6. Additional Computations 
With N restitution centres having measured the two models of a flight, there were N co-ordinate 
means available for each point. These were accepted as independent measuring results and from them 
a relative accuracy m4 was determined, as well as the overall quadratic average of the systematic 
errors mg, similar to the errors m4 and rng in section 4 (see figs. 2a and 2b). This causes the r.m.s. 
error mg to be resolved into two parts. mg is thus smaller than mg. Moreover, the error ma has 
another meaning than that of the error m4. Besides the adjustment errors of the instruments, it con- 
tains for example also the printing errors, which might occur when different diapositives are pre- 
pared (see [5]). 
In general, the following formula is valid: 
5 i— 1 2 N—1., — 
ms = ; ma + — m4 ma. 1 
em mi + N MH mE (1) 
In our case, the number of measurement repetitions i — 5 for each model; moreover, N averages 5 
for the analogue instruments. The original publication comprises also the values m4 and mg for the 
analogue instruments. For the measurements in stereocomparators, an insufficient number of resti- 
tutions is available. 
7. Analysis of the r.m.s. Errors (Estimates of the Standard Deviation) 
The tables mentioned in sections 5 and 6 already contain the answers to the first basic question of 
the test programme, viz. data concerning the point accuracy attainable with various picture scales 
and flight conditions. When comparing the r.m.s. errors, it should, however, be noticed that neither 
N, the number of restitutions of a flight, nor oy, the ratio between model scale and image scale, are 
constant throughout. Moreover, different copies of the original pictures and different instruments 
have been used, whilst different operators have taken part. 
If the expected distance error ms has to be derived from the co-ordinate error mg, then for random 
errors 
mg = Mk V 2. 
For the additional problems, the values of the single measurements had to be combined differently. 
There are two possibilities for doing this: 
(1) Only such restitutions as yield the necessary combination are taken. This offers the advantage 
that the same restitution instruments have always been used, and probably by the same opera- 
tors. On the other hand, it has to be accepted that the number of comparison values is reduced 
in this case. 
(2) The average values of all available restitutions are used. 
The question remains which alternative is to be preferred. In many cases, there is no choice but to 
use all available measurements. 
8. Summary 
[n table 1, some of the r.m.s. errors are reviewed. In the heading of the table, the number of restitu- 
tions, N, the ratio vw between model scale and picture scale and the base ratio d, are indicated. In 
order to be able to compare the r.m.s. distance error ms with the other r.m.s. errors, ms has been 
converted into a r.m.s. co-ordinate error. For the comparator measurements, the “image errors in 
microns“ equal to the “model errors in microns“, since v» = 1. 
In particular, it should be noted that: 
— The fitting error mg and the absolute error mg are nearly equal. 
— The r.m.s. errors of the short stretches with end points in the same model (groups 1 and 5) are 
equally large. The height difference between the end points of the distances plays no part. This 
distance error, converted into co-ordinate errors, nearly corresponds to the relative error m4 
(mean dispersion of the co-ordinates as found after repeated absolute orientation). The r.m.s. 
errors of the long distances are also equally large, regardless of whether the end points are in 
the same model or in different models (groups 2 and 4). When converted into co-ordinate errors, 
they are a little smaller than the r.m.s. absolute error m3.