All Figures

$\begin{figure} \par\includegraphics[width=7cm,clip]{6259_01.eps}\end{figure}$ Figure 1: Largest (dashed, blue) and smallest (solid, black) diagonal elements of the covariance matrix M^T M as a function of $\beta$ at $n_{\max}=10$ . Deviation from unity indicates the loss of orthonormality. The image size was $50\times 50$ pixels with ${\vec x}_{\rm c}$ at (25, 25).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm]{6259_02.eps}\end{figure}$ Figure 2: Largest non-diagonal element of the covariance matrix M^T M as a function of $\beta$ at $n_{\max}=10$ (solid, black). Deviation from zero indicates the loss of orthogonality. The second curve (dotted, red) shows the effect of using integrated basis functions. The third curve (dashed, blue) shows the effect of including a constant function in the basis set. The image size was $50\times 50$ pixels with ${\vec x}_{\rm c}$ at (25, 25).
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{6259_03.eps}\end{figure}$ Figure 3: Example galaxy from GOODS CDF South. The image was chosen because of its typical deep field signal-noise-ratio and its significant substructure. The image size is $64 \times 64$ pixels.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{6259_04.eps}\end{figure}$ Figure 4: $\log_{10}~(\chi^2)$ for the decomposition of the galaxy from Fig. 3. The centroid was fixed. The dashed line delimits the $\chi ^2 \leq 1$ region, where the shapelet parameters are degenerate.
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In the text

$\begin{figure} \par\includegraphics[height=0.7\textheight]{6259_05.eps}\end{figure}$ Figure 5: Impact of the variation of $n_{\max}$ on the decomposition. In the top panel the $\chi ^2$ of the fit is plotted. The other panels show the deviations of the flux (middle), and the components of the ellipticity (bottom) from the values at the selected optimum. The vertical line indicates the optimum value.
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In the text

$\begin{figure} \includegraphics[height=0.7\textheight]{6259_06.eps}\end{figure}$ Figure 6: Impact of the variation of $\beta$ on the decomposition. All panels as explained in Fig. 5.
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In the text

$\begin{figure} \includegraphics[height=0.7\textheight]{6259_07.eps}\end{figure}$ Figure 7: Impact of the variation of ${\vec x}_{\rm c}$ on the decomposition. All panels as explained in Fig. 5.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm]{6259_08.eps}\end{figure}$ Figure 8: Comparison of the final decomposition $\chi ^2$ for the two implementations using simulated images with underlying shapelet models.
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In the text

$\begin{figure} \par\includegraphics[height=8.6cm]{6259_09.eps}\end{figure}$ Figure 9: Comparison of the final decomposition $n_{\max}$ for the two implementations using simulated images with underlying shapelet models ( $n_{\max} \equiv 8$ ). Since $n_{\max}$ is a discrete parameter, the data points have been randomized with a Gaussian distribution (standard deviation 1/3 pixel).
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In the text

$\begin{figure} \par\includegraphics[height=8.6cm]{6259_10.eps}\end{figure}$ Figure 10: Comparison of the final decomposition $\beta ^{\rm c++}$ (bottom, black) $\beta ^{\rm idl}$ (top, red) with $\beta ^0$ of the underlying shapelet models. The values of $\beta ^{\rm idl}$ have been shifted upwards by 5 units for better discrimination.
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In the text

$\begin{figure} \par\includegraphics[height=8.6cm]{6259_11.eps}\end{figure}$ Figure 11: Comparison of the final decomposition $\chi ^2$ for the two implementations using GOODS galaxy images.
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In the text

$\begin{figure} \par\includegraphics[height=8.6cm]{6259_12.eps}\end{figure}$ Figure 12: Comparison of the final decomposition $n_{\max}$ for the two implementations using GOODS galaxy images. The numbers have again been randomized with a Gaussian distribution (standard deviation 1/3 pixel).
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In the text

