## Abstract

Communications are short papers. Appropriate material for this section includes reports of incidental research results, comments on papers previously published, and short descriptions of theoretical and experimental techniques. Communications are handled much the same as regular papers. Proofs are provided.

The rotational properties of Zernike polynomials allow for an easy generation of variable amounts of aberration using two rotated phase plates, each one encoding one or several Zernike modes. This effect may be used to build variable aberration generators useful for calibrating different kinds of aberrometer.

© 2005 Optical Society of America

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### Equations (5)

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(1)
$$\left(\begin{array}{c}{\widehat{a}}_{n}^{m}\\ {\widehat{a}}_{n}^{-m}\end{array}\right)=R\left(m\alpha \right)\left(\begin{array}{c}{a}_{n}^{m}\\ {a}_{n}^{-m}\end{array}\right)=\left[\begin{array}{cc}\mathrm{cos}\left(m\alpha \right)& \mathrm{sin}\left(m\alpha \right)\\ -\mathrm{sin}\left(m\alpha \right)& \mathrm{cos}\left(m\alpha \right)\end{array}\right]\left(\begin{array}{c}{a}_{n}^{m}\\ {a}_{n}^{-m}\end{array}\right).$$
(2)
$$\left(\begin{array}{c}{\widehat{a}}^{+}\\ {\widehat{a}}^{-}\end{array}\right)=R\left(m\alpha \right)\left(\begin{array}{c}{a}_{1}^{+}\\ {a}_{1}^{-}\end{array}\right)+R(-m\alpha )\left(\begin{array}{c}{a}_{2}^{+}\\ {a}_{2}^{-}\end{array}\right)=\left(\begin{array}{c}[{a}_{1}^{+}+{a}_{2}^{+}]\mathrm{cos}\left(m\alpha \right)+[{a}_{1}^{-}-{a}_{2}^{-}]\mathrm{sin}\left(m\alpha \right)\\ -[{a}_{1}^{+}-{a}_{2}^{+}]\mathrm{sin}\left(m\alpha \right)+[{a}_{1}^{-}+{a}_{2}^{-}]\mathrm{cos}\left(m\alpha \right)\end{array}\right).$$
(3)
$$\left(\begin{array}{c}{\widehat{a}}^{+}\\ {\widehat{a}}^{-}\end{array}\right)=\left(\begin{array}{c}[{a}_{1}^{+}+{a}_{2}^{+}]\mathrm{cos}\left(m\alpha \right)\\ -[{a}_{1}^{+}-{a}_{2}^{+}]\mathrm{sin}\left(m\alpha \right)\end{array}\right).$$
(4)
$$\left(\begin{array}{c}{\widehat{a}}^{+}\\ {\widehat{a}}^{-}\end{array}\right)=\left(\begin{array}{c}2\phantom{\rule{0.3em}{0ex}}{a}^{+}\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\left(m\alpha \right)\\ 0\end{array}\right),$$
(5)
$$\left(\begin{array}{c}{\widehat{a}}^{+}\\ {\widehat{a}}^{-}\end{array}\right)=\left(\begin{array}{c}0\\ 2\phantom{\rule{0.3em}{0ex}}{a}^{+}\phantom{\rule{0.2em}{0ex}}\mathrm{sin}\left(m\alpha \right)\end{array}\right).$$