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This article [ Opt. Eng. 33(12), 4055–4059 (1994) 10.1117/12.183402 ] was published in December 1994. We correct two mathematical expressions. In the original paper, a negative sign is missing in Eq. (6). The correct expression is Eq. 1[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{equation} \hat \xi = \hat \eta \times \hat \zeta = - \frac{{\hat R_n \times ( {\hat R_n \times \hat R_{n + 1} } )}}{{| {\hat R_n \times \hat R_{n + 1} } |}}. \end{equation}\end{document}The same mistake appears in Eq. (16). The correct expression is Eq. 2[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{eqnarray} I_n &=& 2\arctan \left[ {\frac{{\displaystyle\frac{{\hat q \cdot ( {\hat R_n \times \hat R_{n + 1} } )}}{{| {\hat R_n \times \hat R_{n + 1} } |}}\left( {\frac{{1 - \hat R_n \cdot \hat R_{n + 1} }}{{1 + \hat R_n \cdot \hat R_{n + 1} }}} \right)^{1/2} }}{{1 - \hat q \cdot \hat R_n + \displaystyle\frac{{\hat q \cdot [ {\hat R_n \times ( {\hat R_n \times \hat R_{n + 1} } )} ]}}{{| {\hat R_n \times \hat R_{n + 1} } |}}\left( {\displaystyle\frac{{1 - \hat R_n \cdot \hat R_{n {+} 1} }}{{1 {+} \hat R_n \cdot \hat R_{n + 1} }}} \right)^{1/2} }}} \right]. \end{eqnarray}\end{document}All the results presented in the original paper are correct. In numerical implementations1 1 the atan2 function should be used for the arctangent. |
Solids
Optical engineering
Antennas
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