EXTRACT: Optimal Spectrum Extraction (Horne's Method)

EXTRACT is an "optimal extraction" routine for extracting the spectra of 1-dimensional sources (point-sources) from 2-D spectral images. It is based on the algorithm described by Keith Horne (``An Optimal Extraction Algorithm for CCD Spectroscopy'', 1986, PASP, 98, 609). In brief, each pixel in the spectral extraction is weighted according to the fraction of the flux which is expected in that pixel assuming a uniform spatial profile. The weighting scheme is optimized to retrieve the maximum signal-to-noise without biasing the resulting fluxes.

EXTRACT operates much like MASH, and should result in better signal-to-noise in those cases where the noise in the spectrum is dominated by the background (either from the sky or from the detector read-out noise).

WARNING: It is inappropriate to use EXTRACT for moderate or bright objects in which the noise is dominated by the Poisson statistics of the object itself. In such cases the extraction routine may discard so many points from the spatial profile fits it does that parts of the spectrum can become meaningless. It is also inappropriate to use EXTRACT for objects whose spectra are dominated by bright, unresolved emission lines (as EXTRACT might reject them as being ``cosmic rays''), and for extended sources. For bright sources, emission-line objects, and extended sources, use MASH or SPECTROID as appropriate.

The steps which EXTRACT goes through are as follows:

  1. The detector characteristics are specified. These are the readout noise in electrons (which can be changed using the keyword RONOISE= from its default value of 7) and the inverse gain in electrons per DN (using EPERDN= to change this from the default of 2.5). Usually the user will not wish to change these values, as the defaults are appropriate for the T.I. CCDs at Lick.

  2. The background rows are fitted with polynomials of order "pord." (Use the keyword SORDER= to change this from its default value of 2.) The expected uncertainties in this fit are then calculated (using the read-out noise and the gain) and any points more than 4-sigma from the fit are ignored and the fit recalculated. This fit iteration is performed until no new points are ignored or until 5 iterations have been done.

  3. The object profile is then parameterized and fit with a polynomial of order 2 (unless the PORDER= keyword has been used). Again, the fit is iterated a maximum of 8 times, using a rejection threshold of 4-sigma.

  4. Using the resulting parameterization the weights are calculated for each pixel and the spectrum extracted. An automatic point rejection is performed at this stage to remove bad pixels on the spectrum rows themselves. A more conservative 5-sigma rejection level is used and only one point (the one with the largest difference) is removed at each iteration. A maximum of five iterations is allowed (hence up to five points may be removed at each wavelength). The resulting spectrum is placed into the specified buffer.

  5. If the SKY= and/or VAR= keywords have been specified then the appropriate buffers are loaded with the requested spectra. If the SUB keyword has been specified then the fitted background rows are subtracted from the original image.

Note that the uncertainties at all stages are estimated using the assumed detector characteristics. When the data are of sufficient quality this means that the uncertainties in the fits will be so small that the inability of the fit parameterizations (both sky and profile) to accurately model the data will be detectable. The program will then start rejecting large numbers of points because the model assumed is not quite appropriate. In this case the MASH command should be used, as the data are probably of such high signal-to-noise that the optimal extraction routine will not gain anything over a simple summation. The interested user is referred to Keith's article for more details.