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for its knowledge is necessary and adequate for the solution of the basic problem of 
photogrammetry. It will be well to accord this fundamental relation a name of its own. 
In the first place, this will simplify many formulations. What is more, however, this 
designation is in line with the conception that it is not essentially necessary in photo- 
grammetry that a central projection is concerned, but that any kind of a relation may 
exist between the image points and the principal rays. Actually, indeed, the camera 
function considerably deviates from the tangent function in lenses with marked distor- 
tion (such as the Pleon), so that in this case the new concept name is almost compelling. 
Whoever does not need it can, of course, avoid its use without attendant disadvantage. 
The image function does not, as might be thought, belong among the technical con- 
cepts. At the present time, anyway, regular film shrinkage is not below the limit of ac- 
curate measurement, but can without difficulty be considered in the plotting process. 
In the sense of photogrammetry, it therefore is not to be rated as a manufacturing error 
(whereas irregular film shrinkage is a manufacturing error and does not enter into the 
physical definition). For the rest, the difference between the camera function and the 
image function is conditioned by all other changes in scale ratio (as, for instance, in the 
reduction of the original photo for plotting). 
Inner orientation of a camera or an image are terms signifying the geometrical 
counterparts of the camera and image functions. They are the spatial arrangements 
whereby those analytical functions materialize. By this confrontation, the descriptive 
geometrical import of the term "inner orientation" is made to stand out distinctly. 
It has been tried to work out as clearly as possible the analogy between the mathe- 
matical definition and the two physical definitions (for the camera and the image). On 
the other hand, however, it is imperative in inner orientation to allow for the fact that 
different conceptions underlie the description of the image forming process in the camera 
and the use of the photographic picture removed from the camera. Both views are jus- 
tified and necessary, and it would not be compatible with the facts if one way of view- 
ing should be suppressed to favor the other merely for the sake of uniformity. For the 
camera, i.e. for the union of an image plane with a lens, the relation between the object- 
side principal ray bundle passing through the center of the entrance pupil and the cor- 
responding points of the image plane alone is important, as is indicated by the schematic 
sketch heading the right-hand column. By contrast, the plotting of an image outside the 
camera is more or less linked with the idea that first — by a mechanical or optical device, 
or even only in the imagination — the image points are so displaced in their plane as 
to produce a distortion-free image, and that from this image and with the aid of a cent- 
ral projection, the object-side bundle of rays is derived. This conception, which is illu- 
strated by the corresponding sketch, therefore establishes the relation to the mathema- 
tical definition. Accordingly, the inner orientation of an image was allotted to the 
columns of both the mathematical and the physical concepts. 
Camera constant and image constant. The designation of the constant c, in the 
equation: 7/ — c,.tan zr t 4 ?/ has undergone some changes in the various languages. 
In English practice the terms “focal length”, or more accurately “calibrated focal length” 
have frequently been used. More lately “calibrated principal distance” was proposed 
[7, 8]. In German, the expression *Bildweite" formerly was customary, whereas in recent 
years "Kammerkonstante" and correspondingly “Bildkonstante” (camera constant and 
image constant) have widely come into use. 
The expressions ‘focal length” and “Bildweite” for designating the photogrammetric 
concept should be definitely eliminated, seeing that they have always been current in 
optical parlance. There they designate the distance of the image point lying on the 
optical axis from the image-side lens principal point, Bildweite being the general term, 
while focal length is applied only in the case of infinite object distance. This distance 
in many instances is of a similar magnitude as the constant c,, but coincides with it 
neither in a conceptual nor generally in a numerical sense. The term Bildweite refers to 
13