SURVEYING FROM AIR PHOTOGRAPHS A photograph is a perspective view of the ground it represents. In certain cases, though rarely, the ground surface is truly parallel to the plane of the photographic plate. In this case the photo graph is a correct plan. Any other relationship of ground (or map) and photographic plane results in a true perspective plan so long as the surface to be mapped is flat, the angle between the two planes being known as the tilt. In this case the map can be wholly reconstructed on perspective lines.
The general case differs from either of the above in that the surface to be mapped is rarely flat, presenting the three ordinary dimensions of nature, whilst, as in the second case, the photographic plane is inclined or tilted to the map plane. There are then two difficulties to surmount, the perspective effect and that of differ ence of altitude. These two effects act from different points on the plane of the photograph. It is one of the hardest problems of surveying from air photographs to disentangle these two effects and to correct them in the proper way. The photograph is a central perspective of the ground mapped, which is true in so far as lens, shutter, photographic material, temperature changes and rigidity of the camera allow. The perspective centre is the point on, or with reference to, the plate from which directions to points on the ground correspond to those from the camera. Height, however, introduces in the perspective view distortions which radiate from a point in the plane of the photograph verti cally below the front nodal point of the lens. This point is com monly known as the Photo Plumb Point. The perspective centre and photo plumb point coincide with each other, and with the optical centre, when the two planes (ground and photo) are parallel. In all other cases these three points are distinct from each other and lie on a line perpendicular to the axis of tilt at distances which are functions of the tilt.
As nearly all photographic surveying demands a knowledge of the position of these points the first step is so to calibrate and to adjust the camera that the optical centre corresponds to the principal point (the point at which a perpendicular from the front nodal point meets the plane of the photo). Fiducial marks
photographed on the four edges of the plate can then be joined up to give the correct position. It is with reference to this posi tion that the perspective centre and photo plumb point can be found. The principal distance (between the lens and the prin cipal point) must also be measured. In the remainder of this article it will be assumed that the camera has been properly calibrated and adjusted.
The Single Photograph in Perspective. (a) Where the Ground is Flat.—If S is the representative fraction of the scale, L be a distance on the ground, and 1 the corresponding distance on the photograph, then for any given small area S= 1 —. But 1 is con ditioned by the tilt and the scale varies accordingly. Where photographs are taken as nearly as possible with a vertical axis then S= f where f is the principal distance (not quite the same thing as the focal length), and H is the height of flight. Whether or not photographs are nearly vertical the prob lem is the same because it has not been found possible hitherto to maintain the axis truly vertical, to record such deviations from the vertical as may occur, or to keep a constant height. In every case then the photograph is a perspective view at an un known tilt and from an unknown height. The effect of tilt can be eliminated by perspective treatment founded on the cor responding positions (on ground and photograph) of four points. Such treatment may be either graphic or photographic and is generally called rectification.
Graphic methods are seldom applied to the whole photograph. In practice it is easy to find straight lines through points clear on the photograph, and already mapped, which will intersect on, or sufficiently close to, the new point which is to be added.