Open Access
Add to BibSonomy
Abstract
Corrections are given for errors in the presentation of equations in J. Opt. Soc. Am. A 34, 1411 (2017) [CrossRef] .
© 2022 Optica Publishing Group
In [1], Eq. (2) had a typo and should read
$$\sigma _{e -}^2 = \eta {\mu _{e
-}}\left[{\frac{{{e^{hc/\lambda kT}}}}{{{e^{hc/\lambda kT}} - 1}}}
\right].$$
Additionally Eq. (19) is of the form $${F_{{\hat{\textbf p}}}}(\hat p)
= \int_0^\infty {f_{{\hat{\textbf y}}}}(\hat y){F_{{\hat{\textbf
x}}}}(\hat p + \hat y) {\rm{d}}\hat y,$$
which holds for all $\hat p \in {\mathbb
R}$ since ${F_{{\hat{\textbf x}}}}(t) =
0$ for all $t \le 0$. However, when substituting an explicit form
for ${F_{{\hat{\textbf
x}}}}$ one must take this into account so that
Eq. (19) should read
$${F_{{\hat{\textbf p}}}}(\hat p)
= \frac{{\beta _2^{{\alpha _2}}}}{{\Gamma ({\alpha _1})\Gamma ({\alpha
_2})}}\int_{\max \{0, - \hat p\}}^\infty {\hat y^{{\alpha _2} - 1}} {e^{-
{\beta _2}\hat y}} \gamma \!\left({{\alpha _1},{\beta _1}(\hat p + \hat
y)} \right) {\rm{d}}\hat y.$$
This
same error was also carried through to Eqs. (50) and (51), where the
maximizations need only be performed on the intervals $x \in [- \sigma _{\textbf{y}}^2,
\infty)$ and $x \in (- \infty , \sigma
_{\textbf{x}}^2]$, respectively.These errors do not affect any of the results or conclusions presented in the paper.
Acknowledgment
The author would like to thank Martina Hančová, Andrej Gajdoš, and Jozef Hanč from Pavol Jozef Šafárik University in Košice for taking the time to highlight the errors in the presentation of these equations.
REFERENCE
1. A. J. Hendrickson, “Centralized inverse-Fano distribution for controlling conversion gain measurement accuracy of detector elements,” J. Opt. Soc. Am. A 34, 1411–1423 (2017). [CrossRef]