Hempenius, Makarovié, Van der Weele, Tests of Restitution Instruments 
II. 2. 2. Monocular or stereoscopic tests. 
II. 2. 2.1. In this context the term monocular is used to indicate that only one projector is 
included in the measurements as opposed to the case where a stereoscopic model 
is formed by combining two projections. The question whether the observations are done 
by monocular or binocular vision is not being considered here, because experience has 
shown that the measurements on grid-lines are so accurate, that there is hardly any dif 
ference in precision between monocular and binocular observations, provided that the 
optical magnification of the viewing system is sufficient. 
It is obvious that a separation of measurements for each projector facilitates the 
analysis of the differences between expected and measured coordinates and that this 
procedure is also necessary where each projector has to be adjusted separately. 
The measurements in a stereoscopic model may be useful as a final check in the 
instrument for X, Y and Z coordinates. The residual errors in a stereoscopic model could 
also be computed from the separate measurements of each projector; 
To simplify the computations, the instruments are generally tested in a position with 
vertical axis of the projectors. For a constant value of Z the X and Y coordinates of a 
number of points are measured and compared with the expected coordinates. Again, to 
simplify the computations, the analyses of the differences is generally based on a linearisa 
tion of the general formulae for the central projection, which for the case of vertical 
axes, can be written in the form : 
Y 2 + Z 2 XY X Z X 
AX — n— Aop + —yjr Aco Y Ax Abz -h Abx -h — Ax — Ac 
Z Z ¿i c c 
XY Y 2 + Z 2 Y Z Y 
AY — Aw + =— Aw + XAx + Abz + A by Ay + — Ac 
z z z c c 
In equation (2) : 
AX and zlF are difference between measured and expected coordinates. 
X, Y and Z are coordinates in the machine-system which has its origin in the 
projection centre. 
Acp, Aw, Ax, Abx, Aby and Abz are corrections to be applied to the elements of outer 
orientation of the projector. 
Ax, Ay and Ac are corrections to the inner-orientation elements. The' signs for all 
terms in this formula are arbitrarily taken positive. To apply the formula to a particular 
instrument the signs should be adapted to its individual positive direction of counting for 
each element. 
By using the observed values of AX and AY in a first instance to compute corrections 
to the orientation elements a set of residuals is obtained which cannot be improved by these 
orientation movements. These residuals, therefore, reveal the mechanical, optical or ad 
justment errors of the instrument as well as the errors in reading or registering coordina 
tes, and should be submitted to a further analysis when they are too great to be accepted. 
Examples of influences which could be expected are given in [2] and [3]. 
From equations (2) it will be obvious that a separation of the influences of Abz and 
Ac is only possible when at least two different values of Z are introduced. 
Using more values of Z has the additional advantage that errors in the projectors 
(which have an influence proportional to Z) can be separated from errors in the coordinate 
measuring device (which are mainly independant of Z). For the same reason it may be 
of advantage to use different values of c. 
For a simple test on the stability of the instrument, however, such complete sets of 
observations are generally not required. 
II. 2. 2. 2. Instruments which are not specially built for aerial-triangulation have general