Deconvolution of spectra


Following the same fundamental principles as for our image deconvolution algorithm, a technique for spatial deconvolution of spectra has been developed. The spectrum of a stellar-like object can be used to spatially resolve the spectra of very blended objects. As in the image deconvolution algorithm, the spectrum is decomposed into a sum of point sources and diffuse numerical background, so that the spectrum of extended sources blended with point sources may be obtained.


The images below show examples of applications to simulated and real spectra. The algorithm takes into account seeing variations as a function of wavelength and atmospheric refraction, which are both included in the present simulations.



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Deconvolution of two very blended spectra

decspectre001From left to right:
1. A simulated two-dimentional spectrum of 2 blended point sources. The seeing is 4 pixels FWHM and the separation between the two objects is only 2 pixels. The two blended input spectra consist of a QSO (continuum + emission lines) about 1.5 magnitude brighter than a star (continuum only). Note the curvature of the spectrum, simulating the effect of strong atmospheric refraction.
2. The deconvolved spectra, where the 2 objects are now visible.
3. Residual map, i.e., data minus deconvolved model (reconvolved by the PSF), in units of the photon noise. The residual map is flat and equal to 1 almost everywhere in the field, indicating the result of the deconvolution is good.


Spatial profiles of the spectrum before and after deconvolution.



1-D deconvolved spectra compared with input spectra.

decspectre005 One dimensional deconvolved spectra of the QSO (top) and the star (bottom). For both objects, the inset show the division of the deconvolved spectrum by the input spectrum, and demonstrates how well the deconvolution procedure recover the spectra, in spite of their severe degree of blending.


Deconvolution of the spectrum of a lensed QSO and its lensing galaxy

decspectre007From left to right:
1. Simulated spectrum of a doubly imaged QSO. The lensing galaxy is 4.5 magnitudes fainter than the QSO images and is situated at only 2 pixels away from the QSO images on the left. The seeing is 4 pixels FWHM.
2. Deconvolution of the simulated spectrum
3. Deconvolved spectrum of the lensing galaxy
4. Input spectrum of the lensing galaxy
5. Residual map, as in the first example.


decspectre0091-D deconvolved spectra of the QSO images (top). The bottom panels show the result of the division of the deconvolved spectra by the input spectra.


decspectre0111-D deconvolved spectrum of the faint lensing galaxy with simulated 3000 Å break and OII emission line (top). As for the QSO images, the bottom panel show the result of the division of the deconvolved spectrum by the input spectrum. Note the very good agreement between the recovered and input spectrum. Only the very right part of the spectrum is slightly (2σ) overestimated by the deconvolution. However, (i) this is visible on the upper part of the residual map of figure 1 (2σ residuals in the upper part of the residual map), (ii) the position of the emission line is recovered with an accuracy of 0.1 pixels and allows one to measure for example the redshift of the lensing galaxy. (iii) Such results can not be obtained with any other existing method.


decspectre013VLT/FORS1 spectrum of the quasar HE 1503+0228 at a redshift of 0.13. The figure shows the total spectrum (quasar + host galaxy). Note the very high signal-to-noise ratio attained despite the relatively high dispersion, R=700. This spectrum is not flux-calibrated.


decspectre015After deconvolution and subtraction of the quasar spectrum, the spectrum of the host galaxy is obtained. Note that the spectrum shows no trace of contamination by the central quasar.


decspectre017Zooms on two emission lines in the spectrum of the host galaxy. In each figure, the raw 2-D spectra are shown on the left. The right part shows the spectrum of the galaxy alone, with a spatial resolution of 0.2" after deconvolution. This will allow to study the variation of the spectral properties with distance from the central quasar. The emission lines visible on these spectra are Hβ and OIII (left figure), and OII (right figure). The latter also shows the H and K lines of Ca II in absorption, as well as the 4000 Å break. Note the tilt of the lines as a consequence of rotation. The total field is 10".