...$r_{\max}=2$

Considering an emission model with a given emissivity $N_{\rm F}$, the number of observed counts N is expected to fluctuate like the standard deviation of the Poisson parameter $N_{\rm F}$: $\sigma_{N_{\rm F}} = \sqrt{N_{\rm F}}$, so that the $r = \frac{{\rm N}}{N_{\rm F}}$ values are expected to fluctuate like $\sigma_{r} = \frac{\sqrt{N_{\rm F}}}{N_{\rm F}}\cdot$ Consequently the expected rvalues can be bounded within the $[-\Delta_r, +\Delta_r]$ interval, provided that $\Delta_r > \sigma_{r}$. The $\Delta_r$ value of 1, corresponding to $\sigma_{r}$ for one photon per pixel was chosen. Indeed, $\sigma_{r}$ decreases with increasing statistics, - for instance $\sigma_{r} = 0.32$ for $N_{\rm F}= 10$ -, so that we always get $\sigma_{r} < \Delta_r$.

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...$N_{\rm F} {\rm F} \left(T,e,\frac{a}{2},k,l\right)$

The scale parameter a has now been added because $N_{\rm F} {\rm F} \left(T,e,\frac{a}{2},k,l\right)$ is in fact the weighted mean of emission models corresponding to each event found within the square bin of edge a.

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...${\rm W}^{(0)}_{\widehat{{\rm T}}^{k,l}}(a,k,l)$

The p index is hereafter omitted because the following processes do not depend on the orientation of the coefficients.

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