Numerical Experiments

Fig. 1 shows the results of a simulation of sub-stepping and

optimal combination of the sub-stepped spectra. A model spectrum with fine channels consisting of an absorption line was generated, then each set of four channels was averaged and random noise added. This set of four sub-stepped spectra were then subjected to optimal combination and the fine channel result was compared to the input model. Fig. 1 shows the four sub-stepped spectra, the ``merged'' result (as produced by calhrs), and the optimally combined spectrum without regularization (i.e., =0). Over-fitting to the noise is apparent in this combined spectrum.

Fig. 2 shows the comparison of optimally combined quarter

sub-stepped GHRS data (dotted line) against the observed data, i.e., as presented by the merged spectrum from calhrs (histogram). The data is of the chemically peculiar star Lupi and was taken with the G160M grating and the small aperture; only a part of the 2000 channel spectrum is illustrated. The LSF on the fine grid was taken to be a Gaussian whose width was that of the GHRS instrumental resolution (assumed to be 1.0 diodes FWHM). Here 100 iterations were performed without regularization. The code with the regularization was applied to the same data and Fig. 3 shows the result. Here the

regularization constant, , was set at 0.3 after a series of runs varying the value of . The effect of the regularization in controlling the fit to the noise in the combined spectrum is evident. GHRS fluxed data must be converted to equivalent counts in order to perform the necessary statistical tests. After combination the data can be renormalized to flux. This operation is faciliated by multiplication by a numerical constant, which could be determined from the statistical errors delivered by the PODPS pipeline.