Extraction of Nodded Spectra

Portable--CGS4DR now has the ability to extract up to 3 spectra nodded along the slit in an automated way. For one spectrum on the array, the result is analogous to the simple Figaro EXTRACT command. For two spectra, the upper row is assumed to be negative and the lower positive. For three spectra, the middle beam is assumed to be positive and is flanked by two negative beams. Note that in the two and three beam cases, a switch to invert the spectrum is included in case the beams are not in the sense expected. Note that the number of rows over which the extraction occurs is not taken into account when combining multiple beams: just the total extracted flux is used.

Further, for three beam extraction, two algorithms are provided i.e. viz. for bright and faint sources. The fundamental difference is the weighting given to the outer beams. Let the signal from the star in one chop beam be S and the error . Assuming that there is no beam imbalance, the final reduced group will contain three spectra in which the middle is the positive beam (P) and has twice the signal of the outer negative beams (N1 and N2).

This reduced group is formed from the difference of two observations, namely an OBJECT and a SKY. These individual reduced observations will each have two spectra offset by the nodding distance. For the OBJECT observation, the upper beam with be negative and the lower beam positive. For the SKY frame the situation is reversed but the position on the array of the upper beam in the SKY matches the lower beam in the OBJECT.

For the bright source algorithm, the final signal, is given by:

For the faint source algorithm, the final signal, is given by:

If and are the errors in the bright and faint source algorithm, then:

Note that the faint source algorithm will give better cancellation of any residual atmospheric lines on the array and a more representative error for the case where the dominant source of noise is the infra-red background.