Taking 1/2,000 radian as the mean sharpness of vision and 21 in. as the mean separation of the eyes, and calling d and d' the distances of the point A and the plane P from the observer (all distances being measured in inches)— from the similar triangles A and Aa„A,, we get a d' –d d' - whence d = 2•5 d a - I 2.5 and since, at the limit, a = c/72,000, we find for the distance of a point A from the back ground P d + I or ; 0^0002 d d The zone of depth d' –d in front of a plane in which all objects appear to be in the plane P is sometimes termed the neutral zone, and the depth d, measured from the observer in which binocular relief can be appreciated, the efficient zone. The following table gives the depth of the efficient zones and neutral zones for various distances of background 815. Increase in Range of Stereoscopic Relief. There are two ways of extending the limits of perception of relief and of decreasing the depth of the neutral zones.
By the use of a binocular system (binoculars, field glasses) magnifying n times one can resolve an angle it times as small. At great distances the depth of the neutral zone is thus reduced to 'In its original depth, and the sharpness of vision of relief is n times as great.
By the use of a system of mirrors mm, (Fig. 202) of the telestereoscope of Helmholtz (1857), which enables an observer to use as viewpoint instead of his eyes at 0„0,, two virtual eyes 0„'O,', in times as far apart, the distance between the two projections of the same point The same means can be used to increase the intensity of relief in the examination of stereo scopic photographs and extending the range of the stereoscopic vision.
In general it would be fruitless to attempt to augment the power of separation by examining photographs under high magnification, but one can at least examine at short distance photo graphs taken at great distance, bearing in mind that under these conditions the reconstructed object is no longer similar to the original, but is a deformation of it (§ 27 and § 822).
Increase of the base (distance apart of the two viewpoints or stations) is the most usual means of reproducing stereoscopically objects situated outside the range of stereoscopic vision on the background (§ 814) is increased 111 times ; this reduces the depth of the neutral zone to xim of its original value and gives a power of perception of relief m times as great.
These two methods put in the place of the object examined a virtual object similar to the object itself, and situated hi. the efficient zone of perception of relief. In the case of the telestereoscope the visual rays used coming from the object ABCD appear to come from the object abed, forming a model reduced in the ratio and situated at a distance from the observer equal to rim of the distance of the object in question.'
whatever the distance of the objects from the observer may be. Stereoscopic photographs have been obtained of the satellites of Jupiter, and even of stars, with bases of enormous length obtained by the displacement of the earth in its orbit. Bases of the order of a mile are frequently used in aerial photography at high altitude. Bases up to 'co yards are used on the earth to obtain stereograms for the con struction of maps.' This process is usually known as stereoscopic photography with a large base ; also under the name, incorrect in our opinion, hyperstereo scopic photography.
Take two photographs 7' and T' of a distant object ABCD (Fig. 203), the camera being moved horizontally in a direction parallel to the plate between the two exposures. The lens thus passes from the position 0 to the position 0' such that 00' is m times the separation of the eyes. Each of the prints and T,' observed with one eye occupying the position of the corres pon.ding viewpoint will give us the same sensa tion as that experienced in observing the object directly from the corres ponding position.
Place the two photo graphs side by side, taking account of their orientation (left and right), and separate their principal points by a distance equal to the mean distance between the eyes ; and examine the result in a stereoscope, the eyes being placed at 0 and 0" opposite the principal points at a distance from them equal to the principal distance. We shall then experience the same effect as we should obtain by viewing direct the object abcd, which is a reduced model of the object ABCD in the ratio rim and situated at a distance m times as near Photographs of this reduced model taken from the positions 0 and 0" would give exactly the same effect as photographs of the real object ABCD taken from positions 0 and 0'.
8i6. Stereoscopic Transposition. In the usual practice of amateur stereoscopic photography, the two negatives of the stereoscopic pair are taken simultaneously on the same plate in a camera fitted with two lenses and divisions. 1 It can easily be seen (Figs. 200 and 204) that in order to place before each eye in its correct position the image corresponding with it, it is necessary to separate the two images, turning each through to compensate for the rotation through 18o° suffered by each in the camera.