All Figures

$\begin{figure} \par\includegraphics[width=15cm]{09819fig1.eps} \end{figure}$ Figure 1: Hinode/SOT observations from top to bottom: a) limb observation, c) the total eclipse from March 19th, 2007, e) the partial eclipse from February 17th, 2007, and g) the Mercury transit from November 8th 2006 on the solar disc ( $x = -52~\hbox{$^{\prime\prime}$ }$ , $y = -426~\hbox{$^{\prime\prime}$ }$ , $\mu = 0.9$ ) and i) at the solar limb. For all cases an exemplary image for a wavelength of 555 nm is selected, except for the partial eclipse which was only observed in G-band (431 nm). The panels to the right show intensity profiles of the image shown on the left (black solid) and for all other available images of the same kind (dark-grey). The profiles are averaged over all rows, aligned perpendicular to the terminator/limb. The intensity is normalised to the intensity of the bright solar disc close to the limb / terminator. The left half of the panels h) and j) show averages over the three rows and columns through the centre of the Mercury disc, whereas the radial averages can be seen in the right half. The dotted lines are for orientation only. For comparison profiles from the total eclipse observed in G-band are plotted in panel f) (dashed lines).
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{09819fig2.eps}\end{figure}$ Figure 2: Residual intensity as function of mean count rate at a distance of 5 $^{\prime \prime }$ from the (eclipse) terminator, which corresponds to the centre of the Mercury disc. The panels in the upper row a)- c) and the leftmost column d), g), j) show the residual intensity $I_{\rm res, \lambda }$ as function of the mean count rate $\mathcal{C}$ for the individual images of the Mercury transit (circles), the total eclipse (squares), the partial eclipse (diamonds, 431 nm only), and the solar limb (triangles) at all six BFI bands. Symbols are filled for $\mu > 0.5$ and unfilled and dark-grey otherwise. The adopted $\mu$ -value for a data point is the average over the whole individual image. An image of the solar limb thus can have $\mu < 0.0$ . A relation between residual intensity and mean count rate is derived by linear regression (solid lines), where the solar limb data is neglected. It is justified by the uncertainties in choosing the right reference intensity (see text for details). More information is shown for the three wavelengths 450 nm, 555 nm, and 668 nm. First, the heliocentric position $\mu$ is plotted as function of $\mathcal{C}$ in the middle column e), h), k) but not b) for the eclipse and Mercury transit data and for images of ``regular'' quiet Sun (dots). The relation between $I_{\rm res, \lambda }$ and $\mathcal{C}$ is then used to estimate $I_{\rm res, \lambda }$ from the mean count rate of the regular (unocculted) images. The results are presented in the right column f), i), l). As abscissa $\mu$ is chosen. Finally, a linear regression is performed for the data points of regular granulation (solid lines).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{09819fig3.eps}\end{figure}$ Figure 3: Stray-light in a SOT green continuum filtergram of the total eclipse from March 19th, 2007 ( $0.78 < \mu < 0.92$ ): Image ( left) and profiles along the x-axis ( right). In order to make the stray-light visible, the data range is limited to a value of 120, which is about 10% of the mean value of the bright solar disc ( lower left corner of the image). The vertical positions of the profiles are indicated by tick marks on the right side of the image. Profile a lies in a ``shadow'', whereas profile b crosses a ``streak'' at a position of x = -300 $^{\prime \prime }$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{09819fig4.eps}\end{figure}$ Figure 4: Theoretical point spread functions for a wavelength of 555 nm: Original diffraction-limited PSF ( top row), after convolution with a Voigt function with $\gamma = 0~\hbox{$.\!\!^{\prime\prime}$ }004$ and $\sigma =0~\hbox{$.\!\!^{\prime\prime}$ }012$ ( middle), and after linear combination with a Lorentzian with the parameters $\alpha = 0.25$ and $\beta = 0.05$ ( bottom). The left columns shows the inner part of the PSFs on a logarithmic grey-scale, which covers six orders of magnitude, whereas the corresponding profiles along the x-axis are plotted in the middle column. The rightmost panels display the PSF core on a linear scale (solid) together with the original PSF (dotted). The dashed line in the lower right panel is the used Lorentzian profile.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{09819fig5.eps} \end{figure}$ Figure 5: Artificial observation of a Mercury transit at a wavelength of 555 nm: a) innermost region of the original intensity mask; b) degraded image after convolution with a non-ideal PSF that was calculated by a diffraction-limited PSF and a Voigt profile with $\gamma = 0~\hbox{$.\!\!^{\prime\prime}$ }012$ and $\sigma = 0~\hbox{$.\!\!^{\prime\prime}$ }098$ ; c) radial-averaged intensity profiles for the original image (dotted) and the degraded image (solid); and d) close-up of panel c). The dot-dashed line is an empirical intensity profile derived from a SOT image.
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In the text

