## Abstract

Simply by push-pull shear action at their outer edge, large circular telescope mirrors can be laterally supported free from bending distortion, if the upright mirror is kept in balance by a cosine distribution of weak axial forces applied at its outer rim and possibly also at the central hole. The flexure-induced comalike wave-front aberration of a thin 8-m meniscus mirror was reduced to an rms value of 0.5 nm over the full aperture; the largest path difference was reduced to 2.4 nm. A comparable result has also been calculated for a meniscus mirror of different geometry and a material with different elastic constants. Realizing such possibilities in practice demands accurate engineering. A helpful artifice is investigated for the correct application of the tangential supporting forces.

© 1994 Optical Society of America

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### Equations (11)

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(1)
$${N}_{r}={P}_{r}\hspace{0.17em}\text{cos}\hspace{0.17em}\mathrm{\theta},$$
(2)
$${N}_{t}={P}_{t}\hspace{0.17em}\text{sin}\hspace{0.17em}\mathrm{\theta},$$
(3)
$${\int}_{0}^{2\mathrm{\pi}}{V}_{0}\hspace{0.17em}\text{cos}\hspace{0.17em}\mathrm{\theta}\times {R}_{0}\hspace{0.17em}\text{cos}\hspace{0.17em}\mathrm{\theta}\times {R}_{0}\text{d}\mathrm{\theta}=\mathrm{\pi}{{R}_{0}}^{2}{V}_{0}={\mathrm{\varepsilon}}_{0}Ga.$$
(4)
$${\mathrm{\varepsilon}}_{0}-\mathrm{\varepsilon}+\mathrm{\tau}-\mathrm{\zeta}=0.$$
(5)
$$\mathrm{\beta}=\frac{{P}_{t}}{{P}_{t}+{P}_{r}}.$$
(6)
$$M={N}_{t}b={P}_{t}b\hspace{0.17em}\text{sin}\hspace{0.17em}\mathrm{\theta}.$$
(7)
$${U}_{r}=-dM/ds=-(dM/d\mathrm{\theta})/R=-{P}_{t}b\hspace{0.17em}\text{cos}\hspace{0.17em}\mathrm{\theta}/R.$$
(8)
$${U}_{t}=Md\mathrm{\theta}/ds=M/R={P}_{t}b\hspace{0.17em}\text{sin}\hspace{0.17em}\mathrm{\theta}/R.$$
(9)
$${{P}_{r}}^{\prime}={P}_{r}+{P}_{t}b/R,$$
(10)
$${{P}_{t}}^{\prime}={P}_{t}(1-b/R).$$
(11)
$$\begin{array}{l}{\mathrm{\beta}}^{\prime}={{P}_{t}}^{\prime}/({{P}_{t}}^{\prime}+{{P}_{r}}^{\prime})={P}_{t}(1-b/R)/({P}_{t}+{P}_{r}),\\ {\mathrm{\beta}}^{\prime}=\mathrm{\beta}(1-b/R).\end{array}$$