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The removal of unwanted spikes, above an otherwise featureless background such as the inter-order space of echelle spectra, is done most easily with a median filter. Therefore, in a first step a median filter is applied to the entire frame. This then enables the true background to be determined as described in Section `Background Definition' of this chapter. The subtraction of the background calculated completes the second step, and, as far as the inter-order space is concerned, the final result is reached already. The removal of cosmics from the object spectrum forms the third step and is restricted to the regions covered by the spectral orders in the background-corrected, but otherwise raw frame. This step comprises the following operations performed within a sliding (along and separately for each spectral order) window of user-specified width:
of the window, normalize the spatial profile to the total
flux in the associated slice (i.e. all 
of the order considered).
in the window.
) in the central slice, c, of the window
compare their re-normalised flux, 
, with the properly scaled
contents 
of
pixel j in the median profile. If the difference exceeds the expected
statistical error of 
(calculated from the number of
photons detected and the readout noise) by a user-specified factor,
replace 
with 
.
4 
) and the spectral information within the spatial
profile does not change (point sources are best), this
procedure does not redistribute the flux or dilute the point spread
function.
These three steps are the backbone of command FILTER/ECHELLE. The final output frame is the merger of the median-filtered inter-order domains with the spectral orders after having been subjected to step three. Note that the background has been subtracted already. A keyword BACKGROUND with contents SUBTRACTED is appended to the frame as a flag to subsequent high-level procedures so as not to have to go through the very time consuming step of the background modeling again. Delete that descriptor or change its contents if re-modeling of the residual background is desired.