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} $$\widehat{\xi}=\widehat{\eta}\times \widehat{\zeta}=-\frac{{\widehat{R}}_{n}\times \left({\widehat{R}}_{n}\times {\widehat{R}}_{n+1}\right)}{|{\widehat{R}}_{n}\times {\widehat{R}}_{n+1}|}.$$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} $$\begin{array}{ccc}\hfill {I}_{n}& =& 2\mathrm{arctan}\left[\frac{{\displaystyle \frac{\widehat{q}\xb7\left({\widehat{R}}_{n}\times {\widehat{R}}_{n+1}\right)}{|{\widehat{R}}_{n}\times {\widehat{R}}_{n+1}|}{\left(\frac{1-{\widehat{R}}_{n}\xb7{\widehat{R}}_{n+1}}{1+{\widehat{R}}_{n}\xb7{\widehat{R}}_{n+1}}\right)}^{1/2}}}{{\displaystyle 1-\widehat{q}\xb7{\widehat{R}}_{n}+\frac{\widehat{q}\xb7\left[{\widehat{R}}_{n}\times \left({\widehat{R}}_{n}\times {\widehat{R}}_{n+1}\right)\right]}{|{\widehat{R}}_{n}\times {\widehat{R}}_{n+1}|}{\left({\displaystyle \frac{1-{\widehat{R}}_{n}\xb7{\widehat{R}}_{n+1}}{1+{\widehat{R}}_{n}\xb7{\widehat{R}}_{n+1}}}\right)}^{1/2}}}\right].\hfill \end{array}$$All the results presented in the original paper are correct. In numerical implementations^{1}
^{1} the atan2 function should be used for the arctangent.