ANALYTICAL PHOTOGRAMMETRIC INSTRUMENTS 
4 
From a strictly mathematical standpoint, 
such an approach undeniably has the 
theoretical potential of simulating the geom 
etry of the most complex sensor character 
istics, thus requiring the specific data acquisi 
tion and data evaluation components to 
merely perform with high resolution; i.e., with 
low noise or, in other words, with high in 
ternal precision. 
A strictly mathematical interpretation of 
such an approach will, therefore, consider 
numerical analysis as the means for detecting 
and compensating for bias errors, independent 
of their character and amounts. The meas 
uring engineer should, however, view such an 
approach with a certain amount of skepticism 
when high-accuracy measuring systems are 
under consideration. 
Fully acknowledging the unique potential 
of numerical evaluation methods, there ap 
pears, nevertheless, no substitute for the 
classic requirement of having the primary 
sensor and the corresponding evaluation 
equipment designed and manufactured to the 
highest possible accuracy. Such a request re 
quires not only metric stability, or metric re 
producibility, but the specific components 
should perform as closely as possible to a cer 
tain a priori established theoretical model. 
The unavoidable tolerances should cause 
biases which are small and which are com 
patible with the resolution of the measuring 
method. Subsequently, such data are then 
submitted during the data evaluation to a 
least squares fit to a complex model, which, 
to the best of a priori knowledge, simulates 
most of the theoretically possible bias errors. 
During this step, the classic least squares 
technique can be considered as a rigorous 
procedure for handling normally distributed 
errors. But even very complex mathematical 
models are only approximations to the 
physical realities of the data acquisition and 
data evaluation processes. The lack of ab 
solute fidelity of the model, and the correla 
tion existing between the various parameters 
describing the mathematical model (which 
tends to be more severe the greater the com 
plexity of the model), will effect the sig 
nificance of the determination of the in 
dividual parameters less if the number and 
sizes of the various bias errors are kept to a 
minimum. 
Therefore, one must conclude that the re 
quirements for highly accurate measuring 
results still have to follow the three basic 
rules, which are: 
1. To design and manufacture all instru 
mental components used for a specific 
measuring procedure as close to a priori 
defined models as the state of the art 
allows. 
2. To arrange the measuring method and 
the data measuring process in such a 
way as to eliminate bias errors by ad 
hering as much as possible to the prin 
ciples of a zero-method, and 
3. To correct for all conceivable sources of 
biases during the final phase of the data 
evaluation by subjecting the raw data 
to a least squares fit with respect to a 
sophisticated mathematical model, us 
ing in the adjustment as much data as 
is economically feasible. 
The application of these thoughts to the 
presently developing field of analytical 
photogrammetry suggests using the method 
of numerical analysis by establishing certain 
mathematical models which express the func 
tional relations between the information con 
tents of the individual photographs and the 
spatial positions of the corresponding object 
points. 
Although photogrammetric data acquisi 
tion systems are as much “analytical photo 
grammetric instruments” as the correspond 
ing data evaluation systems, the content of 
this presentation is directed only to a discus 
sion of the later. 
The purpose of the data reduction equip 
ment for analytical photogrammetry is to 
provide means for measuring the information 
contained in a specific photograph and for 
presenting the results of each measurement 
in the form of a pair of coordinates expressed 
in digital form. These coordinates are meas 
ured almost exclusively as x and y coordinates 
of the two-dimensional cartesian coordinate 
systems which are integral features of most 
machines. 
The coordinate measurements are then 
processed in electronic computers. The final 
results are the triangulated object coordinates 
in digital form, or, after transformation into 
some kind of analogue presentation, the 
means for producing a graphical presentation 
in the form of maps, profiles, etc. 
If the electronic computer is on-line equip 
ment, one refers to the evaluation equipment