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References

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  1. P. Connes, G. Michel, Appl. Opt. 14, 2067 (1975).
    [CrossRef] [PubMed]
  2. E. Bin-Nun, F. Dothan-Deutsch, Rev. Sci. Instrum. 44, 512 (1973).
    [CrossRef]
  3. S. Mikoshiba, B. Ahlborn, Rev. Sci. Instrum. 44, 508 (1973).
    [CrossRef]
  4. G. Lemaitre, C. R. Acad. Sci. Ser. B 282, 87 (1976).
  5. J. H. McElroy, P. E. Thompson, H. E. Walker, E. H. Johnson, D. J. Radecki, R. S. Reynolds, Appl. Opt. 14, 1297 (1975).
    [CrossRef] [PubMed]
  6. Y. Stavsky, N. J. Hoff, in Composite Engineering Laminates, A. G. H. Dietz, Ed. (MIT Press, Cambridge, 1969), Chap. 1.
  7. A. H. Meitzler, H. M. O’Bryan, H. F. Tiersten, IEEE Trans. Son. Ultrason. SU-20, 233 (1973).
    [CrossRef]

1976 (1)

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

1975 (2)

1973 (3)

E. Bin-Nun, F. Dothan-Deutsch, Rev. Sci. Instrum. 44, 512 (1973).
[CrossRef]

S. Mikoshiba, B. Ahlborn, Rev. Sci. Instrum. 44, 508 (1973).
[CrossRef]

A. H. Meitzler, H. M. O’Bryan, H. F. Tiersten, IEEE Trans. Son. Ultrason. SU-20, 233 (1973).
[CrossRef]

Ahlborn, B.

S. Mikoshiba, B. Ahlborn, Rev. Sci. Instrum. 44, 508 (1973).
[CrossRef]

Bin-Nun, E.

E. Bin-Nun, F. Dothan-Deutsch, Rev. Sci. Instrum. 44, 512 (1973).
[CrossRef]

Connes, P.

Dothan-Deutsch, F.

E. Bin-Nun, F. Dothan-Deutsch, Rev. Sci. Instrum. 44, 512 (1973).
[CrossRef]

Hoff, N. J.

Y. Stavsky, N. J. Hoff, in Composite Engineering Laminates, A. G. H. Dietz, Ed. (MIT Press, Cambridge, 1969), Chap. 1.

Johnson, E. H.

Lemaitre, G.

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

McElroy, J. H.

Meitzler, A. H.

A. H. Meitzler, H. M. O’Bryan, H. F. Tiersten, IEEE Trans. Son. Ultrason. SU-20, 233 (1973).
[CrossRef]

Michel, G.

Mikoshiba, S.

S. Mikoshiba, B. Ahlborn, Rev. Sci. Instrum. 44, 508 (1973).
[CrossRef]

O’Bryan, H. M.

A. H. Meitzler, H. M. O’Bryan, H. F. Tiersten, IEEE Trans. Son. Ultrason. SU-20, 233 (1973).
[CrossRef]

Radecki, D. J.

Reynolds, R. S.

Stavsky, Y.

Y. Stavsky, N. J. Hoff, in Composite Engineering Laminates, A. G. H. Dietz, Ed. (MIT Press, Cambridge, 1969), Chap. 1.

Thompson, P. E.

Tiersten, H. F.

A. H. Meitzler, H. M. O’Bryan, H. F. Tiersten, IEEE Trans. Son. Ultrason. SU-20, 233 (1973).
[CrossRef]

Walker, H. E.

Appl. Opt. (2)

C. R. Acad. Sci. Ser. B (1)

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

IEEE Trans. Son. Ultrason. (1)

A. H. Meitzler, H. M. O’Bryan, H. F. Tiersten, IEEE Trans. Son. Ultrason. SU-20, 233 (1973).
[CrossRef]

Rev. Sci. Instrum. (2)

E. Bin-Nun, F. Dothan-Deutsch, Rev. Sci. Instrum. 44, 512 (1973).
[CrossRef]

S. Mikoshiba, B. Ahlborn, Rev. Sci. Instrum. 44, 508 (1973).
[CrossRef]

Other (1)

Y. Stavsky, N. J. Hoff, in Composite Engineering Laminates, A. G. H. Dietz, Ed. (MIT Press, Cambridge, 1969), Chap. 1.

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Figures (2)

Fig. 1
Fig. 1

Cross section of piezoelectrically activated deformable mirror.

Fig. 2
Fig. 2

Curvature of mirror as a function of geometry and material properties.

Tables (1)

Tables Icon

Table I Selected Physical Properties of PZT-5H and Fused Silica

Equations (18)

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T r r , r + ( T r r - T θ θ ) / r = 0 ,
T r r = c ¯ 11 u r , r + c ¯ 12 u r / r + e ¯ 31 V / h 1 ,
T θ θ = c ¯ 12 u r , r + c ¯ 11 u r / r + e ¯ 31 V / h 1 ,
u r ( r , z ) = u r o ( r ) - z u z o ( r ) ,
u z ( r , z ) = u z o ( r ) ,
( N r , N θ ) = 0 h ( T r r , T θ θ ) d z ,
( M r , M θ ) = 0 h ( T r r , T θ θ ) z d z ,
( A i j , B i j , D i j ) = 0 h c ¯ i j ( 1 , z , z 2 ) d z             ( i , j = 1 , 2 ) ,
( E 1 , E 2 ) = 0 h e ¯ 31 ( 1 , z ) d z ,
N r + ( N r - N θ ) / r = 0 ,
M r + ( M r - M θ ) / r = 0 ,
( N r N θ M r M θ ) = ( A 11 A 12 B 11 B 12 A 12 A 11 B 12 B 11 B 11 B 12 D 11 D 12 B 12 B 11 D 12 D 11 ) × ( u r o u r o / r - u z o - u z o / r ) + ( E 1 E 1 E 2 E 2 ) V h 1 .
u r o = H 1 r ,
u z o = H 2 r 2 + H 3 .
u z o ( 0 ) = N r ( a ) = M r ( a ) = 0.
κ - d 2 u z o d r 2 = [ E 1 ( B 11 + B 12 ) - E 2 ( A 11 + A 12 ) ] V h 1 [ ( A 11 + A 12 ) ( D 11 + D 12 ) - ( B 11 + B 12 ) 2 ] ,
d 31 = e ¯ 31 / ( c ¯ 11 + c ¯ 12 ) ,
κ 10 - 3 V ( m - V ) - 1 .

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