We first mention a typo (error of sign in the expression of ${\mathbf{t}}_4$) in Eq. (A2). The correct version is

Table 1. Summary of the Contrast Values for Noises of Type 1 and Type 2 and Different Imaging Configurations: Adaptive Imager (ada), Total Contrast of the Static Imager (sta), Worst Contrast of the Best Channel of the Static Imager for Exposure Time $\tau ={\tau }_0/4$ (best1), and $\tau ={\tau }_0$ (best1, ${\tau }_0$)^a

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Fig. 1. Square root of the contrast as a function $\Vert \mathrm{\Delta }\mathbf{s}\Vert$ for the different imaging configurations in the presence of type 1 noise and type 2 noise. $\mathrm{\Delta }{S}_0=1$, ${(\eta {\tau }_0/\sigma )}^2=1$, and ${\eta }^2{\tau }_0/a=1$.

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We provide in this erratum the correct versions of these wrong equations and table. A formal demonstration of these results, as well as their physical interpretation and their practical consequences, will be submitted as a separate article.

The correct expressions of Eqs. (34) and (35) of Ref. [1], representing the contrast $C_{\text{sta}}^{\text{best}1}$ in the presence of type 1 and type 2 noise sources, are

In Fig. 1, we have plotted the correct versions of the curves in Fig. 1 of Ref. [1], which represent the square roots of the contrasts in different imaging configurations as a function of $\Vert \mathrm{\Delta }\mathbf{s}\Vert$. Only the red curves, corresponding to $C_{\text{sta}}^{\text{best}1}$ and $C_{\text{sta}}^{\text{best}1,{\tau }_0}$, have changed. Please note that since $\mathrm{\Delta }{S}_0=1$ and $\Vert \mathrm{\Delta }\mathbf{s}\Vert \in [0,3]$, we are always in the case $|\mathrm{\Delta }{S}_0|\ge \Vert \mathrm{\Delta }\mathbf{s}\Vert /3$, so that the second line of Eq. (4) applies.