As a result of the foregoing findings, a completely new version \ 
of the DBA Reseau Platen has been designed.and fabricated. The design of 
this platen renders it totally immune to deformation.caused by the appli- 
cation of the film-flattening vacuum (indeed, even the application of a 
hard vacuum will not alter its surface). The platen can accommodate up to 
169 reseau projectors and has an rms flatness of well under 2um. The 
platen is shortly to be put forward as a standard product by DBA and will 
be offered for sale to interested parties. 
LIKELY FUTURE DEVELOPMENTS 
As the last few sections have indicated, the bundle adjustment 
with self-calibration can lead to considerable improvements in accuracies 
and can produce results helpful in pinpointing physical deficiences of the 
camera system. It is a safe prediction that the bundle adjustment with 
self-calibration will receive increasingly widespread attention over the 
next few years. A great deal of experimentation will inevitably be 
performed with various formulations of the error model. (without doubt, 
spherical harmonics will be tried sooner or later). At DBA, for example, V 
the original error model has been condensed and revised through practical 
experimentation (coupled with analytical considerations) to the following 
form: 
Ax = a,x + ay + axy + ay? + ax?y + aq xy? t a,x*y* 
X 2.,,2 2,7 à 4 
+ 3 | a,4(x?-y?) + a, x’ + a,,Ix"-y | 
+ x [ auelx2+y2)? *a,z;lx? e V? j^ + ays (x24?) 6 
* 419 + 25 5 
(23) 
= 2 2 2 2,,2 
Ay = agxy + ax” + a,,x°y+ a, xy” + a,,x%y 
+4 [415 (x2-42} * ayQx*y* a, x*-y*1 | 
ty [are (23440712 + a, (x24y?2)* + au 214 | 
ta,, + a, (4) s : | 
In these expressions the first 12 coefficients are intended to account mainly 
for persistent, uncompensated film deformation together with non radial 
components of anomalous distortion. The coefficients of this particular subset 
are nearly orthogonal (i.e., their mutual correlations are mostly near zero) 
and are also nearly orthogonal to the next set of 6 coefficients. Of this 
next set, the first three (a s,a;4,a15) serve to represent the component of 
platen unflatness that is not strictly dependent on radial distance. They 
also serve to represent the radial component of anomalous distortion. When 
needed, an asymmetric contribution to platen unflatness is potentially 
available from the combined effect of the terms asx2y and a;;xy? appearing Ó 
in the first part of the error model. The coefficients a16,a17,01e Serve 
-28- 
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