74. Photographic Perspective. The photo graphic image is an exact perspective rendering of the objects represented, the viewpoint of which, relatively to the objects, is the centre of the entrance pupil ; relatively to the image, the ray would be the one originally directed to the point the centre of the entrance pupil, and would appear to emerge, after passing through the lens, from the point E, the centre of the exit pupil. The assembly of the different parts of the ray forms what is sometimes called a principal ray.
In the particular case where the stop is placed with its centre at the optical centre of the instrument (which frequently happens with symmetrical lenses), the centres of the pupils coincide with the nodal points, but this coinci dence does not occur with single lenses, conver tible sets, nor telephotos, and in other types of lenses is not always aimed at.
Just as by consideration of nodal and focal points it is possible to determine the dimensions of the image without considering the construc tion of the optical system forming it, so by consideration of the pupils it is possible to determine the perspective and the centre of projection of images without having to be con cerned with the optical system. The pupils in fact determine which of the rays are used in the formation of the image, without upsetting in any way the conclusions that have been drawn, as viewpoint is usually identical with the nodal point of emergence.
Consider (Fig. 58) the two conjugate planes QQ' of an optical system represented by its nodal points, foci, and pupils, and let us find how the points R and S outside the plane Q will be reproduced on the plane Q', .1?' and S' being the respective images of R and S (the graphical construction is indicated by dotted lines) and being themselves outside Q'.
The bundle of rays used in the formation of the image of the point R is limited by the cone with apex R and base (the entrance pupil). After passing through the lens it forms another cone, having the exit pupil P e as base and R' as apex. These two cones form circular patches (circles of confusion) on the focussed plane Q and on its conjugate Q', where the focussing screen or photographic plate is placed. The circles of confusion are conjugate, with their centres r and r' at the intersections of the principal ray with the respective planes, and the ratio of their sizes is equal to the ratio of the ultra-nodal distances of Q and Q' (say n). If the patch at r' is sufficiently small and the photograph is viewed at a sufficiently large distance, the patch is indistinguishable from the geometrical point image of r (the secondary axis corresponding to r has been drawn in Fig. 58).
75. The fact that the construction of the lens (except in the case of very pronounced distortion) and its focal length have no influence on the perspective of the image can be proved by photographing an architectural subject from the same viewpoint successively with a pinhole (§ 38) and with lenses of very different focal lengths. The different images thus obtained will be identical except for size.
It is thus incorrect to attribute to the use of a short-focus lens the unpleasant, almost dis torted, views which are easily obtained with The photographic image thus coincides with a photograph, made on a scale of reproduction n, of the perspective of the objects projected on the plane Q from a point coinciding with the centre of the entrance pupil. It is thus itself a. perspective view if the lens is free from distor tion and the diameter of the entrance pupil is a small fraction of the distance of the objects represented. so that stereoscopic effects are avoided 58).
Now it is known that different perspectives obtained by proportional enlargement or reduc tion have their principal distances proportional to their respective scales (§ 24). The principal distance of the perspective at Q' (the photo graphic image) is thus the product of the distance of Q from the entrance pupil, multiplied by n. In every case where the object photographed is at a distance from the lens compared with which the distance of the entrance pupil from the nodal point of incidence is negligible, the prin cipal distance of the photograph can be taken as the ultra-nodal distance, and the viewpoint as the nodal point of emergence (L. P. Clerc, 1923).
these lenses. These perspectives, exact but unpleasant, are due solely to the choice of too close a viewpoint. When a photographer pos sesses only one lens, and that of short focus, he unfortunately tries to get as large a picture as possible, and so approaches closer than he would if he used a long-focus lens. Unless he is specially trained, he does not notice, when examining the view, the exaggerated perspective arising from too close a viewpoint, the brain making the objects appear at their correct relative size, whilst binocular vision places them in their correct relative positions. On the plane images these compensations do not exist, and the so-called distortion becomes actually offen sive, especially if the image is viewed from a position other than the correct viewpoint (§§ 25 and 28). These anomalies disappear in stereoscopic vision if the images are viewed at the principal distance.