SPECRES - Point Source Extraction and Background Decomposition of 2-D Spectra

When the background is simple, such as a flat or sloping background, a linear interpolation of the values from both sides of the source is sufficient, but in the case of complex backgrounds, such as galactic nuclei with strong gradients, higher order fitting is required. The general problem is one of spectral decomposition - of separating the spectra of the point sources from the background. If the spatial profile of the point source(s) with wavelength is available, then it can be used with a restoration technique to decompose the point source spectra from the background spectrum. This is analagous to the image restoration case of a known Point Spread Function (PSF); for long slit spectra the Point Spread Function along the slit is referred to here as the Slit Spread Function, SSF.

There are many astrophysically useful applications of spectral decomposition from the simple one of subtracting the sky spectrum, to more complex ones such as determining the spectrum of the cusp of a galaxy nucleus, extracting spectra of closely separated stellar sources, such as binaries, or extracting multiple stellar spectra in crowded regions and extracting emission line spectra from high continuum complex scenes (see Walsh 2001 and Lucy and Walsh 2002). In addition, there are a variety of applications in nebular spectrometry when it may be the complete background spectrum, with the point sources removed, which is of scientific interest.

The "specres" package provides software tools to extract point source spectra from longslit or 2-D spectra with a known SSF. The technique is an extension of familiar image restoration methods used to improve the spatial resolution of imaging data. It can be simply thought of as multiple 1-D image restoration, where the single dimension is the signal distribution along the slit (the cross-dispersion direction) and the multiplicity is provided by the number of channels in the dispersion direction. It must be emphasized that there is no spectral restoration being undertaken, i.e. the spectral resolution remains unchanged as a result of these purely spatial restorations.

The STECF IRAF layered package "specres" provides two tasks to extract point source spectra from 2-D images (either longslit, multislit or cross-dispersed) and decompose the full background over the image. The tasks use the Richardson-Lucy (Lucy, 1974; Richardson 1972) iterative restoration algorithm to perform a maximum likelihood estimation and are fully described in Lucy & Walsh (2002). The codes employ adaptions of the Lucy-Hook (Hook & Lucy 1994) two-channel restoration technique, whereby a smoothing kernel is used to distinguish the extended source from the designated point sources. One of the codes utilises the (strong) constraint that the spectrum of the background is spatially unchanging (the "homogeneous" case). The other code uses the R-L scheme for the decomposition of the point source(s) and background applied independently to each spectral channel (the "inhomogeneous" case). Neither code however employs an entropy constraint in contrast to the Lucy-Hook technique.

The output products are the extracted spectra of the designated point source(s) and the estimated background image. A Point Source Function spectrum image is required as a 2-D spectrum. A task is also provided in the package to produce an SSF image from sets of (2-D spatial) PSF's, by simulating the spatial profile produced by placing a long slit over the PSF images and interpolating between the wavelengths of the individual PSF's.

Components of Package

• specinholucy -- Extract the spectra of one or more point sources and estimate the background spectrum using R-L restoration for the inhomogeneous case where the spectrum of the background can vary with position on the slit. The background is distinguished to be smoother than the point source(s) by a Gaussian smoothing kernel, whose width is set by the user. The input consists of the 2-D spectrum image; the output extracted spectra are STSDAS tables and the estimated background is a 2D image. The statistical error image can also be input to allow multiple Monte Carlo trials to be performed for estimation of the restoration errors. IRAF/STSDAS help file available.

• specholucy -- Extract the spectra of one or more point sources and estimate the background spectrum utilising the constraint that the spectrum of the background is homogeneous, i.e. does not vary with position on the slit. The simplification allows the spatial profile of the background to be collapsed along the wavelength axis and a 1D restoration of sources and background performed. The spatially restored background is then assigned to each spectral channel in a separate Lucy-Richardson iteration scheme which alternates with the 1D restoration of the wavelength-collapsed spatial profile. The background is convolved with a Gaussian smoothing kernel of chosen width. For spectra which have a background which is considered not to spatially vary with wavelength, this method provides a very accurate estimation of the background, freer of local noise than the specinholucy routine. The input and output products are identical to specinholucy. IRAF/STSDAS help file available.

