Neural network gradient-index mapping: erratum

Hiroshi Ohno; Takashi Usui

doi:10.1364/OPTCON.458411

Abstract

This erratum corrects a typographical error in Eq. (13) of our paper [OSA Continuum 4, 2543 (2021) [CrossRef] ].

Erratum

In this erratum we correct a typographical error in Eq. (13) of our recently published paper [1], in which the position of the equal sign is wrong. The correct equation should be:

\frac{{d({n{\boldsymbol u}} )}}{{dz}} = \frac{1}{{\sqrt {1 - {u^2}} }}\left( {\frac{{{u_x}\partial ({n{\boldsymbol u}} )}}{{\partial x}} + \frac{{{u_y}\partial ({n{\boldsymbol u}} )}}{{\partial y}} + \frac{{\sqrt {1 - {u^2}} \partial ({n{\boldsymbol u}} )}}{{\partial z}}} \right) = \frac{1}{{\sqrt {1 - {u^2}} }}\frac{{\partial n}}{{\partial {\boldsymbol q}}}.

We note that all results and figures through the manuscript were obtained using the correct equation and are therefore unaffected by this correction and remain valid.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

References

1. H. Ohno and T. Usui, “Neural network gradient-index mapping,” OSA Continuum 4(10), 2543–2551 (2021). [CrossRef]

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Equations (1)

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\frac{d (n u)}{d z} = \frac{1}{\sqrt{1 - u^{2}}} (\frac{u_{x} \partial (n u)}{\partial x} + \frac{u_{y} \partial (n u)}{\partial y} + \frac{\sqrt{1 - u^{2}} \partial (n u)}{\partial z}) = \frac{1}{\sqrt{1 - u^{2}}} \frac{\partial n}{\partial q} .