exist more observational equations than unknowns, and a least squares 
adjustment leading to a 2n+7 by 2n *7 system of normal equations can be 
performed. Although the size of the normal equations increcses linearly with 
the number of measured points, their solution presents no difficulties, even on 
a small computer. This is because they possess a patterned coefficient matrix 
that can be exploited to collapse the system to one of order 7x7, involving 
only the parameters of the comparator. Once these have been determined, an 
independent, four station, least squares trilateration can be performed to 
establish the coordinates of each point. Details of the data reduction are to be 
found in the reference cited earlier. Suffice it to say here, that the internal 
contradiction resulting from the redundancy of the measuring process can be 
exploited to effect an accurate calibration of the parameters of the comparator 
for the particular plate being measured. Hence, the designation of the 
instrument as a self-calibrating multilaterative comparator. 
THE COMPUTER PROGRAM 
If developed fifteen years ago, the Multilaterative Comparator would have 
been little more than an interesting academic curiosity, for no one could have 
tolerated its computational requirements. Accordingly, the digital computer, so 
commonplace today, is to be regarded as an integral part of the comparator 
system. For this reason, a fully documented FORTRAN program is provided with 
the comparator. The program is designed so that a minimum of modification is 
required to adapt it to almost any computer. One version of the program is 
designed specifically to run on a minimal computer configuration such as an 
IBM 1130 with card input. Another version is designed for medium to large scale 
computers. Both versions feature automatic editing and rigorous error propagation. 
Typical running time on an IBM 7094 for the reduction of a plate containing 50 
measured images is well under one minute. 
In addition to producing the final coordinates of the measured points, the 
program generates the four measuring residuals for each point and the rms closure 
of trilateration. 
RESULTS 
The comparator has undergone extensive testing over the past eighteen 
months. Ten have already been placed in operation and are to be followed by 
another ten by the end of the year. In comparisons employing plates with well 
defined images measured both on a conventional, two screw comparator and on 
the multilaterative comparator, an rms agreement of final coordinates ranging 
between +2 and +3 microns is usually obtained after allowance has been made 
for a translation and rotation of the one coordinate system to conform to the 
other. If one were to assume that the discrepancies between the results are 
equally attributable to both comparators, one would conclude that the rms 
accuracy of the coordinates produced by the multilaterative comparator generally 
range between 41.4 and +2. 1 microns, a range compatible with typical setting 
accuracies. Thus external evidence indicates that the multilaterative comparator 
is capable of producing accuracies at least comparable with those produced by 
conventional, one micron comparators. 
-———— " WB Nau oua 
Lt "se  — pp 
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