From the standpoint of obtaining fair weight factors when the various
measurements of are combined, it is not particularly
important that the general numbers for r, Sm-1, Sm, or
Sm-1 are particularly accurate. However, for the analysis of
absorption line optical depths, a correct value of r is critical.
Sometimes, determining r is very difficult if there are no saturated
lines in the vicinity. Most of the scattered light comes from the
echelle grating. Thus, as one might expect, the levels of r are
correlated with the brightness of the order that is being extracted.
One way to check that an estimate of r is correct is to see if a
vertical slice through an order, after r is subtracted, has a shape
that agrees with [b(i) + b(i-10) + b(i+10)], as shown by the heavy
line in the foreground of Fig. 12 (this assumes that the
derivation of b is correct and universal thoroughout the
format)
.
On some rare occasions, spectral lines appear to be somewhat slanted in the direction: ``\''. This behavior is probably a result of the astigmatism not being perfectly vertical. However, this effect does not appear all of the time, for reasons that are not clear. In extraction, one must be alert for this effect and stagger the sampling in a horizontal direction to obtain the best wavelength resolution.
When combining extractions from groups with different instrument pointing offsets (for a given echelle setting), it is again important to utilize the principle of keeping track of estimated errors and using them to determine relative weights for intensities, as discussed at the end of §7.10.2. Because of the pointing offsets, the spectral ranges will differ somewhat. It is a good idea to avoid sudden discontinuities that inevitably arise across the boundary of where one of the images stops on top of the coverage of another (because of the usual unavoidable systematic errors). One way to do this is to let the extraction of each image terminate gently by artificially multiplying the errors in short intervals near the ends by 1/H, where H is a Hanning window function.
Figure 13:
Extractions of two orders near the middle of
Fig. 11. Associated with every value of ![]() ![]() |
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