Photogrammetria, XIX, No. 6 
Special attention will have to be paid to the device (if available) used to enlarge or 
reduce the scale between model and map. The influence of this device can often be tested 
separately but, when this has to be done in the instrument itself, a recommended method 
is to plot the same model several times with different enlargements to the map scale. 
Residual errors which are not proportional to these ratios may reveal deficiences of the 
pantograph or other construction used for this purpose. 
To be able to use Z measurements to their greatest advantage in instruments with 
graphical output it will be obvious that stereoscopic grid-models are indicated. 
The variety of properties of instruments in this class is too great to enter into details 
about the possibilities of analysing grid measurements for each of them. 
II. 2. 4. Lens distortion in optical-projection systems. 
Instruments with optical or optical-mechanical projection include a lens in their 
projection device and hence we may expect the influence of lens-distortion in the projected 
coordinates. 
This influence is, however, an essential property of the instrument (specially in those 
instruments which are based on the Porro-Koppe principle) but it has the disadvantage 
here that it complicates the analysis of the coordinate differences. 
There are several ways of dealing with this problem: 
1. If the lens distortion is known the measured coordinates could be corrected accordingly 
before the analysis is started. This causes the introduction of notable computational 
load, particularly when the projectors are used in a tilted position. This procedure may 
therefore be only feasable when a limited number of points is used or in cases where 
an electronic computer is available. 
2. The lens distortion can be computed from the measured coordinate e.g. according to 
the procedure published by Hallert in [4]. 
The disadvantage of this method is, however, that some typical instrument errors may 
be interpreted as lens distortion and thus escape notice. 
3. The lens distortion is assumed to have only a radial effect and for the computation of 
residuals only the tangential components together with the asymmetrical part of the 
radial components of the coordinate differences are used. The disadvantage of this 
system is that a great deal of the information is neglected and that some elements can 
not be determined at all (e.g. Abz and Ac). 
4. In those cases where only the stability of the instrumental adjustment is in question, 
the lens distortion can simply be accepted and the analysis limited to a relative com 
parison of new results with previous ones. 
The difference between two measurements at different times can be analyzed as if no 
lens distortion was present. 
II. 2. 5. Additional equations to be checked. 
Apart from the central-projection equation which an instrument is designed to 
realize there are often other properties which are just as important for the functioning of 
an instrument. 
In many photogrammetric procedures use is made of the readings of linear and an 
gular orientation elements either to introduce computed corrections during the execution 
of a relative or absolute orientation or to introduce data from other sources (statoscope, 
horizon-camera etc.). 
Also in this respect the instrument performs a duty as an analogue computer in that 
it changes the coordinates of projected points in accordance with the amounts of move 
ments introduced. A check on this performance may be desired and again grid-plates offer 
an adequate means for this check. 
In section II.2. 2. it has already been shown that the first treatment of coordinate