In our recently published article [J. Opt. Soc. Am. A 33, 9 (2016) [CrossRef] ], there was an error of reasoning that changes some of the results and conclusions, although the key message of the article remains unaltered. We correct these errors in the present erratum.
© 2016 Optical Society of America
We first mention a typo (error of sign in the expression of ) in Eq. (A2). The correct version is1], we claim that the solution of the minimax optimization problem expressed in Eq. (32) is given by Eq. (33). In fact, this is true only when . If this is not the case, the expression of the minimax contrast is different. This makes Eqs. (34), (35), (38), and (39) wrong, as well as the third and fourth rows of Table 1 and, in Fig. 1, the four red curves corresponding to and . The other results are correct, especially the experimental demonstration of Figs. 2–4, which was performed in a situation where .
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. , representing the contrast in the presence of type 1 and type 2 noise sources, are1], representing the contrast obtained when only the optimal channel is observed with the exposure time , are 1, we display the correct version of Table 1 in Ref. . Only the two last rows have changed. Please note that Table 2 of Ref.  is correct since it deals with the case .
In Fig. 1, we have plotted the correct versions of the curves in Fig. 1 of Ref. , which represent the square roots of the contrasts in different imaging configurations as a function of . Only the red curves, corresponding to and , have changed. Please note that since and , we are always in the case , so that the second line of Eq. (4) applies.
1. F. Goudail and M. Boffety, “Optimal configuration of static polarization imagers for target detection,” J. Opt. Soc. Am. A 33, 9–16 (2016). [CrossRef]