$\begin{figure} \includegraphics[height=8.6cm]{6259_13.eps}\end{figure}$ Figure 13: Comparison of the final decomposition $\beta ^{\rm idl}$ with $\beta ^{\rm c++}$ for the selection of GOODS galaxy images.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm]{6259_14.eps}\end{figure}$ Figure 14: Distribution of centroid errors for simulated images with underlying shapelet models. The centroid is obtained from the optimized shapelet coefficients. Only decompositions with $\chi ^{2,\rm c++} \leq 1$ and $\chi ^{2,{\rm idl}}\leq 1$ are considered.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm]{6259_15.eps}\end{figure}$ Figure 15: Distribution of relative $\beta$ errors for simulated images with underlying shapelet models. Only decompositions with $\chi ^{2,c++} \leq 1$ and $\chi ^{2,{\rm idl}}\leq 1$ are considered. The vertical lines indicate the 68% (solid, red), 95% (dotted, blue) and 99% (dashed, green) confidence limits. For the IDL results, the first and the last bin contains undershoot and overshoot, respectively.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{6259_01.eps}\end{figure}$	Figure 1: Largest (dashed, blue) and smallest (solid, black) diagonal elements of the covariance matrix M^T M as a function of $\beta$ at $n_{\max}=10$ . Deviation from unity indicates the loss of orthonormality. The image size was $50\times 50$ pixels with ${\vec x}_{\rm c}$ at (25, 25).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7cm,clip]{6259_03.eps}\end{figure}$	Figure 3: Example galaxy from GOODS CDF South. The image was chosen because of its typical deep field signal-noise-ratio and its significant substructure. The image size is $64 \times 64$ pixels.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7cm,clip]{6259_04.eps}\end{figure}$	Figure 4: $\log_{10}~(\chi^2)$ for the decomposition of the galaxy from Fig. 3. The centroid was fixed. The dashed line delimits the $\chi ^2 \leq 1$ region, where the shapelet parameters are degenerate.
Open with DEXTER

$\begin{figure} \par\includegraphics[height=0.7\textheight]{6259_05.eps}\end{figure}$	Figure 5: Impact of the variation of $n_{\max}$ on the decomposition. In the top panel the $\chi ^2$ of the fit is plotted. The other panels show the deviations of the flux (middle), and the components of the ellipticity (bottom) from the values at the selected optimum. The vertical line indicates the optimum value.
Open with DEXTER

$\begin{figure} \includegraphics[height=0.7\textheight]{6259_06.eps}\end{figure}$	Figure 6: Impact of the variation of $\beta$ on the decomposition. All panels as explained in Fig. 5.
Open with DEXTER

$\begin{figure} \includegraphics[height=0.7\textheight]{6259_07.eps}\end{figure}$	Figure 7: Impact of the variation of ${\vec x}_{\rm c}$ on the decomposition. All panels as explained in Fig. 5.
Open with DEXTER

$\begin{figure} \par\includegraphics[height=8.8cm]{6259_08.eps}\end{figure}$	Figure 8: Comparison of the final decomposition $\chi ^2$ for the two implementations using simulated images with underlying shapelet models.
Open with DEXTER

$\begin{figure} \par\includegraphics[height=8.6cm]{6259_09.eps}\end{figure}$	Figure 9: Comparison of the final decomposition $n_{\max}$ for the two implementations using simulated images with underlying shapelet models ( $n_{\max} \equiv 8$ ). Since $n_{\max}$ is a discrete parameter, the data points have been randomized with a Gaussian distribution (standard deviation 1/3 pixel).
Open with DEXTER

$\begin{figure} \par\includegraphics[height=8.6cm]{6259_10.eps}\end{figure}$	Figure 10: Comparison of the final decomposition $\beta ^{\rm c++}$ (bottom, black) $\beta ^{\rm idl}$ (top, red) with $\beta ^0$ of the underlying shapelet models. The values of $\beta ^{\rm idl}$ have been shifted upwards by 5 units for better discrimination.
Open with DEXTER

$\begin{figure} \par\includegraphics[height=8.6cm]{6259_11.eps}\end{figure}$	Figure 11: Comparison of the final decomposition $\chi ^2$ for the two implementations using GOODS galaxy images.
Open with DEXTER

$\begin{figure} \par\includegraphics[height=8.6cm]{6259_12.eps}\end{figure}$	Figure 12: Comparison of the final decomposition $n_{\max}$ for the two implementations using GOODS galaxy images. The numbers have again been randomized with a Gaussian distribution (standard deviation 1/3 pixel).
Open with DEXTER

$\begin{figure} \includegraphics[height=8.6cm]{6259_13.eps}\end{figure}$	Figure 13: Comparison of the final decomposition $\beta ^{\rm idl}$ with $\beta ^{\rm c++}$ for the selection of GOODS galaxy images.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8.8cm]{6259_14.eps}\end{figure}$	Figure 14: Distribution of centroid errors for simulated images with underlying shapelet models. The centroid is obtained from the optimized shapelet coefficients. Only decompositions with $\chi ^{2,\rm c++} \leq 1$ and $\chi ^{2,{\rm idl}}\leq 1$ are considered.
Open with DEXTER