deletions | additions       diff --git a/sectionAnalysis.tex b/sectionAnalysis.tex  index bb477aa..0a75e1b 100644  --- a/sectionAnalysis.tex  +++ b/sectionAnalysis.tex 
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our Im2shape implementation can recover point-like objects by applying this PSF correction to each star. Figure\,\ref{PSF} shows the results of the shape parameters measurements for these stars, with and wihtout taking into account the PSF in the shape measurement: the size distribution is dominated by point sources, and the orientation is more uniformly distributed after the PSF correction.\\  \begin{figure}  \centering  \subfigure [] {  \includegraphics[width=.25\textwidth]{./../plots/psf/ab.eps}~\hfill  \includegraphics[width=.25\textwidth]{./../plots/psf/ab_correc.eps}  \label{figura}  }  \subfigure []  {  \includegraphics[width=.25\textwidth]{./../plots/psf/map.eps}~\hfill  \includegraphics[width=.25\textwidth]{./../plots/psf/map_correc.eps}  \label{fig:b}  }  \subfigure []  {  \includegraphics[width=.25\textwidth]{./../plots/psf/e1.eps}~\hfill  \includegraphics[width=.25\textwidth]{./../plots/psf/e1_correc.eps}  \label{fig:c}  }  \subfigure []  {  \includegraphics[width=.25\textwidth]{./../plots/psf/e2.eps}~\hfill  \includegraphics[width=.25\textwidth]{./../plots/psf/e2_correc.eps}  \label{fig:d}  }  \subfigure []  {  \includegraphics[width=.25\textwidth]{./../plots/psf/Theta.eps}~\hfill  \includegraphics[width=.25\textwidth]{./../plots/psf/Theta_correc.eps}  \label{fig:e}  }  \caption{PSF treatment applied to stars of one of the images of the DES   simulation:   \subref{figura} Semiaxis product without (\textit{left}) and with (\textit{right}) taking into account the PSF.  \subref{fig:b} Mayor semiaxis ($a$ cos $\theta$, $a$ sin $\theta$) before (\textit{left}) and after (\textit{right}) the PSF deconvolution in the CCD. The first segment in the upper-left corner indicates the scale (3 pix).  \subref{fig:c}, \subref{fig:d} and \subref{fig:e} are the ellipticities components and the angular position of the mayor semi-axis, before (\textit{left}) and after (\textit{right}) the PSF deconvolution. }  \label{PSF}  \end{figure}  \subsection{Shear radial profiles} Gravitational lensing maps the unlensed image, specified by coordinates $(\beta_{1},\beta_{2})$, to the lensed image $(\theta_{1},\theta_{2})$ using a matrix transformation:  \\ 
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Background galaxies for the shear estimation, were selected as the galaxies with magnitude in the filter \textit{r'}, $m_{r}$, higher than $m_{L}$, and lower than $m_{max} + 1.0$, where $m_{L}$ is defined as the lowest magnitude $r'$ such that the probability that the galaxy is behind the cluster is higher than 0.7 and $m_{max}$ correspond to the peak of the magnitude distribution in the filter \textit{r'} of the galaxies (both magnitudes for each cluster are listed in Table\,\ref{table:2}). The later cut in magnitude ensures that we are not taking into account galaxies that are too faint, given that they could have great errors in the shape measurements. Also, as we did for the simulated data, we discard galaxies with FWHM replace_contentlt;$ 5, with companions closer than 16 pixels and with $\sigma_{e} > 0.2$.\\  To compute $m_{L}$ we used the catalogue of photometric redshifts computed by Coupon et al. 2009, based on the public release Deep Field 1 of the Canada-France-Hawaii Telescope Legacy Survey. We estimated the fraction of galaxies with $z > z_{cluster}$ in magnitude bins for the \textit{r'} filter, and then we chose $m_{L}$ as the lowest magnitude for which the fraction of galaxies was greater than 0.7. Background galaxy density after the selection are listed for each cluster in Table 2.