tion consequently means determination of what usually is 
called systematic or regular errors of material, instruments 
and operators. Systematic errors are here referred to the 
population, and regular errors to the sample. The standard 
may be given by many conditions. In photogrammetry for 
instance, the concept of central projection is a very usual 
and important condition or standard. The camera or 
imaging device shall, as a principle, image the object points 
as a central perspective usually in a plane. This is the funda 
mental operation number one of photogrammetry. Syste 
matic deviations from the central projection occur as a 
rule and have to be determined through some form of 
calibration, to be applied also under operational condi 
tions. The second fundamental operation of photogram 
metry is the reconstruction of the ideal bundles of rays 
which in the moment of exposure joined the object points 
and the (outer) perspective center. For this purpose such 
data of the photograph, which allow this reconstruction, 
must be known. They are usually called the elements 
of the interior orientation, and also include the distur 
bances of the central projection. For evident reasons the 
elements of the interior orientation should be completely 
determined through calibration under operational condi 
tions. Usually approximate values are known and correc 
tions are to be determined through the calibration proce 
dure. 
If the bundles of rays are to be reconstructed in a 
projector, the elements of the interior orientation of the 
projector must be known, in order to match the corre 
sponding elements of the photographs. Sometimes, how 
ever, certain elements of the projector are intentionally 
changed, in particular the projector constant (principal 
distance), and the bundles of rays are accordingly deformed 
for the purpose of affine deformations of the models. Also 
in such cases the changed projector constant must be 
carefully determined. 
In all these cases of calibration and moreover in all 
calibration procedures it is most important that the basic 
quality of the calibration procedure and the quality of 
the systematic errors (corrections) are determined and 
expressed in clear terms. Such information can be used for 
instance for the judgement whether or not the instrument 
or device under calibration can be regarded to be of the 
same quality as other devices of the same kind or whether 
or not the estimation of the systematic errors or correc 
tions are significant. Upon such judgements important 
decisions concerning the acceptance or rejection of the 
device or the performance of mechanical adjustment can 
be founded. 
The basic requirement of calibration is in general that 
such data, which can be regarded as correct (free from 
errors), at least in comparison with the expected irregular 
errors which limit the quality of the device under calibra 
tion, are measured with the device in question. This limita 
tion should at least approximately be known or determined 
through some kind of iteration. 
Since the main purpose of calibration is to distinguish as 
far as possible between (significant) systematic errors, 
which later can be corrected for, and irregular errors, the 
magnitude of which shall be statistically estimated, the 
method of least squares is usually regarded to be the most 
effective means for the purpose. The systematic errors are 
introduced as parameters in the adjustment procedure and 
the irregular errors are estimated as standard errors of unit 
weight, which is the square root of the minimized variance 
of residuals (the sum of the squares of the residuals divided 
by the number of degrees of freedom, i.e. the number of 
redundant observations). 
These principles, which are well known from statistics 
and theory of errors of measurement, have been applied 
for the calibration problems, treated by this working 
group and will be presented in more detail below. There 
are numerous applications performed for the partial and 
complete 1 calibrations of photographs from various imaging 
devices (Commission I), and of projectors, comparators, 
coordinatographs, micrometers (parallax bars) etc. (Com 
mission II). It seems very desirable that such calibrations 
and tests be applied to photogrammetry in practice, in 
particular in connection with quality investigations of 
the final results of the photogrammetric procedure as re 
commended in the resolution No. 5 of Commission II, 
I.S.P. from Lisbon. The partial and complete calibrations 
performed under operational conditions have proved that 
there can be considerable differences with the results of 
calibrations under laboratory conditions, which of course 
is to be expected. It is also important that the geometrical 
quality of, for instance, image- and projector coordinates 
be estimated realistically. With the aid of the laws of error 
propagation the quality to be expected in the final results 
can be determined theoretically for a comparison with the 
practical quality, to be determined with other methods. 
Compensation and correlation effects must always be noted 
and taken into account in the development of the theo 
retical formula systems. 
1 The expression partial calibration means here that a limited 
number only of the elements of the interior and exterior orienta 
tion are considered. In complete calibration all elements are 
considered.