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Geometric distortion can be separated into three components: optical distortion, detector distortion, and format-dependent distortion. The optical component of the distortion can be described as any distortion due to the HST+FOC optical configuration, i.e., everything which originates upstream from the intensifier tube. It is determined by ray-tracing models of the optical system. The format-dependent distortions include those aspects which differ from format to format, such as the scan distortion discussed above. Most of these distortions result from events which take place downstream from the intensifier tube. Finally, the detector distortions are those which occur within the tube itself.
The accuracy of the geometric distortion correction of FOC data is currently limited by the coarseness and size of the reseau grid (60 pixel spacing). Nominally, the accuracy of the geometric correction is very good - about 0.2%. That is, the true relative separation between points after geometric correction is good to about 0.5 pixels over a separation of about 250 pixels. However, there are several conditions on this which must be fulfilled.
The geometric distortion is only explicitly defined at the positions of the
reseau marks present in the format. The actual geometric correction is
the result of a 2-D polynomial fit between the observed reseau marks and a
reference grid, hence the pixel-by-pixel distortion is the result of
interpolation between these known points on the assumption that the variation
of the distortion has a relatively long scalelength and is both smooth and
well-behaved.
(Note: As discussed in the last section, the scan component of
the distortion is not modelled by the fitting procedure because it varies on
scale lengths approximately equal to the reseau spacing and so, after geometric
correction, this component remains.) The accuracy of the fit to the distortion
at any given pixel depends only on the order of the fitted function and how
well it is constrained. The order of the 2-D fitting function is determined by
the dimensions of the reseau grid that is present in the format being addressed,
so that if there are columns and
rows then it is normal to use a
polynomial which is
order in
, and
order in
(for both
and
).
If we think about the situation (see Fig. 2), it is clear that the observed
reseau grid marks the limit of the constrained fit and that any areas of the
image which are outside the observed grid can have no reliable geometric
correction based on the reseau grid (light shading in Fig. 2.). Immediately
within the reseau grid boundaries we have a region which is only constrained by
a single point on the outside (dark shading in Fig. 2.) and in this region the
geometric correction can only be considered fair, i.e., position residuals may
be
as much as 1-1.5 pixels.
After taking these considerations into account we see that the geometrically
reliable region, where the position residuals will be 0.5 pixels or less,
is only the unshaded area in the center, representing about 40%of the 512512 (normal) format. (Figures similar to Fig. 2 can be derived for
other formats simply by applying the same rules.) These considerations also
highlight the significance of the missing top row of reseau marks in the full
512
1024 (zoomed) format since there can be no reliable geometric
correction in the region above the reseau grid which, on its own, accounts for
a full 15%of the image.
The significance of this discussion is that
The advent of COSTAR itself, will make no difference to these limitations on the
quality of the geometric correction. However, we are investigating a method
which
should produce a general improvement for most formats, with the exception of the
largest (the 5121024 zoomed). Basically, observations will be
taken of a crowded star field (in 47 Tucanæ), using all of the necessary
formats and, after geometrically correcting the large format, all smaller
formats
will be corrected using a transformation which aligns the stars with the larger
format. In other words, the star positions in the geometrically corrected 512
1024 (zoomed) image will be used as the reference for all smaller
formats.
The standard geometric correction procedure using the reseau grid will only be
used for for the large format. Since most of the smaller formats lie within
the geometrically reliable area of the large format, and since the stars
provide a much finer grid (a random distribution with an average separation
of 10-15 pixels), it should be possible to correct these formats almost
right to their edges with no significant increase in the geometric residuals.
This will mean that the geometrically reliable imaging area of the
smaller formats will, in effect, be virtually the whole image.
One bonus of this method is that the camera platescales will, by default, be identical in each format. A somewhat less important advantage will be that images in different formats will be automatically co-aligned.