Abstract

This paper investigates a simple noncontact optical thermometry technique based on the laser interferometric measurement of the thermal expansion and refractive index change of a thin transparent substrate or temperature sensor. The technique is shown to be extendible from room temperature to at least 900°C with the proper choice of a thermally stable sensor. Sensor materials investigated included c-axis Al2O3, MgO, MgAl2O4 (spinel), Y2O3–ZrO2 (yttria stabilized zirconia), and fused silica. Calibration data were taken at 633 nm by measuring the sensor response to known temperature changes. These data provided (1) the information needed for quantitative thermometry (i.e., the functional relationship between interference fringes and temperature for samples of known thickness) and (2) the thermal coefficient of refractive index for those materials with known thermal expansion coefficients.

© 1991 Optical Society of America

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  1. See, for example, D. M. Hwang et al., “Microstructure of In-Situ Epitaxially Grown Superconducting Y-Ba-Cu-O Thin Films,” Appl. Phys. Lett. 54, 1702–1704 (1989); R. K. Singh, J. Narayan, A. K. Singh, J. Krishnaswamy, “In-Situ Processing of Epitaxial Y-Ba-Cu-O High Tc Superconducting Films on (100) SrTiO3 and (100) YS–ZrO2 Substrates at 500–650°C,” Appl. Phys. Lett. 54, 2271–2273 (1989).
    [CrossRef]
  2. M. Luckiesh, L. L. Holladay, R. H. Sinden, “An Interference Thermometer and Dilatometer Combined,” J. Franklin Inst. 194, 251 (1922).
    [CrossRef]
  3. F. C. Nix, D. MacNair, “An Interferometric-Dilatometer with Photographic Recording,” Rev. Sci. Instrum. 12, 66–70 (1941).
    [CrossRef]
  4. K. Murakami, K. Takita, K. Masuda, “Measurement of Lattice Temperature During Pulsed-Laser Annealing by Time-Dependent Optical Reflectivity,” Jpn. J. Appl. Phys. 20, L867–870 (1981).
    [CrossRef]
  5. R. A. Bond, S. Dzioba, H. M. Naguib, “Temperature Measurements of Glass Substrates During Plasma Etching,” J. Vac. Sci. Technol. 18, 335–338 (1981).
    [CrossRef]
  6. G. Appleby-Hougham, B. Robinson, K. L. Saenger, C. P. Sun, “Non-Intrusive Thermometry for Transparent Thin Films by Laser Interferometric Measurement of Thermal Expansion (LIMOTEX) Using Single or Dual Beams,” IBM Tech. Discl. Bull. 30, 239–243 (1987).
  7. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).
  8. For clarity of notation we have taken the Fresnel reflection coefficients rj to be real. When the refractive index of the sensor’s backing material is complex, i.e., nb = nb + ikb, Eq. (1) becomesR=rf2+2rf{Re(r˜b)cosϕ−Im(r˜b)sinϕ}+|rb|21+rf2|rb|2+2rf{Re(r˜b)cosϕ+Im(r˜b)sinϕ},where Re(r˜b) and Im(r˜b) are the real and imaginary components of the complex Fresnel reflection coefficient r˜b. That is, {rfrb cosϕ} in Eq. (1) is replaced by the quantity {Re(r˜b)cosϕ+Im(r˜b)sinϕ} and rb2 is replaced by |rb|2.
  9. To see this, we divide the slab into infinitesimally thin layers of thickness dz{1 + α × [T(z) − Tz=0]} with index n(z,T) = n(Tz=0){1 + β × [T(z) × Tz=0]}, where we have assumed that α and β are generally constant over the range of T(z) in the sensor. The total optical path length difference for a round trip through the slab is then simply the integral over z from 0 to L of the optical path length differences contributed by each layer, 2n(z,T)dz, This yieldsϕ=2π[2n(0)Lλ]{1+(α+β)[Tav−T(0)]},(6)where Tav≡(1/L)∫0L[T(z)]dz. After differentiation by Tav, the above equation differs from Eq. (3) only by the negligible factor of n(Tav)/n(Tz=0).
  10. Y. S. Touloukian, R. K. Kirby, R. E. Taylor, T. Y. R. Lee, Thermal Expansion—Nonmetallic Solids, Thermophysical Properties of Matter, Vol. 13 (IFI/Plenum, New York, 1977).
  11. I. H. Malitson, “Refraction and Dispersion of Synthetic Sapphire,” J. Opt. Soc. Am. 52, 1377–1379 (1962).
    [CrossRef]
  12. R. E. Stephens, I. H. Malitson, “Index of Refraction of Magnesium Oxide,” J. Res. Natl. Bur. Stand. 49, 249–252 (1952).
    [CrossRef]
  13. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).
  14. I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965).
    [CrossRef]
  15. J. Strong, R. T. Brice, “Optical Properties of Magnesium Oxide,” J. Opt. Soc. Am. 25, 207–210 (1935).
    [CrossRef]
  16. J. H. Wray, J. T. Neu, “Refractive Index of Several Glasses as a Function of Wavelength and Temperature,” J. Opt. Soc. Am. 59, 774–776 (1969).
    [CrossRef]
  17. K. L. Saenger, R. A. Roy, J. Gupta, J. P. Doyle, J. J. Cuomo, “Laser Interferometric Temperature Measurement of Heated Substrates Used for High Tc Superconductor Deposition,” Mat. Res. Soc. Symp. Proc. 169, 1161–1164 (1990).
    [CrossRef]
  18. K. L. Saenger, R. A. Roy, work in progress.

