeball movement is called convergence or simply vergence to the position of object. At the same time, the focal length of the eye lens is adjusted by the tension of the cilliary body muscle to clearly focus the image on the retina. This is called accommodation of the eye to the position of the object. Our brain judges the distance to the object primarily from parallax, but convergence and accommodation are two other major factors. (Certainly it is much more complex, and there are other factors such as occlusion, relative size, shadows, foreshortening, relative brightness, atmosphere and texture gradient, and movement parallax,5-10 to name a few.) It has been clinically shown5 that if the point of convergence is different from that of accommodation, eye fatigue accumulates. In Fig. 4 the points of convergence and accommodation are different. The point of convergence is to the midpoint between the camera phones and the eyes, while the point of accommodation is to a point on the camera phone display. This difference not only becomes a source of eye fatigue, but there are some people who are not able to make binocular fusion and cannot see the 3D effect even with a slight difference between the points of convergence and accommodation. This is analogous to color blindness in which some people cannot see certain colors.

A pair of prisms was used to alleviate this problem as shown in Fig. 5. Prisms with a 5.6 wedge angle were used ( One prism deviates the path of light approximately by 3. The prisms shift the location of the image as shown by the dashed lines in the figure. That brings the image to almost the position where the object was originally located without harming the three dimensionality of the image. This arrangement reduces not only eye fatigue but also lessens the problems associated with poor binocular fusion. The required angle of deviation of the prism depends on the viewing configuration. It certainly can be determined by calculation. An easier way is described as follows. When an observer looks through the pair of glasses with prisms at an ordinary object, the observer sees double images. The wedge angle of the prism is chosen such that the spacing of the double images becomes equal to the spacing between the pair of stereoscopic images.

Fig. 5 Wedge prisms deviate the image to the original location to relieve eye fatigue.

The cross-sectional shape of the pair of prisms resembles a single plano-convex lens with its center portion removed. This suggests an easy method for combating poor binocular fusion. By just looking through an ordinary magnifying glass, the problem of poor binocular fusion may be solved. Select a magnifying lens whose diameter is just large enough to cover both eyes so that your eyes see primarily through the diametrical opposite edges as shown in Fig. 6. The proper position of the stereoscopic pair of pictures for a given focal length of the magnifying lens is found as follows. Make a V sign with your fingers such that the spacing of the pointer and middle fingers matches the spacing between the stereoscopic pair of pictures to observe. Stretch your arm in front of you and look at your finger V sign through the diametrically opposite edges of the magnifying lens. As your stretch your arm further, the single image of your V sign starts to split into a double image and begins to form a three finger V sign. The length of the required stretch of your arm to see the three finger V sign is the distance you need to the stereoscopic pair of pictures. An added bonus of the magnifying glass is that it enlarges the image.

Fig. 6 Use this method to determine the position of the stereoscopic images for a given focal length of the magnifying glass. First, adjust the spacing between the pointer and the middle finger to be equal to the spacing between the pair of the stereoscopic pictures to observe. The V sign image shifts when viewed with the eyes aligned near the edges of a magnifying glass. The shift depends on the stretch of the arm. Find the length of the stretch of the arm for which a three finger V sign is observed. The stereoscopic pair should be placed at this position of the fingers to observe the 3D image.

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