had not conditions (c) and (d) both been exercised. 
The importance of condition (d) is illustrated by the comparison of two Aerial 
SMAC calibrations of a DBA close range camera of 135 mm focal length and circular 
format 150 mm in diameter. The camera was focussed for a distance of 2 meters and 
four exposures were made of a section of the DBA target range. All exposures were 
made with camera axes inclined about 45° to the target array and pointing to a 
common central target from symmetrically placed stations located nominally on the 
vertices of an equilateral triangle located at a height of about 1.5 meters above the 
target array. Exposures from Stations 1, 2 and 3 were made at the common swing 
angle of x=0°. The exposure from Station 4, which was located to coincide 
nominally with Station 1,was made at a swing angle of x =90°. Approximately 125 
targets were measured on each plate. The first of the two Aerial SMAC reductions 
carried only observations from Stations 1, 2 and 3 (all x20?) and produced the 
following results for x,,y, , C: X, =  r6007& „007 mm, 
y: -.355 + ,437 mm, 
c 146.160 + .645 mm, 
RMS Error of Residuals = 2.2 um. 
These results are seen to be very good for x, but quite poor for y, and c. ln the 
second reduction, data from Station 4 (x*90^) were added to the set. This 
caused the results for x, ,y, ,c to be changed to: 
x, = -,687 + .006 mm, 
Y: * -.219 € .009 mm, 
c = 146.405 + ‚009 mm , 
RMS Error of Residuals = — 2.4um. 
This set of results is very good for all three parameters, an outcome that demonstrates 
the effectiveness of exercising appropriate geometry. In addition to those results 
listed above, the two reductions produced almost identically the same values for 
coefficients of radial and decentering distortion, with ms accuracies of better than 
1.2 um being obtained for both distortion functions throughout the format. 
One matter that requires clarification is that in the above discussion we 
consider X to be defined as the clockwise angle between the x axis of the plate 
coordinate system and the line formed by the intersection of the film plane and the 
plane of the target array. We bring up this point because of a seeming contradiction 
between our results and a set of results reported by Torlegard (1967) based on the 
simultaneous reduction of four exposures of a vertical target array located on a wall. 
The four exposures were made with the cameras symmetrically located and directed 
toward the center of the field. Torlegard obtained accurate recoveries of x,y 
and c, even though all four cameras had x's of nominally zero degrees. However, 
Torlegard's definition of x is based on the angle between the x axis of the plate and 
the line formed by the intersection of the film plane and the horizontal plane (instead 
of the plane of the target array as in our definition), Thus, in our system the swing 
angles for Torlegard's set of frames would be nominally 0°, 90°, 180° and 2707, 
respectively, Accordingly, our assertion of the need of exercising at least one pair of 
well spread swing angles is not, in fact, contradicted by Torlegard's results.