\\  Once we obtained a catalogue for the background galaxies, we average the two components of the ellipticities (E-mode and B-mode) in nonoverlapping annuli. In order to take into account the contamination of foreground galaxies in the catalogue, we weighted the estimated shear,$\langle \gamma \rangle$ , with the probability that the galaxy was behind the cluster. We compute this probability using Coupon's catalogue, from the fraction of galaxies with $z > z_{cluster}$ for each bin in magnitude, \textit{r'}, and color (\textit{g' - r'} and \textit{r' - i'}) - Figure\,\ref{weigh}. Hence, given the magnitude and the color of each galaxy, we assigned to it a weigh, \textit{w}, as the fraction of galaxies with $z > z_{cluster}$ in that bin. \\  \begin{figure}  \centering  \includegraphics[width=0.5\textwidth]{./../plots/new-ones/distrib_z05.ps}\\  \caption{Fraction of galaxies with $z > 0.5$ ($N(z>0.5)/N_{tot}$), for different magnitudes in filter \textit{r'} and colors \textit{r'-i'}.}  \label{weigh}  \end{figure}  The average E-mode components correspond to the shear value which depends on the geometrical factor $ \beta = D_{LS}/ D_{S} $, where $D_{LS}$ is the angular diameter distance from the lens to the background source galaxy, and $D_{S}$ is the distance from the observer to the background galaxy. A galaxy at the same radial distance from the center of the cluster but at a different background redshift is sheared differently. To remove this variation, we divide the estimated shear by $\langle\beta\rangle$, which results in the infinite redshift limit (z $\rightarrow \infty$) shear value, that is only function of the radial distance from the cluster center. To estimate $\langle\beta\rangle $ we used once more Coupon's catalogue, since we can consider that this catalogue is complete up to our magnitude limit. We applied the photometric selection criteria to the catalogue and then we computed $\beta$ for the whole distribution of field galaxies, taking into account the contamination by foreground galaxies given our selection criteria by setting $\beta(z_{phot} < z_{cluster}) = 0$. The averaged geometrical factors for each cluster are given in Table\,\ref{table:2}. 
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%  To check the performance of our weak lensing analysis pipeline, we tested it on the DES cluster simulation images publically available \citep{2009arXiv0909.3856G}, with good results. This simulation consists of a sets of images, with different grades of difficulty, of sheared galaxies according to a SIS profile with a velocity dispersion of 1250\,km\,s$^{-1}$.\\  %  \begin{figure}{h!}  \centering  \includegraphics[scale=0.4]{./../plots/des/DES4_shearprofile.eps}\\  \includegraphics[scale=0.4]{./../plots/des/DES2_shearprofile.eps}\\  \includegraphics[scale=0.4]{./../plots/des/DES3_shearprofile.eps}\\  \caption{Shear blabla des.}  \label{DES}  \end{figure}  We applied our pipeline to three of the image files available, High Noise File, High Noise PSF Applied File and Low Noise PSF Applied File. For the PSF Applied files, we checked that our Im2shape implementation can recover point-like objects by applying the PSF correction to each star. The images contain only the sheared galaxies, hence all the galaxies detected were considered as background galaxies at $z=0.8$, which is the average of the redshifts of the galaxies. We cut the catalogue discarding the galaxies with FWHM replace_contentlt;$ 5, with companions closer than 16 pixels and with $\sigma_{e} > 0.2$, where $\sigma_{e}$ is defined as the quadratic sum of the errors $\sigma_{e1}$ and $\sigma_{e2}$ given by IM2SHAPE. These cuts are made in order to consider, for the shear measurements, insulated galaxies with good shape measurements. Shear profiles are shown in Figure\,\ref{DES}. For the most complex image that we treated, we obtained a deviation parameter of 1.6, defined as the number of $\sigma$ that the result is away from the input value of $\sigma_{V} = 1250$ km/sec, i.e. $\sigma = \dfrac{result - input}{error}$ .