It has often been suggested; that for stereo scopic photography the axes of the two lenses should converge on to the point of interest in the subject to be photographed, in the same way as the eyes converge on an object. This reasoning by analogy is unsound, since it neglects an extremely important difference between the eye and the photographic plate, the retina being approximately spherical whilst the plate is flat. The fact that the two images are generally brought into the same plane for viewing causes, on one hand, a discordance which, in the part of the field common to the two images, prevents their stereoscopic fusion to some extent, and, on the other hand, in the parts where this fusion is possible, occasions a deformation of the reconstructed object.
It is easy to show geometrically, and to verify it experimentally, that all the points on a cylinder, generated by a vertical, having for directrix the circle drawn through the two view points and the point of convergence of the axes (sometimes called the horoptic circle) appear, when viewed stereoscopically, to be situated in a front plane. Points inside the horoptic cylinder situated on certain ellipses (or more exactly on cylinders having the ellipses for directrices) containing the two viewpoints, and having their major axes parallel to the base, appear also in front planes, as do also points outside the horop tic cylinder situated on ellipses containing the two viewpoints and having major axes per pendicular to the base, ellipses of which the curvature is greater the greater their distance from the base, appear also in front planes. Conversely, points located on front planes appear to be situated on convex cylinders of greater or less curvature according as the dis tance from the base is greater.' Another deformation occurs if the optical axes, through remaining parallel, are not pr‘r pendicular to the base ; the two pictures are then not in the same plane, but in parallel planes. This condition is often produced accidentally when taking stereoscopic negatives by two successive exposures of a single camera by displacement. This does not occur if the neces sary precautions are taken to ensure the correct placing of the camera in the two positions. 2 In this case there appear as front planes (relative to the direction of the optical axes) inclined planes, of which the inclination is equal and opposite to that of a plane drawn through the two viewpoints perpendicular to the plane which contains the optical axes (strictly, these surfaces are the surfaces of parabolic cylinders with such small curvature that they can be regarded as planes, even when extended over a considerable field).
822. Deformations of the Reconstructed Object in Stereoscopic Viewing. Various deformations arise when examining a normal stereoscopic pair under abnormal conditions. These deformations are the same as those which appear in monocular examination of a perspective when the eye is not placed at the viewpoint (§ 25), but with the sensation of a quasi-materialization of the deformed object owing to the binocular vision.
(r) The most frequent deformation is that caused by viewing a stereogram with the eyes placed at a distance other than the principal distance from the photographs. The dimensions in depth then appear either compressed or extended, relatively to the transverse dimensions, according as the distance of viewing is smaller or greater than the principal distance. If one considers an object whose depth is only a small fraction of the distance at which it is examined, close or distant examination increases or de creases the apparent transverse dimensions without increasing the relief ; for example, a cube resting on a table with one of its faces perpendicular to the direction of vision appears as a rectangular parallelopiped with a square base when viewed at a distance other than the principal distance. The thickness of the solid thus formed is invariable, but the dimensions cf the front and back faces appear greater the smaller the distance from which it is examined.
(2) Assume that the eyes are placed at a distance from the stereogram equal to the principal distance, and the line joining the principal points is equal and parallel to the line joining the centres of rotation of the eyes of the observer. Assume also that the eyes do not occupy the viewpoints (decentring of the eyes relative to the stereogram). The different planes of the object thus formed slide on one another without altering their respective distances, the object thus suffering a twist such that lines of the object perpendicular to the plane of the stereogram appear as oblique lines parallel to the lines joining each eye to the corresponding principal point. A cube photographed under the same conditions as in the preceding case will appear as a parallelopiped with square base but having four edges parallel to the direction in which the principal points are (3) Much more serious deformations occur when the separation of the principal points of a stereoscopic pair is not equal to the separation of the eyes of the observer. If the separation of the eyes is greater than that of the principal points, a cube photographed as in the preceding case will appear as a species of the trunk of a pyramid seen from its larger end, and of smaller depth than the actual cube. Conversely, if the separation of the eyes is smaller than that of the principal points, the reconstructed solid will be a kind of pyramid trunk seen from its smaller end and of greater depth than the cube. In both cases the scale of depth is affected ; an object plane drawn half way between the front and the back face will appear, in the first case, nearer the back face, and, in the second case, nearer the front face.