5.4 Evaluation of the Raw Correlations

After all of the pre-defined fiducial locations have been investigated as individual entities, the computed results are examined as an ensemble of information. The goal is to create an idealized or smoothed version of the actual displacements and then compare the smoothed values to the actual values, making adjustments to the actual displacements if necessary.

The creation of the smoothed displacement image is done in two major stages. First, an averaging procedure is invoked for each successful correlation sample. The closest fiducial locations to the sample in question which also have successful correlations are weighted according to their ``distance'' from the sample in question and if there is deemed to be enough data, the displacements from all of these successful locations are averaged to yield a mean displacement for the smoothed image at the sample location in question. If enough data are not acquired in the pre-defined search region, the data point must be an isolated or semi-isolated correlation. Isolated or semi-isolated correlations which cannot adequately be compared to the immediate surroundings for spatial trends are considered invalid correlations after-the-fact and are permanently removed from consideration.

Once the averaged image is created, the displacements for the ``missing'' fiducial locations are filled in by an interpolation/extrapolation scheme. The search for missing data is performed in a radial sense, starting at the center of the low- or high-dispersion photometric correction region. An extrapolation of the mean displacements is performed well outside the photometric correction limits to ensure that the bi-cubic spline fit done during the last stage of CROSS-CORR is well-behaved for all pertinent data regimes.

The actual displacements are then compared to the smoothed interpretation and any displacements that differ by 0.25 pixel from the smoothed array are modified to conform to the smoothed displacements. These final vector displacements are then expanded into a full 3-D ( 768 × 768 × 2) floating point displacement image ($\Delta$Sample and $\Delta$Line) using a bi-cubic spline interpolation algorithm. The $\Delta$Sample values are located in the first level of the final image; the $\Delta$Line values are located in the second level of the image.