Illustration of how the performance of the 3D interpolation schemes are limited by sampling: because these all use weighted sums of neighbouring points, the interpolant cannot be greater than the largest neighbour. The left panel (panel d) of Fig. 5) shows sampled points (red) and the interpolation grid (green). The right panels show a horizontal cut through 2 different regions. Lower: the grid point to be interpolated lies midway between two sample points, and so cannot trace the true peak of the profile. Upper: since one of the samples is almost at the peak of the profile, the interpolant can provide a more precise estimate of the true value of the peak. It is straightforward to realise that this means the spectral shape of a spatially compact source (e.g. a star) will have a slow ripple pattern at a frequency corresponding to how often the dispersion axis crosses a column of pixels on the detector, as shown in Fig. 13. The multi-reconstruct recipe overcomes this limitation.
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