Abstract

A single-beam ir spectroradiometric system has been used to measure the normal spectral emissivity of specimens of single-crystal and polycrystalline calcium fluoride in the ir at elevated temperatures. The wavelength range was 2–12 μ, and data were taken at sample temperatures of 500°C and 600°C. Room temperature data on the index of refraction of single-crystal calcium fluoride and its rate of change with temperature were extrapolated to 500°C and 600°C; the normal spectral reflectivities were computed from the extrapolated indices at these temperatures. Then the computed reflectivities were used to extract normal spectral absorption coefficients from the emissivity data. It was possible to compute absorption coefficients with reasonable accuracy at wavelengths of 6 μ, 8 μ, and 10 μ; the smallest estimated error was about 2% at 8 μ. The absorption coefficients increased markedly with temperature at these three wavelengths. The absorption coefficients of the polycrystalline material were consistently higher than the corresponding values for the single-crystal calcium fluoride. It was found that the spectral absorption coefficients at 8 μ and 10 μ microns varied approximately as the 2.1 and 1.6 power of the absolute temperature, respectively, between room temperature and 600°C. These exponents lie within the range predicted by theory.

© 1967 Optical Society of America

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References

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  1. I. H. Malitson, Appl. Opt. 2, 1103 (1963).
    [CrossRef]
  2. D. E. Gray, Ed., American Institute of Physics; Handbook (McGraw-Hill Book Co., New York, 1963), 2nd ed., Chap. 6, p. 53.
  3. H. O. McMahon, J. Opt. Soc. Am. 40, 376 (1950).
    [CrossRef]
  4. Reference 2, Chap. 6, p. 103.
  5. D. V. Widder, Advanced Calculus (Prentice–Hall, Inc., New York, 1947), Chap. 1, p. 47
  6. R. H. Hamilton, Ind. and Eng. Chem. (Anal. Ed.) 16, 123 (1944).
  7. M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, London, 1954), Chap. 7, pp. 357–361.

1963 (1)

1950 (1)

1944 (1)

R. H. Hamilton, Ind. and Eng. Chem. (Anal. Ed.) 16, 123 (1944).

Born, M.

M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, London, 1954), Chap. 7, pp. 357–361.

Hamilton, R. H.

R. H. Hamilton, Ind. and Eng. Chem. (Anal. Ed.) 16, 123 (1944).

Huang, K.

M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, London, 1954), Chap. 7, pp. 357–361.

Malitson, I. H.

McMahon, H. O.

Widder, D. V.

D. V. Widder, Advanced Calculus (Prentice–Hall, Inc., New York, 1947), Chap. 1, p. 47

Appl. Opt. (1)

Ind. and Eng. Chem. (1)

R. H. Hamilton, Ind. and Eng. Chem. (Anal. Ed.) 16, 123 (1944).

J. Opt. Soc. Am. (1)

Other (4)

M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, London, 1954), Chap. 7, pp. 357–361.

D. E. Gray, Ed., American Institute of Physics; Handbook (McGraw-Hill Book Co., New York, 1963), 2nd ed., Chap. 6, p. 53.

Reference 2, Chap. 6, p. 103.

D. V. Widder, Advanced Calculus (Prentice–Hall, Inc., New York, 1947), Chap. 1, p. 47

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Figures (4)

Fig. 1
Fig. 1

Schematic plan view of spectroradiometric system for measuring the normal spectral emissivity of optical materials. (Note: all dimensions in centimeters.) AB = 43.8 cm. BD = 26.3 cm. DA 69.9 cm.

Fig. 2
Fig. 2

Detail views of the sample holder and the spectrometer field of view for a point at the entrance slit center (dimensions in inches).

Fig. 3
Fig. 3

Hamilton’s error coefficient (expKt)(Kt)−1 vs Kt.

Fig. 4
Fig. 4

Logarithm of normal spectral absorption coefficients of single-crystal calcium fluoride at room temperature, 500°C and 600°C, at 8 μ and 10 μ wavelength vs logarithm of temperature.

Tables (4)

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Table I Normal Spectral Absorption Coefficients of Single-Crystal and Polycrystalline Calcium Fluoride at Room Temperature, 500°C and 600°C and at 6 μ, 8 μ, and 10 μ Wavelength

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Table II Normal Spectral Emissivity of Samples of Single-Crystal and Polycrystalline Calcium Fluoride at 500°C and 600°C from 2 μ to 12 μ Wavelength

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Table III Index of Refraction and Normal Spectral Surface Reflectance of Single-Crystal Calcium Fluoride from 2 μ to 12 μ Wavelength

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Table IV Approximate Functional Relations between Normal Spectral Absorption Coefficients of Single-Crystal Calcium Fluoride and the Absolute Temperature

Equations (21)

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= ( 1 - ρ s ) ( 1 - τ i ) ( 1 - ρ s τ i ) - 1 ,
τ = τ i ( 1 - ρ s ) 2 ( 1 - τ i 2 ρ s 2 ) - 1 ,
ρ = ρ s ( 1 + τ τ i ) .
ρ s = [ ( n - 1 ) 2 + λ 2 K 2 ( 4 π ) - 2 ] [ ( n + 1 ) 2 + λ 2 K 2 ( 4 π ) - 2 ] - 1 .
1 = A ( t 1 , n , K )
2 = A ( t 2 , n , K )
{ [ A ( t 1 , n , K ) , A ( t , n , K ) ] } / ( n , K )
τ i = ( 1 - - ρ s ) ( 1 - ρ s - ρ s ) - 1 ,
τ i exp ( - K × t ) .
τ i = { - ( 1 - ρ s ) 2 ( 1 - β ) + [ ( 1 - ρ s ) 4 ( 1 - β ) 2 + 4 ( 1 - - ρ s ) ρ s ( 1 - ρ s - ρ s ) ] ½ 2 ρ s ( 1 - ρ s - ρ s ) } .
τ i = ( 1 - ) ( 1 + β + β 2 ) - ρ s ( ) 2 - ρ s β [ 2 - 2 + 3 ( ) 2 ] .
K t = - ln τ i ,
Δ ( K t ) = [ 2 ( K t ) / 2 ( τ i ) ] Δ τ i ,
Δ ( K t ) = - τ i - 1 Δ r i .
t Δ K = τ i - 1 ( 2 τ i / 2 ) Δ
K Δ K = Δ { ( 1 - ρ s ) 2 [ ln ( 1 - - ρ s ) - ln ( 1 - ρ s - ρ s ) ] × [ ( 1 - - ρ s ) ( 1 - ρ s - ρ s ) ] } .
p = 0.623 - 0.968 ρ s ,
K t 0 = 1 - 0.087 ρ s
α = δ { 1 - exp [ - 2 σ T r 2 T 3 S P ( σ T × t ) - 1 ] } ,
Δ = Δ ( ln T R M ) × x R M [ 1 - exp ( - x R M ) ] - 1 τ [ 1 - exp ( - x B B ) ] × [ exp ( x R M + x B B ) - 1 ] - 1 ,
Δ max = Δ ( ln T R M ) [ x R M ( x B B ) - 1 - 1 ] - 1 × τ .

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