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with the mathematical model in the calibration. 
Test Fields 
There are several laboratory methods for calibrating photogrammet- 
ric cameras. Especially designed instruments are very often 
necessary, such as goniometers, collimator banks, multicollimators. 
In addition to this there are field methods for camera calibration. 
Most laboratory methods and many of the field methods are intended 
for cameras that are focussed on infinitely distant objects. The 
methods are not directly applicable for cameras focussed at short 
distances. The goniometers and collimators have to be differently 
focussed and in some field methods the location of the exterior pro 
jection center must be known before the calibration can begin. If the 
position of the exterior projection center is defined in the system of 
the test field by coordinates that are in error, this introduces errors 
in the determination of the principal point and the camera constant. 
This has been the reason why calibrations of close-up cameras 
using, for example, the grid method, only contain a determination 
of the radial distortion and the standard error of unit weight of the 
image coordinates. As the origin of the trouble is the unknown 
position of the exterior projection center this difficulty would be 
eliminated if the position was determined in the calibration itself. 
The grid method has a plane test field, which as a rule is parallel to 
the image plane. The determination of both the interior and the 
exterior orientation is not possible in this case. The corresponding 
normal equations have a non-singular solution. To overcome this, it 
is necessary to extend the test field into three dimensions. 
Three-dimensional Test Fields 
From the viewpoint of theory of errors, it has been regarded as an 
advantage to calibrate cameras under conditions that are as similar 
as possible to those of ordinary work. Firstly there can be regular 
differences in the elements of interior orientation between laboratory 
and field calibration. Secondly the accuracy will be determined under 
operational conditions. Short range photogrammetric cameras are 
used to determine object coordinates in a three-dimensional space. 
It seems to be a consequence that the test field should be of the 
corresponding shape and size. The standard errors of the principal 
point and the camera constant decrease with decreasing standard 
error of unit weight, decrease with increasing opening angle of the 
bundle of rays, and decrease with increasing extension of the test 
field in the direction of the camera axis. For a proper estimation of 
the accuracy the points should be evenly distributed over the image. 
Test objects have been designed with these ideas in mind and used for 
calibrations of stereocameras, photodolites, ordinary cameras, 
X-ray equipment, cinetheodolites, stereomicroscopes, radio-iso- 
topic imaging systems etc. Aerial cameras can be conveniently 
checked over mountainous terrain. 5)