Abstract

We describe what we call the dioptric elasticity method of making Schmidt plates. An oversize disk is supported on a narrow metal ring. Within this ring, the air underneath is partially evacuated; a primary vacuum is formed under the outer annulus. The elastically deformed disk is worked flat. When the loads are removed, the disk takes on an excellent, smooth Kerber profile over the region interior to the supporting ring. This produces more highly aspherical surfaces (F/1) and is more convenient than the method attempted by Schmidt. We give the elasticity theory, discuss our shop methods, and show the very satisfactory results.

© 1972 Optical Society of America

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References

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  1. C. G. Wynne, J. Opt. Soc. Am. 59, 572 (1969).
    [CrossRef]
  2. J. G. Baker, J. Am. Philos. Soc. 82, 339 (1940).
  3. C. R. Burch, Monthly Notices Roy. Astron. Soc. 102, 159 (1942).
  4. D. R. Montgomery, L. A. Adams, Appl. Opt. 9, 277 (1970).
    [CrossRef] [PubMed]
  5. G. Courtes, in New Techniques in Space Astronomy, F. Labuhn, R. Lüst, Eds. (International Union of Astronomy, Paris, 1971).
  6. American Patent969,785 (1910).
  7. B. Schmidt, Mitt. Hamburger Sternv. 7, 15 (1932).
  8. A. Kerber, Central Zeit, f. Opt. und Mech. p. 157 (1886).
  9. H. Chrétien, Calcul des combinaisons optiquesJ. & R. Sennac, Eds. (1959) p. 349.
  10. G. Lemaître, D. E. A., Fac. Sc. Marseille (unpublished) (1968); Compt. Rend. t. 270A, 226 (1970).
  11. G. Lemaître, ESO Bull. No. 8, 21 (1971).
  12. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1963).
  13. French Patent, ANVAR 70,19,261 (1969).
  14. S. C. B. Gascoigne, The Observatory 85, 79 (1965).
  15. D. H. Schulte, Appl. Opt. 5, 309 (1966).
    [CrossRef] [PubMed]
  16. A. Pourcelot, Compt. Rend. t. 262B, 982 (1966).
  17. H. Köhler, ESO Bull. No. 2, 13 (1967).

1971

G. Lemaître, ESO Bull. No. 8, 21 (1971).

1970

1969

1967

H. Köhler, ESO Bull. No. 2, 13 (1967).

1966

D. H. Schulte, Appl. Opt. 5, 309 (1966).
[CrossRef] [PubMed]

A. Pourcelot, Compt. Rend. t. 262B, 982 (1966).

1965

S. C. B. Gascoigne, The Observatory 85, 79 (1965).

1942

C. R. Burch, Monthly Notices Roy. Astron. Soc. 102, 159 (1942).

1940

J. G. Baker, J. Am. Philos. Soc. 82, 339 (1940).

1932

B. Schmidt, Mitt. Hamburger Sternv. 7, 15 (1932).

Adams, L. A.

Baker, J. G.

J. G. Baker, J. Am. Philos. Soc. 82, 339 (1940).

Burch, C. R.

C. R. Burch, Monthly Notices Roy. Astron. Soc. 102, 159 (1942).

Chrétien, H.

H. Chrétien, Calcul des combinaisons optiquesJ. & R. Sennac, Eds. (1959) p. 349.

Courtes, G.

G. Courtes, in New Techniques in Space Astronomy, F. Labuhn, R. Lüst, Eds. (International Union of Astronomy, Paris, 1971).

Gascoigne, S. C. B.

S. C. B. Gascoigne, The Observatory 85, 79 (1965).

Kerber, A.

A. Kerber, Central Zeit, f. Opt. und Mech. p. 157 (1886).

Köhler, H.

H. Köhler, ESO Bull. No. 2, 13 (1967).

Lemaître, G.

G. Lemaître, ESO Bull. No. 8, 21 (1971).

G. Lemaître, D. E. A., Fac. Sc. Marseille (unpublished) (1968); Compt. Rend. t. 270A, 226 (1970).

Montgomery, D. R.

Pourcelot, A.

A. Pourcelot, Compt. Rend. t. 262B, 982 (1966).

Schmidt, B.

B. Schmidt, Mitt. Hamburger Sternv. 7, 15 (1932).

Schulte, D. H.

Wynne, C. G.

Appl. Opt.

Compt. Rend.

A. Pourcelot, Compt. Rend. t. 262B, 982 (1966).

ESO Bull. No. 2

H. Köhler, ESO Bull. No. 2, 13 (1967).

ESO Bull. No. 8

G. Lemaître, ESO Bull. No. 8, 21 (1971).

J. Am. Philos. Soc.

J. G. Baker, J. Am. Philos. Soc. 82, 339 (1940).

J. Opt. Soc. Am.

Mitt. Hamburger Sternv.

B. Schmidt, Mitt. Hamburger Sternv. 7, 15 (1932).

Monthly Notices Roy. Astron. Soc.

C. R. Burch, Monthly Notices Roy. Astron. Soc. 102, 159 (1942).

The Observatory

S. C. B. Gascoigne, The Observatory 85, 79 (1965).

Other

A. Kerber, Central Zeit, f. Opt. und Mech. p. 157 (1886).

H. Chrétien, Calcul des combinaisons optiquesJ. & R. Sennac, Eds. (1959) p. 349.

G. Lemaître, D. E. A., Fac. Sc. Marseille (unpublished) (1968); Compt. Rend. t. 270A, 226 (1970).

D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1963).

