A new reduction was then performed, modeling the data now with a 12
parameter model instead of the 22 parameter one used before. This new
model was simply the addition of three Gaussian curves with identical
A, 
, 
, s, t and B, together with
the corresponding 6 coordinates for the three image centres:
An internal comparison of the plate was again performed following the same
method already described. There is an improvement in comparison with the
results obtained when using the 22 free parameter model, as can be seen
in the fourth row in Table 2 (click here). We noted that
, again due to border effects as
we obtained
when working with a
circular area of radius 5 cm around the plate centre (note that it is
the same obtained for the same region with the 22 parameter model).
It seems from Table 2 (click here) that the 22 free parameter model was able
to deal with this trend when considering the whole plate while the 12
parameter model was not. This means that distortions in the plate borders
introduce significant deviations from the hypothetical identity of the three
exposures, which is assumed in the 12 parameter model.
A remarkable improvement is obtained when working with the
12 parameter model when performing the reduction with the PPM as before
(see last row in Table 3 (click here)). Again,
due to the poor quality of the
reference stars and
possible telescope tracking errors, as explained in Sect. 4.2 (click here).
A second order polynomial has been fitted to the data as before, after removing
from the sample the seven ones which were found to be to severely affected
by saturation and optical aberrations (see Sect. 5 (click here)). The
magnitudes are obtained with an accuracy of
, to be compared with the one obtained
with the 22 parameter model,
.
It is clear that both methods lead to the same accuracy in the photometry.