Stereoscope

STEREOSCOPE (from the Greek stereos—solid and skopeo—I look). When fixing any drawing on a frontal plane, its images on the retinas of the right and left eye will be copies of each other and, within the limits of the fovea centralis, will fall on identical points. The impression obtained from such a planar object during binocular vision will not differ in any way from that during monocular vision. The most valuable property of binocular vision is the ability to perceive and very finely evaluate the depth of space and to feel relief. Vision with one eye is not devoid of this property; the evaluation of depth and relief here is simply not as perfect and is based on the perspective change in the size of objects, on shades of lighting, and on aerial perspective. In binocular vision, thanks to the difference in the position of the eyes relative to the solid object being viewed, the right eye captures a larger part of the right side of the object facing it, and the left eye captures a larger part of the left side facing it. Under such conditions, it is clear that the images on the retinas will not be identical, and consequently, not all elements constituting the image of the object will fall simultaneously on identical points. The ability to combine these elements, located in different planes, into a single whole, and the ability to evaluate their mutual relationships in space, constitutes the main advantage of binocular vision.

The difference between monocular and binocular vision appears clearly when viewing two drawings (Fig. 1), of which one (L) gives the image of a truncated pyramid for the left eye and the other (R)—as it is drawn for the right. By crossing the eyes so that the large squares ABDC and A1B1C1D1 coincide, we will see that all corresponding points of both drawings also coincide, although the small squares will take a position in front of the large squares, which, together with the coinciding edges, will give the image of a solid object—a truncated pyramid facing the observer with its apex. Comparing these images with each other, it is not difficult to note that the elements constituting them, namely the bases and vertices, are completely identical in both drawings, but the mutual relationships of these parts are not the same. In Fig. 1 L, the small square is shifted to the right; in Fig. 1 R, to the left, as a result of which the distances between the corresponding sides of these squares are not the same. Line AB is further removed from A1B1 than ac is from a1c1, and consequently, the centers of the vertices are closer together than the centers of the bases. With some practice, it is easy to move the fixation point behind the plane of these two images, for which it is required to gradually weaken convergence until the visual axes pass through the centers or other corresponding elements of the large or small squares. Let us assume that we have weakened convergence so much that the visual axes of both eyes have passed through the centers of the small squares; then their images will fall on identical points and will take a place in space corresponding to the position of the intersection point of the visual axes. For the fusion of the large squares, even less convergence is required, which is why the intersection point of the visual axes passing through their centers will move further away; in other words, in the observer's perception, the base of the pyramid will be further away than the apex. For viewing such paired images obtained for the right and left eye, a stereoscope is convenient—an instrument first proposed by Wheatstone (1838) and subsequently improved by Brewster (1843). The Wheatstone mirror stereoscope consists of two mirrors A and B, positioned at such an angle that the eyes of the observer view the images L and R reflected from the mirrors with converging visual axes.

Figure 2.

Figure 3.

From Fig. 2, it is clear that both images L and R will merge into one and give a relief picture in KK. In the Brewster stereoscope (Fig. 3), the mirrors are replaced by convex prisms A and B, in front of which are placed the stereoscopic pictures L and R, from which the rays, upon exiting the lenses, take on, as in the Wheatstone stereoscope, a diverging direction, thanks to which the observer's eyes view the plastic image obtained from the fusion of L and R in KK with converging axes. The difference in the pictures constitutes the most important condition for the perception of relief, and the greater this difference (up to a certain limit), the more strongly the relief is perceived. This difference is greater the closer the object is to the observer, and with equal distances of the object, the greater the distance between the observer's eyes. According to Helmholtz, the geometric conditions for the perception of relief disappear if, during viewing, the visual axes form an angle (convergence) of less than 1 minute between them; if we perceive depth and relief beyond these limits, it is only thanks to the relationships of the sizes of objects, aerial perspective, and shades of lighting. To obtain an impression of solidity from such distant objects, Hardie (1853) and Helmholtz (1857) constructed an apparatus that received the name telestereoscope, with the help of which the distance between the observer's eyes is artificially increased; the eyes are, as it were, moved away from each other to a greater distance, thanks to which the limit of relief perception is correspondingly moved further away. A diagram of the telestereoscope is shown in Fig. 4. Diverging rays from the object fall on mirrors A and B and, having reflected from them, are directed into the eyes with the help of other mirrors a and b. Thus, the observer's eyes fix the object as if the normal distance between the pupils had been increased to the dimensions of the apparatus. The mirrors in telestereoscopes are usually replaced by prisms with total internal reflection.