THE USE OF NON-METRIC CAMERAS 101 
was inserted in the wall of the test section, opposite the window. This grid provided the 
information needed to correct systematic errors introduced by the observation window and by 
the beam splitter attachment. It also offered the necessary control for the analytical relative 
and absolute orientation procedure». The effect of the convergence of the stereo images, 
resulting from the orientation of the outer mirrors of the beam splitter attachment, was 
corrected during the relative orientation. It was therefore not necessary to calibrate the 
orientation of the mirrors prior to the photography. 
The camera used in this application had been built at the NRC laboratories for close-range 
application. Its principal distance is 340 mm and it is permanently focussed at the same 
distance, which results in a photo scale of 1:1. Although this camera can be considered to be a 
metric camera, the particular arrangement of this test, including the use of the reference grid, 
would have permitted the use of a non-metric camera. 
Based on the grid measurements, the standard error ofthe photogrammetrically determined 
coordinates was estimated to be 0.06 mm. Based on this result, the photogrammetric method 
was judged to be sufficiently precise to measure the three components of the particle velocity 
in axial, lateral, and transversal directions. 
ExAMPLE FOR DouBLE CAMERA SOLUTION 
Two Graflex press cameras were used for photogrammetric determination of three- 
dimensional flow patterns in water tunnel experiments at NRC's National Aeronautical 
Establishment. In order to provide the necessary means for self-calibration ofthe cameras and 
for correcting distortions caused by the observation' window and by the water, two regularly 
spaced grids were used throughout the experiments (Figure 8). 
One ofthese grids was located on the back wall ofthe tank and the other on the inside ofthe 
observation window at the water-glass interface at a distance of 25 cm from each other. Since 
both grids were in contact with the body of water in the tunnel, it was possible to determine, in 
each individual exposure, the equivalent principal distance of the cameras for the water 
medium and to reconstruct the bundle of projecting light rays within the tunnel. 
The flow in the tunnel was made visible in the photographs by illuminating tracer particles 
with a stroboscopic light source. A frequency of 120 cycles/sec was found to give a satisfactory 
spacing of the particle images for the speed of flow in the tunnel which, during the experi- 
ment, was 25 cm/sec. The time base of the stroboscope served to calculate particle velocities 
from the photogrammetrically determined particle coordinates. The cameras were oriented 
with their optical axes normal to the observation window. The distance between each camera 
and this window was 2.1 m, resulting in a photo scale of 1:12. The distance between the two 
cameras was 50 cm. 
The photographs were measured on a Zeiss Jena Stereocomparator 1818; and standard 
programs for relative and absolute orientation, developed for aerial photogrammetry, were 
used for calculating the coordinates of the particle images and the grid points*$. Standard 
errors of the photogrammetrically determined grid points were m,,, = 0.2 mm (parallel to the 
image plane) and m, ^ 1.3 mm (normal to the image plane). Standard errors ofthe photogram- 
metrically determined particle coordinates were calculated from consecutive particle images, 
assuming that the particle velocity is constant during the short time interval of 0.1 — 0.2 sec 
  
   
  
  
sur: à 3 17 ] 
= mm meom " = cmm 
* . » . , 
   
  
  
— 4 —« 7 | 
C — BE rm A 
—— D 
Fic. 8. Watertunnel experiments.