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A different approach is also available at this stage, as an
alternative to the method described in the last Section. It consists
of a correction for the blaze function by using a suitable model of
the blaze effect introduced by the echelle grating. In this approach,
no correction for the chromatic response of the instrument is applied.
It is noteworthy however to say that the standard star correction is a
much more efficient way to perform the instrumental response
correction. The model assumes a plane grating, used in near--Littrow
mode. The blaze function R at wavelength 
is approximated
by
where 
is a grating `constant' with value between 0.5 and 1, and
, in which m is the order number, and
is the central wavelength of order m. Both parameters are
related through the grating `constant' k by 
.
This correction is done with the command RIPPLE/ECHELLE; the command
includes three methods to compute the parameters k and 
:
The first one, method SINC, is a modification of the method suggested by Ahmad, 1981, NASA IUE Newsletter, 14, 129. This algorithm approximates the blaze function by a sinc square and finds the function parameters by a non--linear least squares fit to the order profile. The method is suitable for objects without strong emission or absorption features and can be used to get a first estimation of the blaze parameters.
The second method, named OVER, is
based on Barker, 1984, Astron.J., 89, 899. This method uses the
overlapping region of adjacent orders to estimate, in a few iterations,
the parameter k of the blaze function which is, as before, assumed to be
a sinc square. The method works well, provided that orders are overlapping
and that there is a very good estimation of the parameter 
,
assumed to be a contant.
The third method, FIT,
is an extension of the previous one. It uses, as before,
the overlapping region of the adjacent orders but has the advantage of
assuming that both parameters k and 
can vary. The method
minimises the difference of the corrected orders in each of the
overlapping intervals.
