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3. Data reduction, calibration and image analysis

Two independent methods have been used to preprocess and analyse all CCD frames obtained for the Cloverleaf at ESO and with the NOT. These are described below.

3.1. Automatic image decomposition technique

Classical preprocessing (flat-field correction and bias subtraction) has been applied to the raw data using ESO MIDAS routines. Whenever necessary, CCD non-linearities have been corrected for. Other defects such as column offsets and cosmic rays have been removed before sky subtraction. On each image frame, bi-quadratic polynomial surfaces have been fitted to numerous selected empty regions of the observed fields, in order to accurately subtract the sky from each individual CCD frame.

Also in the MIDAS environment, a general, automatic procedure has been developed in order to derive the best photometric measurements of multiply imaged point sources. The magnitudes of the lensed components have been determined by fitting multiple numerical point spread functions (hereafter PSFs), using a tex2html_wrap_inline1101 minimization method.

The numerical PSF has been determined by summation of the images of isolated point sources recorded on the same CCD frames as the gravitational lens system, after re-centering at the same position by bi-quadratic interpolations. Figure 1 in Kayser et al. (1990) shows a finding chart around H1413+117, with several of the used PSF stars. Star 40 has been adopted as our photometric reference. Among others, stars 8, 19, 40, 45 and 47 have frequently been used to construct the PSF. After fitting the composite PSF to the individual stars present on the CCD frame, incompatible objects were removed and the PSF redetermined. Making use of the coordinates of the stars derived from the previous fits, the linear transformation of the positions between different frames could be determined very accurately, including any relative rotation, translation and scaling.

On each individual frame, four free PSFs were first fitted to the complex QSO image, leading to positions for each of the four lensed components and preliminary values for the intensities. In Fig. 1 (click here) the relative positions of the four lensed images of the QSO are plotted. In the final measurements, the relative positions of the four PSFs have been fixed, reducing the number of free parameters from 12 to 6 (i.e. 4 intensity parameters and 2 position parameters). The values of these average relative image positions are shown in Table 2 (click here); the estimated uncertainties being tex2html_wrap_inline1103. A complete description of this automatic decomposition technique may be found in Remy (1996). Let us finally note that a total of 157 distinct ESO and NOT observations have been successfully analysed with the above method, even the lower quality data.

Figure 1: Relative positions of the four lensed components of H1413+117 derived from multiple PSF fittings of the 80 best ESO and NOT observations. The four crosses in this figure refer to the adopted average relative positions of the four lensed QSO images used in subsequent PSF fittings (see Table 2 (click here))


Comp. tex2html_wrap_inline1113 ('') tex2html_wrap_inline1117 ('')
A +0.000 +0.000
B +0.726 +0.201
C -0.518 +0.705
D +0.324 +1.058
Table 2: Average relative positions of the B, C and D lensed components with respect to A, as derived from the multiple fitting of 4 free PSFs applied to a set of the 80 best ESO and NOT observations

3.2. Interactive CLEAN processing

We have independently applied the IRAF/ccdred package developed and maintained by NOAO (National Optical Astronomy Observatories, Tucson, Arizona) to preprocess the same ESO and NOT data.

A program for CLEAN deconvolution of overlapping point sources has been developed by Østensen (1994), and implemented using IDL. This program, XECClean, was especially developed for doing high precision photometry of the quadruply imaged system, Q2237+0305 (the Einstein Cross). XECClean applies a semi-analytical PSF-profile fitting procedure adopted from the DAOPHOT package by Stetson (1987) and deconvolves the images using the interactive CLEAN algorithm (Teuber 1993), where the individual images are iteratively removed, until satisfactory residuals are obtained. Unlike for the case of the Einstein Cross, the analysis of the Cloverleaf system does not suffer from the additional presence of a bright foreground lens, and it is therefore easier to determine the individual fluxes of the four QSO components.

For some of the ESO data, photometric standard stars have been simultaneously observed in the V and R bands. From this, we have calibrated in magnitude several of the used PSF stars. Adopting the numbering used by Kayser et al. (1990) for the identification of the comparison stars, we report in Table 3 (click here) their V and R magnitudes. The photometric variability of star 40 has been checked against star 45. These stars are found to be photometrically
stable with respect to each other and to other PSF stars. Since star 40 is present on all CCD frames obtained for H1413+117, it has been used as our photometric reference star.


40 18.55 17.89
8 18.72 18.41
19 18.09 17.38
45 16.88 16.41
47 20.32 19.56
Table 3: V and R magnitudes of PSF stars in the field of H1413+117. See Kayser et al. (1990) for a finding chart. The tex2html_wrap_inline1147 uncertainty on the zero point magnitude determinations is about 0.10 mag

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