Abstract

Variable curvature mirrors of large amplitude are designed by using finite element analysis. The specific case studied reaches at least a 800 μm sag with an optical quality better than λ5 over a 120 mm clear aperture. We highlight the geometrical nonlinearity and the plasticity effect.

© 2009 Optical Society of America

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References

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  1. G. R. Lemaitre, C. R. Acad. Sci. Paris Ser. B 282, 87 (1976).
  2. M. Ferrari, Astron. Astrophys. Suppl. Ser. 128, 221 (1998).
    [CrossRef]
  3. S. P. Timoshenko and S. Woinovsky-Krieger, Theory of Plates and Shells (McGraw-Hill. 1959).
  4. G. R. Lemaitre, Astronomical Optics and Elasticity Theory (Springer2009), Chap. 2.
  5. O. Pichler, Ph.D. dissertation (1928).
  6. Marc/Mentat, MSC Software Corporation.

1998

M. Ferrari, Astron. Astrophys. Suppl. Ser. 128, 221 (1998).
[CrossRef]

1976

G. R. Lemaitre, C. R. Acad. Sci. Paris Ser. B 282, 87 (1976).

Ferrari, M.

M. Ferrari, Astron. Astrophys. Suppl. Ser. 128, 221 (1998).
[CrossRef]

Lemaitre, G. R.

G. R. Lemaitre, C. R. Acad. Sci. Paris Ser. B 282, 87 (1976).

G. R. Lemaitre, Astronomical Optics and Elasticity Theory (Springer2009), Chap. 2.

Pichler, O.

O. Pichler, Ph.D. dissertation (1928).

Timoshenko, S. P.

S. P. Timoshenko and S. Woinovsky-Krieger, Theory of Plates and Shells (McGraw-Hill. 1959).

Woinovsky-Krieger, S.

S. P. Timoshenko and S. Woinovsky-Krieger, Theory of Plates and Shells (McGraw-Hill. 1959).

Astron. Astrophys. Suppl. Ser.

M. Ferrari, Astron. Astrophys. Suppl. Ser. 128, 221 (1998).
[CrossRef]

C. R. Acad. Sci. Paris Ser. B

G. R. Lemaitre, C. R. Acad. Sci. Paris Ser. B 282, 87 (1976).

Other

S. P. Timoshenko and S. Woinovsky-Krieger, Theory of Plates and Shells (McGraw-Hill. 1959).

G. R. Lemaitre, Astronomical Optics and Elasticity Theory (Springer2009), Chap. 2.

O. Pichler, Ph.D. dissertation (1928).

Marc/Mentat, MSC Software Corporation.

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Figures (4)

Fig. 1
Fig. 1

VCM profile and zoom on the thin collar.

Fig. 2
Fig. 2

The vertex displacement curve shows that a geometrical nonlinearity appears when the sag is equal to 1 10 of the central thickness.

Fig. 3
Fig. 3

Modification of the VTD allows compensating for the nonlinear behavior. This modification is obtained by a finite element optimization.

Fig. 4
Fig. 4

Plot of RMS residual versus the sag on the clear aperture. Plain curve, no plasticity; dotted curve, before plastic deformation; dashed curve, after plastic deformation.

Tables (1)

Tables Icon

Table 1 Deflection Amplitude and RMS Residual with Respect to a Sphere for Cases without Plasticity and before and after Plastic Deformation

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

w max = ( 5 + ν ) q max a 4 64 ( 1 + ν ) D , D = E t 0 3 12 ( 1 ν 2 ) .
a 2 [ ( 1 + ν ) ( 5 + ν ) ( 1 ν 2 ) 9 E q max ] 1 4 × w max .
w max = 1.2 ( 1 ν 2 ) a 4 q max E t 0 3 .
a [ 27 E 1.2 ( 1 ν 2 ) q max ] 1 4 × w max .

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