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Astron. Astrophys. 324, L1-L4 (1997)

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3. Deconvolution - a new algorithm

The images were deconvolved using a new method, described by Magain, Courbin & Sohy (1997), that allows precise photometric and astrometric measurements of strongly blended point sources superimposed on a diffuse background. The main idea of this algorithm is to deconvolve by a PSF narrower than the total observed PSF so as to preserve a good sampling of the deconvolved image. As a consequence, 1) the image can be decomposed in a sum of point sources, plus diffuse background and 2) the final resolution of the deconvolved images is chosen by the user.

We chose the final deconvolved PSF of the CFHT as a Gaussian with a Full-Width-Half-Maximum (FWHM) of 3 pixels. The NOT images were deconvolved on a grid of pixels two times smaller than the original frames (i.e. 0:0005355) in order to keep a good sampling of the lensing galaxy, and the final PSF was a Gaussian with a FWHM of 6 (smaller) pixels. This led to resolutions of 0:0026 for the CFHT and 0:0032 for the NOT. The PSF used to reach these resolutions was constructed from two stars about one magnitude brighter than the quasar image and situated [FORMULA] away from the lens.

The weight attributed to the local smoothing of the background component in our deconvolved model image (see Magain et al. (1997) for more details) was chosen so that the residuals at the location of the lensing galaxy had the correct statistical distribution, i.e. Gaussian with a standard deviation of 1 (in units of the photon noise). In this way we avoided under- or over-fitting in the area of interest. A constant smoothing term was used for the whole image and was adapted to the area of the lensing galaxy. This leads to slight overfitting of the sky noise farther away from the target and produces some noise amplification at low light levels.

In the CFHT images, the PSF shows variations of the order of 5-10% from one side of the total field to the other. Therefore, we allowed the PSF to depart slightly from that derived from the two neighboring stars. The PSF was constrained to deviate by the smallest amount consistent with an artefact-free deconvolution of the 4 quasar images.

Fig. 1 shows the result of the deconvolution for a CFHT and a NOT image. Since the greyscale was chosen to display the full dynamic range, this image clearly shows that there are no "deconvolution artefacts" or "ringing effects" around the point sources.

[FIGURE] Fig. 1. Top panels: I band images of PG 1115+080 obtained at the CFHT (600s exposure, field of 5:005) and at the NOT (200s exposure, field of 6:008). Middle panels: the same images, but deconvolved using our new algorithm. Bottom panels: the deconvolved lensing galaxy alone. Note that the greyscale was chosen to display the full dynamic range of the images.
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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998