Abstract

A simple interferometric test setup for measuring thermal expansion coefficients as low as 1 × 10−8/°C is described. The sample to be tested is polished optically flat, interference fringes are formed between the front surface of the sample and a reference surface, and their movement, as boiling water is applied to the back side of the test piece, is observed. When this process was applied to Zerodur, approximate agreement with expected values was achieved. A small permanent change in the Zerodur optical figure occurred as a result of this test procedure, suggesting that Zerodur should not be exposed to strong thermal shock during use.

© 1984 Optical Society of America

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References

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  1. ULE titanium silicate, Code 7971 data sheet from Corning Glass Works, Corning, N.Y. 14830.
  2. Zerodur data sheet from Schott, Spezial-Glas GMBH, P.O. Box 3833, Rheinallee 143, D-6500 Mainz, West Germany.
  3. Cervit was manufactured by Owens Illinois Corp. but is no longer available.
  4. D. E. Gray, Ed., American Institute of Physics Handbook, (McGraw-Hill, New York, 1972), pp. 4–138.
  5. J. W. Berthold, S. F. Jacobs, “Ultraprecise Thermal Expansion Measurements of Seven Low Expansion Materials,” Appl. Opt. 15, 2344 (1976).
    [CrossRef]
  6. J. W. Berthold, S. F. Jacobs, M. A. Norton, “Dimensional, Stability of Fused Silica, Invar, and Several Ultralow Thermal Expansion Materials,” Appl. Opt. 15, 1898 (1976).
    [CrossRef]
  7. B. A. Boley, J. H. Weiner, Theory of Thermal Stress (Wiley, New York, 1960), p. 279.
  8. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U.P., London, 1959), p. 60.
  9. Ref. 8, p. 482.
  10. Manufactured by the Zygo Corp., Laurel Brook Rd., Middlefield, Conn. 06455.
  11. J. J. Shaffer, H. E. Bennett, “Effect of Thermal Cycling on Dimensional Stability of Zerodur and ULE,” Appl. Opt.23, 0000 (1984), in press.
    [CrossRef]

1976

Bennett, H. E.

J. J. Shaffer, H. E. Bennett, “Effect of Thermal Cycling on Dimensional Stability of Zerodur and ULE,” Appl. Opt.23, 0000 (1984), in press.
[CrossRef]

Berthold, J. W.

Boley, B. A.

B. A. Boley, J. H. Weiner, Theory of Thermal Stress (Wiley, New York, 1960), p. 279.

Carslaw, H. S.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U.P., London, 1959), p. 60.

Jacobs, S. F.

Jaeger, J. C.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U.P., London, 1959), p. 60.

Norton, M. A.

Shaffer, J. J.

J. J. Shaffer, H. E. Bennett, “Effect of Thermal Cycling on Dimensional Stability of Zerodur and ULE,” Appl. Opt.23, 0000 (1984), in press.
[CrossRef]

Weiner, J. H.

B. A. Boley, J. H. Weiner, Theory of Thermal Stress (Wiley, New York, 1960), p. 279.

Appl. Opt.

Other

B. A. Boley, J. H. Weiner, Theory of Thermal Stress (Wiley, New York, 1960), p. 279.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U.P., London, 1959), p. 60.

Ref. 8, p. 482.

Manufactured by the Zygo Corp., Laurel Brook Rd., Middlefield, Conn. 06455.

J. J. Shaffer, H. E. Bennett, “Effect of Thermal Cycling on Dimensional Stability of Zerodur and ULE,” Appl. Opt.23, 0000 (1984), in press.
[CrossRef]

ULE titanium silicate, Code 7971 data sheet from Corning Glass Works, Corning, N.Y. 14830.

Zerodur data sheet from Schott, Spezial-Glas GMBH, P.O. Box 3833, Rheinallee 143, D-6500 Mainz, West Germany.

Cervit was manufactured by Owens Illinois Corp. but is no longer available.

D. E. Gray, Ed., American Institute of Physics Handbook, (McGraw-Hill, New York, 1972), pp. 4–138.

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Figures (4)

Fig. 1
Fig. 1

Test setup used to measure the expansion coefficient. Near-boiling water flowed from the Ehrlenmeyer flask at upper right to the sample at upper center and then to the heated reservoir at lower left.

Fig. 2
Fig. 2

Detail of the test facility in which the expansion coefficient of Zerodur was measured. Interference fringes formed between the bottom of the Zerodur flat and the top of the reference flat on which it was placed. The bottom edge of the Zerodur reference flat rested on a Pyrex ring.

Fig. 3
Fig. 3

Typical interferogram taken during the tests. The optical figure was measured to be 0.054 waves of power, 0.019 waves rms, and 0.085 waves peak-to-valley deviation from a best-fit sphere. The need for a sensitive figure analysis system to handle such data is clearly shown in this example.

Fig. 4
Fig. 4

Bowing of a Zerodur flat caused by heating of the back side. The dashed line indicates the time at which the temperature rise was calculated to be halfway through the flat.

Equations (8)

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w = - 6 α ( a 2 - ρ 2 ) l 3 - l / 2 l / 2 T ( z , t ) z d z + 1 1 - ν [ ( 1 + ν ) α 0 z T d z - ν α z l / 2 - l / 2 l / 2 T d z - 3 ν α z 2 2 ( l / 2 ) 3 - l / 2 l / 2 T z d z ] ,
w = - 6 α a 2 l 3 γ / 2 l / 2 T 0 z d z
= 3 4 α a 2 l T 0 [ 1 - ( γ l ) 2 ] .
T = T 0 erfc z 2 κ t ,
erfc x 2 π x exp ( - ξ 2 ) d ξ ,
erfc x 1 - 2 π ( x - x 3 3 + x 5 10 + ) .
t = l 2 / π κ .
α = 4 w l 3 a 2 T 0 .

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