All Figures

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{0472fig1.eps} \end{figure}$ Figure 1: One-dimensional convolution $h = B_4(x;\beta _f) \star B_2(x;\beta _g)$ . We plot the modulus of h_n with n even (all odd modes have vanishing power), normalized by $\sum _n \vert h_n\vert$ .
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0472fig2.eps} \end{figure}$ Figure 2: Sketch of the effect of a convolution on the power of shapelet coefficients. The detailed shape of the curves is neither realistic nor important, but typical shapelet models show decreasing coefficient power with increasing order n. The noise regime (represented by the gray area) is constant in the case of uncorrelated noise.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{0472fig3.eps} \end{figure}$ Figure 3: Example of simulated galaxies used in our testbed: a) intrinsic galaxy model with $\beta _f=2$ and flux equaling unity; b) after applying a shear $\vec{\gamma} = (0.1,0)$ ; c) after convolving with PSFb from Fig. 4 with $\beta _g=2$ . The bottom panels show c) after addition of Gaussian noise of zero mean and variance $\sigma _n^2$ : d) moderate noise, $\sigma _n = 10^{-4}$ ; e) high noise, $\sigma _n = 10^{-3}$ ; f) is the shapelet reconstruction of e). The scale is logarithmic.
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In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{0472fig4.eps} \end{figure}$ Figure 4: The kernels used in our benchmark: a) model of PSF2 from STEP1 (Heymans et al. 2006) with $n_{\rm max}^g=4$ ; b) model of PSF3 from STEP1 with $n_{\rm max}^g=4$ ; c) airy disk model with $n_{\rm max}^g=6$ ; d) model from a raytracing simulation of a space-bourne telescope's PSF with $n_{\rm max}^g=8$ and $n_{\rm max}^g=12$ (shown here). The scale is logarithmic.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{0472fig5.eps} \end{figure}$ Figure 5: Recovered shear $\tilde{\vec\gamma}$ and intrinsic scale size $\tilde\beta_f$ in a moderate-noise simulation ( $\sigma _n = 10^{-4}$ , $\beta _f=3$ , PSFb) as functions of the kernel scale $\beta _g$ . In each panel the horizontal dashed line shows the true value of the quantity and the vertical dotted line shows the true value for $\beta _f$ as reference. Errorbars (which are often too small to be visible) exhibit the standard deviation of the mean of N=100 realizations. For visualization purposes, each method is slightly offset along $\beta _g$ . Simulations with different PSF models or $\beta _f$ are qualitatively equivalent.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{0472fig6.eps} \end{figure}$ Figure 6: Recovered shear $\tilde{\vec\gamma}$ and intrinsic scale size $\tilde\beta_f$ (in units of the true scale size $\beta _f$ ) in the moderate-noise simulations in dependence on the PSF models from Fig. 4 (subscripts denote $n_{\rm max}^g$ ). Each data point represents the mean of the quantity for all available values of $\beta _f$ and $\beta _g$ (in total 60 independent combinations), and errorbars show the standard deviation of the mean. For visualization purposes, each method is slightly offset horizontally with respect to the others.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{0472fig7.eps} \end{figure}$ Figure 7: Analogous to Fig. 6 but for the high-noise simulations.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{0472fig8.eps} \end{figure}$ Figure 8: Distance in shapelet space $R_{\rm s}$ between the mean deconvolved and the true intrinsic coefficients in dependence of the PSF model for the three methods F ULL ( top panel), S IGNIFIC ( middle panel), and S AME ( bottom panel). The mean is computed by averaging over all available values of $\beta _f$ and $\beta _g$ (in total 60 independent combinations). Shown are the results for the moderate-noise simulations (solid line) and the high-noise simulations (dotted line).
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{0472fig9.eps} \end{figure}$ Figure 9: Recovered shear $\tilde{\vec\gamma}$ and intrinsic scale size $\tilde\beta_f$ (in units of the true scale size $\beta _f$ ) in the high-noise simulations in dependence on the S/N of the convolved galaxy. The binning (dotted lines) is defined by the octiles of the S/N distribution, therefore all bins contain the mean values of approx. 7 combinations of $\beta _f$ , $\beta _g$ for each PSF model, in total $\approx$ 35 independent settings. The data are plotted at the center of the bins and the methods are slightly offset horizontally for visualization purposes. Color code is as explained in Fig. 6.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{0472fig1.eps} \end{figure}$	Figure 1: One-dimensional convolution $h = B_4(x;\beta _f) \star B_2(x;\beta _g)$ . We plot the modulus of h_n with n even (all odd modes have vanishing power), normalized by $\sum _n \vert h_n\vert$ .
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$\begin{figure} \par\includegraphics[width=7cm,clip]{0472fig2.eps} \end{figure}$	Figure 2: Sketch of the effect of a convolution on the power of shapelet coefficients. The detailed shape of the curves is neither realistic nor important, but typical shapelet models show decreasing coefficient power with increasing order n. The noise regime (represented by the gray area) is constant in the case of uncorrelated noise.
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$\begin{figure} \par\includegraphics[width=8.4cm,clip]{0472fig4.eps} \end{figure}$	Figure 4: The kernels used in our benchmark: a) model of PSF2 from STEP1 (Heymans et al. 2006) with $n_{\rm max}^g=4$ ; b) model of PSF3 from STEP1 with $n_{\rm max}^g=4$ ; c) airy disk model with $n_{\rm max}^g=6$ ; d) model from a raytracing simulation of a space-bourne telescope's PSF with $n_{\rm max}^g=8$ and $n_{\rm max}^g=12$ (shown here). The scale is logarithmic.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{0472fig7.eps} \end{figure}$	Figure 7: Analogous to Fig. 6 but for the high-noise simulations.
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