Abstract

A membrane mirror assembly is described that has a membrane deflected by a region of electrostatic actuators, consisting of conducting pads. The procedure for fabrication of typical membranes is described and involves evaporation of the material onto a substrate in a vacuum chamber. Parametric equations, developed from basic vibration theory, are given for establishing transient and steady-state performance criteria. Experimental data, using both titanium and nickel test membranes, shows that the performance satisfies the predicted requirements.

© 1977 Optical Society of America

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References

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  1. M. Yellin, “Using membrane mirrors in adaptive optics,” SPIE Proc. 75, 97 (1976).
    [Crossref]
  2. P. M. Morse, Vibration and Sound, 2nd ed. (McGraw-Hill, New York, 1948).
  3. R. J. Noll, “Dynamic Atmospheric Turbulence Corrections,” SPIE Proc. 75, 39 (1976).
    [Crossref]
  4. P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), p. 194.
  5. M. J. E. Golay (private correspondence).

1976 (2)

M. Yellin, “Using membrane mirrors in adaptive optics,” SPIE Proc. 75, 97 (1976).
[Crossref]

R. J. Noll, “Dynamic Atmospheric Turbulence Corrections,” SPIE Proc. 75, 39 (1976).
[Crossref]

Golay, M. J. E.

M. J. E. Golay (private correspondence).

Ingard, K. U.

P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), p. 194.

Morse, P. M.

P. M. Morse, Vibration and Sound, 2nd ed. (McGraw-Hill, New York, 1948).

P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), p. 194.

Noll, R. J.

R. J. Noll, “Dynamic Atmospheric Turbulence Corrections,” SPIE Proc. 75, 39 (1976).
[Crossref]

Yellin, M.

M. Yellin, “Using membrane mirrors in adaptive optics,” SPIE Proc. 75, 97 (1976).
[Crossref]

SPIE Proc. (2)

M. Yellin, “Using membrane mirrors in adaptive optics,” SPIE Proc. 75, 97 (1976).
[Crossref]

R. J. Noll, “Dynamic Atmospheric Turbulence Corrections,” SPIE Proc. 75, 39 (1976).
[Crossref]

Other (3)

P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), p. 194.

M. J. E. Golay (private correspondence).

P. M. Morse, Vibration and Sound, 2nd ed. (McGraw-Hill, New York, 1948).

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Figures (13)

FIG. 1
FIG. 1

Membrane actuator drive schematic.

FIG. 2
FIG. 2

Wave-front corrector.

FIG. 3
FIG. 3

Membrane mirror assembly.

FIG. 4
FIG. 4

Titanium membrane facility.

FIG. 5
FIG. 5

Membrane damping mechanism.

FIG. 6
FIG. 6

Wave-front corrector assembly.

FIG. 7
FIG. 7

1 in. diameter region of 2 in. 0.6 μm titanium membrane.

FIG. 8
FIG. 8

Experimental setup.

FIG. 9
FIG. 9

Static deflection system.

FIG. 10
FIG. 10

Fundamental frequency vs time.

FIG. 11
FIG. 11

Fundamental frequency vs pressure.

FIG. 12
FIG. 12

l computation for screen and pad array.

FIG. 13
FIG. 13

Integrated ac. Response for a 1 2 μ m nickel membrane vs pressure (time scale 500 μs/unit).

Tables (2)

Tables Icon

TABLE I Breadboard specifications.

Tables Icon

TABLE II Harmonic ratio for titanium membrane.

Equations (16)

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2 Z t 2 = T σ 2 Z ,
2 Z t 2 = T σ 2 Z + F ( r , t ) σ ,
2 Z = - ( F / T ) ( r , t ) .
W ( k , f ) k - 11 / 13 0 C N 2 ( h ) δ ( k ν h - f ) d h ,
Z ( r ) = F 2 π T [ l n R S + 1 2 S 2 ( S 2 - r 2 ) ] ,             0 < r < S = F 2 π T [ l n R r ] ,             S < r R
P = F A = 0 2 [ V p 2 l p 2 - V s 2 l s 2 ]
F = 0 π r p 2 [ V p 2 l p 2 - V s 2 l s 2 ] ,
Z ( r ) = 0 4 T [ V p 2 l p 2 - V s 2 l s 2 ] ( S 2 - r 2 ) .
Z ( r ) = 0 S 2 4 T [ V p 2 l s 2 - V s 2 l s 2 ] .
V p = V s + Δ V , Δ V max = 0.5 V s .
Z ( r ) max 0 S 2 4 T l 2 ( 1.25 V s 2 ) .
ν 0 n = ( γ 0 n 2 a ) T / σ ,
ν m n = β m n 2 a ( T σ ) 1 / 2 ,
χ = π 0 C a a 4 / V 0 T ,
ν 0 n ν 0 ( 1 + C 0 P / T l ) ,
ν 0 = β 00 2 a ( T σ ) 1 / 2 = 2.4 π D ( T σ ) 1 / 2 ,