5 Estimating scattered light

Figure 8: Comparison of spectra of HD 217522 optimally extracted with REDUCE (narrow black line) and reduced with IRAF (wider grey line). Top panel: continuum normalized order 83 containing H$\alpha$. Dots show the difference between the two reductions, shifted upwards by 0.5. Middle panel: segment of the same order in more detail. Bottom panel: extracted spectra and difference for order 101.

Flat field normalization and spectral extraction both require estimates of the scattered light background beneath each spectral order. The spectrum itself precludes direct measurement of the background beneath an order, but interpolation of the background between orders often provides an adequate estimate.

First we locate the position and extent of background regions between orders. This step can be non-trivial if the spectrum is obtained with an image slicer. We decompose a central group of columns in each order, empirically measuring noise from the standard deviation of the observed order minus the reconstructed model (Fig. 5). We then fit a linear background to the bottom envelope of the recovered spatial profile, using a threshold that allows background points to fall below the fit within the estimated noise level.

We define a background region at the beginning and another at the end of each spatial profile. Each background region contains several consecutive detector pixels below the linear fit just described. Robust estimation of a smooth background typically requires at least 8 pixels in a background region. This assessment is based on comparisons of background determinations in adjacent columns. A more elaborate procedure may be required to handle ghosts or scattered light from bright emission lines. Currently, sky emission is included in the background estimate and hence gets subtracted automatically from the target spectrum. If an image slicer is used, we do not attempt to use pixels between the slices to estimate background because the amount of overlap is very hard to estimate.

Background intervals defined with respect to the spatial profile are mapped into background stripes in the observed image by applying the selected offsets to the nominal order location y₀. For each column, separate medians are calculated for background pixels above and below each order. The resulting pair of background vectors for each order are filtered in the dispersion direction to remove vertical defects. Finally, linear interpolation in y is used to estimate the scattered light beneath each pixel of the spectral order.

Figure 9: Comparison of optimal extraction performed with REDUCE (narrow black line) and BERP (wider grey line) of the roAp star HD 217522 taken with an image slicer. Top panel: normalized order 83 containing H$\alpha$. Dots show the difference between the two reductions, shifted upwards by 0.5. Middle panel: segment of the same order in more detail. Bottom panel: extracted spectra and difference for order 101.