$\begin{figure} \par\includegraphics[width=15.6cm,clip]{09819fig6.eps} \end{figure}$ Figure 6: Goodness $\varepsilon$ of the fits for the reference case of the Mercury transit at $\lambda = 555$ nm. It represents the difference between a prescribed synthetic intensity profile for a parameter pair of $\gamma = 0~\hbox{$.\!\!^{\prime\prime}$ }005$ and $\sigma = 0~\hbox{$.\!\!^{\prime\prime}$ }01$ and all other profiles. They are derived with non-ideal PSFs calculated by convolution with a Voigt function. a) The goodness $\varepsilon$ as defined in Eq. (9) as function of $\gamma$ and $\sigma$ ; b) close-up of the lower left corner; c) $\varepsilon$ along the ``minimum error trench'' (MET, marked with white dotted line in panels a); and d) the applied intensity offset $I_{\rm o}$ along the MET. Overplotted in panels a) and b) are contours of constant Strehl ratio (solid, black and white) and of constant broadening (dashed) of the combined PSF. The broadening is given in percent points increase of the FWHM of the PSF with respect to the diffraction-limited PSF. The circles in panels a) and b) mark the parameter pair with the smallest $\varepsilon$ below the ``knee'' of the MET, while the ``knee'' is indicated by a triangle. The dot-dashed lines in panel a) are for constant Voigt damping parameter a, whereas the dotted vertical lines in panels c) and d) show the rough location of the MET ``knee''.
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In the text

$\begin{figure} \par\includegraphics[width=15.5cm,clip]{09819fig7.eps} \end{figure}$ Figure 7: Goodness $\varepsilon$ of the fits between artificial and observed intensity profiles for a selected image of the Mercury transit at $\lambda = 555$ nm. The synthetic profiles are generated with non-ideal PSF that are calculated by convolution with a Voigt function. See Fig. 6 for a detailed explanation of the figure.
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In the text

$\begin{figure} \includegraphics[width=9cm,clip]{09819fig8.eps}\end{figure}$ Figure 8: Goodness $\varepsilon$ ( left column, solid lines) of the fits between artificial and observed intensity profiles for the Mercury transit at $\lambda = 555$ nm and applied intensity offset $I_{\rm o}$ ( right column, solid lines) for PSFs with convolution with a Lorentzian ( top row) and a Gaussian ( bottom row). The goodness is averaged over the individual observations. The dashed lines are the Strehl ratio in the left column and the FWHM of the combined PSF in the right column, respectively.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{09819fig9.eps}\end{figure}$ Figure 9: Goodness $\varepsilon$ of the fits between artificial and observed intensity profiles for the Mercury transit at $\lambda = 555$ nm (cf. Fig. 6). The non-ideal PSF contribution is calculated by linear combination with a Lorentzian. a) The goodness $\varepsilon$ as defined in Eq. (9) as function of $\alpha$ and $\beta$ ; b) $\varepsilon$ along the ``minimum error trench'' (MET, marked with white dotted line in panel a); and c) the applied intensity offset $I_{\rm o}$ along the MET. Overplotted in panel a) are contours of constant Strehl ratio (solid) and of constant broadening (dashed) of the combined PSF. The broadening is given in percent points increase of the FWHM of the PSF ( ${FWHM}_{\rm PSF}$ ) with respect to the one of the diffraction-limited PSF ( ${FWHM}_{\rm dl}$ ). All parameter combinations with a $\beta$ smaller than ${FWHM}_{\rm dl}$ (with except for combinations with $\alpha = 0$ ) produce unphysical PSFs with ${FWHM}_{\rm PSF} < {FWHM}_{\rm dl}$ . The cases are found left of the thick solid line, which marks ${FWHM}_{\rm PSF} = {FWHM}_{\rm dl}$ (in all panels).
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In the text

$\begin{figure} \par\includegraphics[width=15.5cm,clip]{09819fig7.eps} \end{figure}$	Figure 7: Goodness $\varepsilon$ of the fits between artificial and observed intensity profiles for a selected image of the Mercury transit at $\lambda = 555$ nm. The synthetic profiles are generated with non-ideal PSF that are calculated by convolution with a Voigt function. See Fig. 6 for a detailed explanation of the figure.
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