96 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976 
® Non-metric cameras can be focused, thus the lens distortion often changes with a change in the 
focusing distance; and 
® Non-metric cameras often have rather small lens angles, hence only a few collimators of a standard 
calibrator may be imaged. 
It should be noted here that the lens distortion has not been corrected in any of the 
applications to be discussed later in this report. 
DETERMINATION OF THE IMAGE DEFORMATION 
Image deformation consists of dimensional changes in the actual photographic record 
occurring between exposure and the measurement, and of image displacements resulting 
from improper placement of the photographic material (film or glass) into the image plane. 
Since non-metric cameras are not equipped with fiducial marks, dimensional changes of the 
original photographic record cannot be determined and therefore remain uncorrected. An 
overall scale change will result in a projection distance change. A differential scale change is 
unlikely if modern films with a polyester base are used. Older films with a less stable base, for 
example acetate cellulose, often displayed not only differential scale changes but also shear 
between the two coordinate axes. If such films were used, Jahn's! partial matrix 
Cu i72Cy1,0 
0 C 0 
0 0 1 
could be included as well. 
Improper placement of the photographic surface into the image plane must be considered a 
more serious error source because non-metric cameras using film are hardly ever equipped 
with a satisfactory film flattening mechanism. The resulting positional displacements are 
directed in radial directions and, therefore, interpretable as lens distortion. Since the improp- 
er film flattening may result in rather irregular radial distortion, the determination of the lens 
distortion by introducing additional parameters becomes somewhat questionable for lenses 
with larger lens angles. 
It should be noted here that the attempted placement ofthe photographic emulsion into the 
image plane will produce a different result for each frame. If the possibility of a change in 
focus is also considered, it must be concluded that the interior orientation must be redeter- 
mined for each new photograph. 
EXAMPLES FOR SiNGLE CAMERA SOLUTIONS 
DETERMINATION OF TWO-DIMENSIONAL INFORMATION 
In the photogrammetric determination of small distances or displacement vectors, systemat- 
ic image errors caused by inaccuracies in the camera's interior orientation, including the film 
flatness, have little effect, and satisfactory results can therefore be expected from non-metric 
cameras. This is particularly true when the information is derived from a single photograph, 
which, in deformation measurements, is possible by multiple exposures on the same photo- 
graphic emulsion. 
An example of such an application is the determination of the mode shapes of a thin wing, 
vibrating at various frequencies between 50 and 500 cps?. The size of the wing was approxi- 
mately 60 cm by 30 cm. In deformation measurements of thin objects, photogrammetry is 
particularly suitable since it does not interfere with the actual process, which is usually the 
case with mechanical or electrical pick-up systems. 
Reference points were provided on the wing by means ofa regular grid consisting of narrow 
grooves (0.2 mm thick) which were filled with a yellow dye. These points offered a good 
photographic contrast against the wing surface which was painted matte black. After the wing 
was forced to oscillate, using a jet exciter, it was photographically recorded using a one-second 
exposure. The camera was oriented with its optical axis nearly perpendicular to the oscillation 
direction at a distance of 1.5 m from the wing, slightly above the plane ofthe wing. The image 
plane was parallel to one ofthe directions ofthe reference grid defined by the chordline ofthe 
wing, so that the photographic scale (approximately 1:10) was constant for each grid line. The 
scale factor was independently determined for the various reference points from the distances 
between adjacent grid points along these grid lines and corresponding values measured in the 
photograph.