French Patent, ANVAR 70,19,261 (1969).

G. Courtes, in New Techniques in Space Astronomy, F. Labuhn, R. Lüst, Eds. (International Union of Astronomy, Paris, 1971).

American Patent969,785 (1910).

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Figures (10)

Fig. 1
Fig. 1

Kerber profile (nondimensional coordinates).

Fig. 2
Fig. 2

Principle of the dioptric elasticity method.

Fig. 3
Fig. 3

Grid of profiles for different values of ρ2 for η = 1 and ν = 1/5.

Fig. 4
Fig. 4

Rupture pattern of a fused silica disk.

Fig. 5
Fig. 5

Pressure apparatus showing (1) liquid in equilibrium with its vapor, (2) ice water, (3) liquid nitrogen, and (4) airtight sliding O-ring.

Fig. 6
Fig. 6

Interferometric mountings.

Fig. 7
Fig. 7

Fringes of equal thickness (mounting 1) of a plate made by the dioptric elasticity method.

Fig. 8
Fig. 8

Fringes of equal thickness (mounting 2) of a plate made by the dioptric elasticity method.

Fig. 9
Fig. 9

Region of δ Ori (lower right) mυ = 2.5 and Ori (upper left) mυ = 1.7 photographed with a F/1.5 Schmidt system. Corrector plate in BSC B1664 of 24-cm aperture produced with a pressure ratio η = 6. Kodak IIaO, 3 min, no filter. The absence of circles around bright stars attests to the continuity of the surface of the plate.

Fig. 10
Fig. 10

Fringes of equal thickness of a plate figured to F/1.1.

Tables (1)

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Table I Vapor Pressure of Some Compounds at 273 K

Equations (26)

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Z Sch = 1 4 4 ( n 1 ) Ω 3 ( 3 2 ρ 2 ρ 4 ) · H , 0 ρ 1.
Z Elas = 3 ( 1 ν ) 16 q E ( H h ) 3 ( 2 3 + ν 1 + ν ρ 2 ρ 4 ) · H , 0 ρ 1 ,
Z Σ = ω ˜ ( ρ 2 + ω ˜ 2 ρ 4 ) · H , 0 ρ 1.
z Sch z E as + Z Σ = 0.
4 5 3 + ν 1 + ν ω ˜ 3 + 4 5 1 2 ω ˜ 21 + 5 ν ( 1 + ν ) ( n 1 ) 1 Ω 3 = 0.
R = 64 ( 1 + ν ) ( n 1 ) 21 + 5 ν Ω 2 · r .
h = [ 3 8 ( 1 ν 2 ) ( n 1 ) q E ] 1 3 · r .
D · 2 ( 2 w ) p = 0 ,
D = E h 3 / 12 ( 1 ν 2 ) ·
2 = 2 R 2 + 1 R R = 1 R R ( R R ) .
ρ = R / R 1 and Y = ( 64 D / R 1 p 0 ) w ,
Δ . = ( 1 / ρ ) ( / ρ ) [ ρ ( . / ρ ) ] ,
Δ ( Δ Y ) 64 p / p 0 = 0.
Y ( ρ ) = ( p / p 0 ) ρ 4 + C I ρ 2 ln ρ + ( C II C I ) ρ 2 + C III ln ρ + C IV .
ρ = 0 [ Y 1 / ρ = 0 Δ Y 1 / ρ = 0 ( slope ) , ( transverse shear stresses ) , ρ = ρ 2 [ Δ Y 2 / ρ = 0 ( transverse shear stresses ) , 2 Y 2 / ρ 2 + ( ν / ρ ) Y 2 / ρ = 0 ( bending couple ) .
ρ = 1 [ Y 1 = 0 Y 2 = 0 Y 1 / ρ = Y 2 / ρ 2 Y 1 / ρ 2 = 2 Y 2 / ρ 2 ( origin of deformations ) , ( origin of deformations ) , ( slope continuity ) , ( continuity of bending couple ) .
q 1 = p 1 / p 0 and q 2 = p 2 / p 0 .
Y 1 ( ρ ) = q 1 ρ 4 + X 1 ρ 2 + X 2 , 0 ρ 1.
Y 2 ( ρ ) = q 2 ρ 4 + X 3 ρ 2 ln ρ + ( X 4 X 3 ) ρ 2 + X 5 ln ρ + X 6 , 1 ρ ρ 2 .
M R = D · ( 2 w R 2 + ν R w R ) = 1 64 R 1 p 0 · ( 2 Y ρ 2 + ν ρ Y ρ ) .
M R = 1 64 R 1 p 0 · M ( ρ ) .
M 1 ( ρ ) = 4 ( 3 + ν ) q 1 ρ 2 + 2 ( 1 + ν ) X 1 , 0 ρ 1 , M 2 ( ρ ) = 4 ( 3 + ν ) q 2 ρ 2 + 2 ( 1 + ν ) X 3 ln ρ + 2 ( 1 + ν ) X 4 + ( 1 ν ) X 3 ( 1 ν ) X 5 / ρ 2 , 1 ρ ρ 2 ,
σ 1,2 ( ρ ) max i = 3 32 ( R 1 h ) 2 · M 1,2 ( ρ ) max i .
E = 3 16 ( 5 + ν ) ( 1 ν ) ( p 0 p ) R 4 a h 3 ·
σ rupt = 3 8 ( 3 + ν ) ( p 0 p rupt ) ( R h ) 2 .
log p = α β T γ log T .

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