Table 4: Parametersa of the convolved non-ideal PSFs that produce the best fit of the intensity profiles across the Mercury disc and the total eclipse.
$\lambda$ 450.45 nm 555.00 nm 668.40 nm 450.45 nm 555.00 nm 668.40 nm
  Mercury transit Eclipse

Convolution with Voigt function: best fit b
$\gamma_{\rm opt}$ $4 \ (4 \pm 2)$ $5 \ (6 \pm 2)$ $6 \ (6 \pm 2)$ $5 \ (5 \pm 2)$ $ 5 \ (4 \pm 2)$ $ 4 \ (4 \pm 1)$
$\sigma_{\rm opt}$ $8 \ (8 \pm 5)$ $ 8 \ (8 \pm 4)$ $8 \ (8 \pm 5)$ $7 \ (7 \pm 5)$ $ 7 \ (7 \pm 3)$ $ 7 \ (7 \pm 3)$
$I_{\rm o}$ $ 0.3 \ (0.5 \pm 0.4)$ $0.4 \ (0.3 \pm 0.3) $ $0.4 \ (0.4 \pm 0.3)$ $ 0.1 \ (0.2 \pm 0.2)$ $2.5 \ (2.7 \pm 0.4) $ $3.0 \ (3.2 \pm 0.3)$
b $ 0.8 \ (0.8 \pm 0.2) $ $ 1.4 \ (1.4 \pm 0.1) $ $ 1.3 \ (1.3 \pm 0.1)$ $ 0.9 \ (0.8 \pm 0.2) $ $ 0.9 \ (0.8 \pm 0.3) $ $ 0.8 \ (0.7 \pm 0.2)$
S $ 0.84 \ (0.84 \pm 0.03)$ $0.78 \ (0.78 \pm 0.01)$ $0.78 \ (0.78 \pm 0.01)$ $ 0.83 \ (0.84 \pm 0.02)$ $0.84 \ (0.86 \pm 0.04)$ $0.85 \ (0.87 \pm 0.03)$

Linear regression of MET below the ``knee'' c
$\Delta\sigma/\Delta\gamma$ ${-}2.672 \pm 0.218 $ ${-}2.228 \pm 0.164 $ ${-}2.277 \pm 0.148$ ${-}2.587 \pm 0.309 $ ${-}2.528 \pm 0.237 $ ${-}2.619 \pm 0.097$
$\sigma_C$ $ 18.2 \pm 1.6 $ $ 20.4 \pm 1.7 $ $ 21.0 \pm 1.5$ $ 18.7 \pm 0.9 $ $ 17.7 \pm 3.2 $ $ 17.8 \pm 2.1$
b $ 0.8 \pm 0.2 $ $1.4 \pm 0.3 $ $1.2 \pm 0.2$ $ 0.9 \pm 0.2 $ $0.9 \pm 0.3 $ $ 0.8 \pm 0.2 $
S $ 0.85 \pm 0.03 $ $0.78 \pm 0.03 $ $0.79 \pm 0.03$ $ 0.84 \pm 0.03 $ $0.86 \pm 0.04 $ $0.86 \pm 0.03$

Convolution with Voigt function: at MET ``knee'' d
$\gamma $ $ 3 \pm 1 $ $ 4 \pm 1 $ $ 4 \pm 1 $ $ 3 \pm 1 $ $ 3 \pm 1 $ $ 3 \pm 1 $
$\sigma $ $ 13 \pm 2 $ $ 12 \pm 1 $ $ 12 \pm 1 $ $ 14 \pm 2 $ $ 12 \pm 2 $ $ 13 \pm 5 $
$I_{\rm o}$ $ 0.4 \pm 0.3 $ $ 0.4 \pm 0.6 $ $ 0.4 \pm 0.3 $ $ 0.1 \pm 0.2 $ $ 2.5 \pm 0.4 $ $ 3.0 \pm 0.4 $
b $ 0.9 \pm 0.2 $ $1.5 \pm 0.2$ $ 1.4 \pm 0.2 $ $ 1.0 \pm 0.1 $ $ 1.1 \pm 0.5 $ $ 0.9 \pm 0.2 $
S $ 0.84 \pm 0.02$ $0.78 \pm 0.01$ $0.78 \pm 0.02$ $0.83 \pm 0.02$ $0.84 \pm 0.05$ $0.85 \pm 0.04$

Convolution with Lorentzian ( $\sigma = 0$) d
$\gamma $ $ 7 \pm 1 $ $ 9 \pm 1 $ $ 9 \pm 1 $ $ 8 \pm 1 $ $ 7 \pm 1 $ $ 7 \pm 1 $
$I_{\rm o}$ $ 0.8 \pm 0.7 $ $ 0.6 \pm 0.3 $ $ 0.9 \pm 0.5$ $ 0.1 \pm 0.2 $ $ 2.7 \pm 0.4 $ $ 3.2 \pm 0.4$
b $ 0.7 \pm 0.1 $ $ 1.3 \pm 0.1 $ $ 1.2 \pm 0.1$ $ 0.8 \pm 0.1 $ $ 0.8 \pm 0.3 $ $ 0.7 \pm 0.2$
S $0.86 \pm 0.02$ $0.79 \pm 0.02$ $0.79 \pm 0.02$ $ 0.84 \pm 0.02$ $0.86 \pm 0.04 $ $0.87 \pm 0.03$
a $\gamma $ and $\sigma $ in units of 10-3  $^{\prime \prime }$, intensity offset $I_{\rm o}$ in %, broadening factor b of the FWHM with respect to the ideal PSF in %, and the Strehl ratio S. b The values in parentheses are the arithmetic averages over the best fits for the individual observational profiles for each case. Please note that the errors in $\gamma $ and $\sigma $ are not independent (refer to the text for more details). The value in front of the parentheses is the $\varepsilon $-weighted mean value projected onto the mean MET. c The MET below the ``knee'' is approximated by $\sigma_{\rm MET,b} = \sigma_C + (\Delta\sigma/\Delta\gamma) \cdot \gamma$. The positions of the individual METs have a rms variation of $\delta\gamma \sim 0~\hbox{$.\!\!^{\prime\prime}$ }001$ and $\delta\sigma \sim 0~\hbox{$.\!\!^{\prime\prime}$ }002$- $0~\hbox{$.\!\!^{\prime\prime}$ }003$, which is of the order of the grid increment. Only the METs for the eclipse at 555 nm show a larger variation with $\delta\gamma \sim 0~\hbox{$.\!\!^{\prime\prime}$ }002$ and $\delta\sigma \sim 0~\hbox{$.\!\!^{\prime\prime}$ }005$. d The range of reasonable PSFs is limited by the position just at the ``knee'' of the mean MET and on the other side by a convolution with a pure Lorentzian ( $\sigma = 0$).

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