u 
Diagram c 
Diagram b 
Diagram a 
BALLISTIC PHOTOGRAMMETRY, SCHMID 45 
of the inaccuracies in the positions of the ground control points, surveyed by Coast and 
Geodetic Survey, and assumed to be + 5 cm was taken into account by the use of cor- 
responding weighting factors. 
Both the star photography and the aerial photographs were of average quality. No 
attempt was made to select sets of especially favorable measuring results. The chosen 
examples are typical and the numerical results are conservative estimates for the pre- 
cision obtainable. The three values of the mean square errors for a single plate coordinate 
measurement, after adjustment, are close to a value of = 2.5u to = 3.0 p, which has been 
found for production work to be representative for this kind of measurement. With 
+ 1.5u as a typical value for the mean square error of the coordinate measuring pro- 
cedure, the amount of residual error introduced by the camera and the photographic 
process is thus = 2.0 pn to == 2.5 p. 
From these results, a few conclusions can be drawn which appear to be of signifi- 
cance, in connection with earlier remarks in this paper. 
1. À value of + 2.5u for the mean square error of a single plate measurement after 
adjustment and the type of distribution of the corresponding residuals presented, well 
support the claim that Ballistic Photogrammetry will provide, a practically unbiased 
measuring accuracy of 1 :100000, if presently available precision cameras, having 
focal lengths of 200-300 mm, are used. 
2. The presentation of a mean square error of a single plate measurement, as a uniform 
estimate of precision for the contents of a photograph, ignores the fact that quite a 
few of the individual error sources vary quantitatively, depending on the location of 
the image on the photograph. Therefore, it will be necessary eventually to employ 
weighting factors for the fundamental observations. Such a procedure will ascertain 
that each individual ray is being properly adjusted according to its relative position 
within the bundle. For instance, for a critical study of the potential of convergent 
photography, proper weighting of the measured plate coordinates appears to be of 
major importance. 
3. Present results indicate the possibility of keeping the mean square error of the coor- 
dinate measuring procedure, at least for clearly defined image points, at a level sig- 
nificantly below the corresponding value of the metric error of the photograph. The 
classical feature of the Stereocomparator to measure especially precise coordinate 
parallaxes loses under such conditions, its significance. Consequently, coordinate meas- 
uring machines could be considered which employ the stereoscopic observation method, 
but feature independent cross slide systems, for the measurement of the image coor- 
dinates of each photograph under observation. This line of thinking obviously sup- 
ports the idea of using the stereoscopic observation method for marking correspond- 
ing points on various photographs and later measuring, automatically, the corre- 
sponding image coordinates, using for the setting operation some kind of electronic 
scanning technique. 
4. Generally speaking, it appears that any attempt to analyse or improve the precision 
of the photogrammetric measuring method, must concern itself with the investigation 
of the precision of the numerous basic components contributing to the precision of the 
fundamental observations. A quantitative study of the corresponding individual errors 
will, however, lead to significant results only if the design of any such experiment is 
carried out in a manner which allows resolving significantly, fraction of a micron. 
The significance of the results of photogrammetric measurements undoubtedly 
depends on the properties of the specific data reduction method applied. But even an 
optimum data reduction method must operate within the potential of rigorous geometry 
and mathematical statistics. In other words, nothing can be regained in the phase of data 
reduction that was lost in the phase of data acquisition. Therefore, the process of taking