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.