Stokes polarimeter performance: general noise model and analysis: erratum

Nathan Hagen; Tingkui Mu; Yukitoshi Otani

doi:10.1364/AO.57.006998

On page 4285 of the original paper [1], the unnumbered equation appearing immediately before the numbered Eq. (5) was given incorrectly. The covariance matrix should be diagonal, i.e.,

K_{IG} = (\begin{matrix} var ({\hat{s}}_{0}) & cov ({\hat{s}}_{0}, {\hat{s}}_{1}) & cov ({\hat{s}}_{0}, {\hat{s}}_{2}) \\ cov ({\hat{s}}_{1}, {\hat{s}}_{0}) & var ({\hat{s}}_{1}) & cov ({\hat{s}}_{1}, {\hat{s}}_{2}) \\ cov ({\hat{s}}_{2}, {\hat{s}}_{0}) & cov ({\hat{s}}_{2}, {\hat{s}}_{1}) & var ({\hat{s}}_{2}) \end{matrix}) = \frac{v_{d}}{ε^{2}} (\begin{matrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{matrix}) .

In addition, for Sabatke’s RRFP, the covariance matrix in the PP noise limit given in Section 4.B (page 4289) of the original paper is not correct. Two terms are missing from the diagonal, so that the result should be

K_{PP} = \frac{s_{0}}{2 ε} (\begin{matrix} 1 & {\tilde{s}}_{1} & {\tilde{s}}_{2} & {\tilde{s}}_{3} \\ {\tilde{s}}_{1} & 3 & {\tilde{s}}_{2} - \sqrt{2} {\tilde{s}}_{3} & - \sqrt{2} {\tilde{s}}_{2} - {\tilde{s}}_{3} \\ {\tilde{s}}_{2} & {\tilde{s}}_{2} - \sqrt{2} {\tilde{s}}_{3} & 3 + {\tilde{s}}_{1} & - \sqrt{2} {\tilde{s}}_{1} \\ {\tilde{s}}_{3} & - \sqrt{2} {\tilde{s}}_{2} & - \sqrt{2} {\tilde{s}}_{1} & 3 - {\tilde{s}}_{1} \end{matrix}) .

This change affects one of the assertions given in the Conclusion, where it is stated that “Any system optimized under IG noise will be “equivariant” under PP noise.” The corrected form of the matrix is obviously not equivariant. Likewise, the covariance matrices for Tyo’s DVRFP and Zallat’s DRRFP polarimeter (Tables 9 and 10 on page 4294) demonstrate that these systems will not be equivariant as well. Thus, this assertion is incorrect.

The remainder of the paper is unaffected, and these changes do not affect the code provided with the paper for calculating the covariance matrices.

REFERENCE

1. N. Hagen and Y. Otani, “Stokes polarimeter performance: general noise model and analysis,” Appl. Opt. 57, 4283–4296 (2018). [CrossRef]

Stokes polarimeter performance: general noise model and analysis: erratum

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Applied Optics