• specpsf -- Produce a 2-D longslit spectrum from a set of Point Spread Functions in the range of wavelengths of a reference image. A reference image provides the dimensions for the output image and the required wavelength range. The set of spatial PSF's must be included in the wavelength range of the reference image. The simulated slit is placed on the PSF images to form the spatial Slit Spread Function (SSF); the slit can be offset from the centre of the PSF's and be of any width, as defined by the pixel size of the PSF images. The output 2-D PSF spectrum can be subsampled in the spatial direction with respect to the input PSF's. The SSF's at their respective wavelengths are cubic spline interpolated onto the wavelength extent of the reference image. IRAF/STSDAS help file available.

See the demo directory to try out the package.

Examples of simulated and real data

Figure 1. Longslit PSF image formed from three Gaussian spatial Point Spread Function Images of FWHM 4.0, 6.0 and 8.0 pixels at wavelengths of 7150, 7750 and 8300A. The wavelength coverage of the reference image was 7100 to 8345A and the SSF has been subsampled by a factor of 4 with respect to the input PSF images. The output SSF is centred at Y pixel 104.75 (256x256 image).

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Figure 2. Left figure shows a simulated image consisting of three point sources of Gaussian FWHM 4.0 pixels with fluxes in ratio 1.0:5.0:0.5 (bottom to top) on a tilted elliptical background and with a simulated night sky spectrum. The upper and lower point source spectra are tilted. The image has random Gaussian noise.
Right figure shows the resulting background fit for a specinholucy restoration with 50 iterations. The positions of the point sources was exactly given by the input table specifying their positions. The FWHM of the background smoothing kernel was 11.8 pixels and the PSF was not subsampled.
Below are shown the three restored spectra of the point sources (The simulated fluxes were 1000, 5000 and 500 counts):

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Figure 3. Left figure shows a simulated image consisting of three point sources of Gaussian FWHM 4.0 pixels with fluxes in ratio 1.0:5.0:0.5 (bottom to top) on a broad pedestal, whose spatial profile is wavelength independent, and with "sky" lines included. The image has random Gaussian noise.
Right figure shows the resulting background fit for a specholucy restoration with 50 iterations for the point sources and background spectra and the collapsed background. The position of the point sources was exactly given by the input table specifying their positions. The FWHM of the background smoothing kernel was 19 pixels and the PSF was not subsampled.
Below are shown the three restored spectra of the point sources (The simulated fluxes were 1000, 5000 and 500 counts):

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Figure 4. Left figure shows an HST STIS G430M spectrum of the nucleus of the Seyfert galaxy NGC 4151 (PI: J. Hutchings, Programme 7569; see Hutchings et al. 1998, ApJ, 492, 115). The spectral range is 4820 to 5100A and shows the H-beta and [O III] 4959 & 5007A emission lines.
Right figure shows the background with the nuclear point source removed using the specnlucy code. The PSF was provided by TinyTim. A high quality removal of the very bright point source is achieved; the mis-match is caused by the inadequacy of the Tiny Tim PSF model for this very high signal-to-noise (>200) continuum source.
Below is shown the extracted point source spectrum of the NGC 4151 nucleus.

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Figure 5. Left figure shows an HST STIS G750M longslit spectrum of the nucleus of the active galaxy M 81 (NGC 3031) taken in Programme 7350 (PI: G. Bower). The image was formed by shifting and combining 12 separate images taken with a series of offsets of the nucleus of M 81 along the slit. The spectral range is 8275 to 8850A to include the Ca II triplet absorption lines. The ugly sets of bad pixels arise from incompletely elimated hot pixels in the individual images. These pixels have been appropriately flagged in the data quality image and so are not considered in the restoration.
Right figure shows the background with the nuclear point source removed using the specslucy code. The PSF was again provided by TinyTim.
Below is shown the extracted point source spectrum of the M 81 nucleus with an asymmetric emission line of [Fe II] 8617A, not present in the underlying galaxy continuum.

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