1990 (1)

K. L. Saenger, R. A. Roy, J. Gupta, J. P. Doyle, J. J. Cuomo, “Laser Interferometric Temperature Measurement of Heated Substrates Used for High Tc Superconductor Deposition,” Mat. Res. Soc. Symp. Proc. 169, 1161–1164 (1990).
[CrossRef]

1989 (1)

See, for example, D. M. Hwang et al., “Microstructure of In-Situ Epitaxially Grown Superconducting Y-Ba-Cu-O Thin Films,” Appl. Phys. Lett. 54, 1702–1704 (1989); R. K. Singh, J. Narayan, A. K. Singh, J. Krishnaswamy, “In-Situ Processing of Epitaxial Y-Ba-Cu-O High Tc Superconducting Films on (100) SrTiO3 and (100) YS–ZrO2 Substrates at 500–650°C,” Appl. Phys. Lett. 54, 2271–2273 (1989).
[CrossRef]

1987 (1)

G. Appleby-Hougham, B. Robinson, K. L. Saenger, C. P. Sun, “Non-Intrusive Thermometry for Transparent Thin Films by Laser Interferometric Measurement of Thermal Expansion (LIMOTEX) Using Single or Dual Beams,” IBM Tech. Discl. Bull. 30, 239–243 (1987).

1981 (2)

K. Murakami, K. Takita, K. Masuda, “Measurement of Lattice Temperature During Pulsed-Laser Annealing by Time-Dependent Optical Reflectivity,” Jpn. J. Appl. Phys. 20, L867–870 (1981).
[CrossRef]

R. A. Bond, S. Dzioba, H. M. Naguib, “Temperature Measurements of Glass Substrates During Plasma Etching,” J. Vac. Sci. Technol. 18, 335–338 (1981).
[CrossRef]

1969 (1)

1965 (1)

1962 (1)

1952 (1)

R. E. Stephens, I. H. Malitson, “Index of Refraction of Magnesium Oxide,” J. Res. Natl. Bur. Stand. 49, 249–252 (1952).
[CrossRef]

1941 (1)

F. C. Nix, D. MacNair, “An Interferometric-Dilatometer with Photographic Recording,” Rev. Sci. Instrum. 12, 66–70 (1941).
[CrossRef]

1935 (1)

1922 (1)

M. Luckiesh, L. L. Holladay, R. H. Sinden, “An Interference Thermometer and Dilatometer Combined,” J. Franklin Inst. 194, 251 (1922).
[CrossRef]

Appleby-Hougham, G.

G. Appleby-Hougham, B. Robinson, K. L. Saenger, C. P. Sun, “Non-Intrusive Thermometry for Transparent Thin Films by Laser Interferometric Measurement of Thermal Expansion (LIMOTEX) Using Single or Dual Beams,” IBM Tech. Discl. Bull. 30, 239–243 (1987).

Bond, R. A.

R. A. Bond, S. Dzioba, H. M. Naguib, “Temperature Measurements of Glass Substrates During Plasma Etching,” J. Vac. Sci. Technol. 18, 335–338 (1981).
[CrossRef]

Brice, R. T.

Cuomo, J. J.

K. L. Saenger, R. A. Roy, J. Gupta, J. P. Doyle, J. J. Cuomo, “Laser Interferometric Temperature Measurement of Heated Substrates Used for High Tc Superconductor Deposition,” Mat. Res. Soc. Symp. Proc. 169, 1161–1164 (1990).
[CrossRef]

Doyle, J. P.

K. L. Saenger, R. A. Roy, J. Gupta, J. P. Doyle, J. J. Cuomo, “Laser Interferometric Temperature Measurement of Heated Substrates Used for High Tc Superconductor Deposition,” Mat. Res. Soc. Symp. Proc. 169, 1161–1164 (1990).
[CrossRef]

Dzioba, S.

R. A. Bond, S. Dzioba, H. M. Naguib, “Temperature Measurements of Glass Substrates During Plasma Etching,” J. Vac. Sci. Technol. 18, 335–338 (1981).
[CrossRef]

Gupta, J.

K. L. Saenger, R. A. Roy, J. Gupta, J. P. Doyle, J. J. Cuomo, “Laser Interferometric Temperature Measurement of Heated Substrates Used for High Tc Superconductor Deposition,” Mat. Res. Soc. Symp. Proc. 169, 1161–1164 (1990).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

Holladay, L. L.

M. Luckiesh, L. L. Holladay, R. H. Sinden, “An Interference Thermometer and Dilatometer Combined,” J. Franklin Inst. 194, 251 (1922).
[CrossRef]

Hwang, D. M.

See, for example, D. M. Hwang et al., “Microstructure of In-Situ Epitaxially Grown Superconducting Y-Ba-Cu-O Thin Films,” Appl. Phys. Lett. 54, 1702–1704 (1989); R. K. Singh, J. Narayan, A. K. Singh, J. Krishnaswamy, “In-Situ Processing of Epitaxial Y-Ba-Cu-O High Tc Superconducting Films on (100) SrTiO3 and (100) YS–ZrO2 Substrates at 500–650°C,” Appl. Phys. Lett. 54, 2271–2273 (1989).
[CrossRef]

Kirby, R. K.

Y. S. Touloukian, R. K. Kirby, R. E. Taylor, T. Y. R. Lee, Thermal Expansion—Nonmetallic Solids, Thermophysical Properties of Matter, Vol. 13 (IFI/Plenum, New York, 1977).

Lee, T. Y. R.

Y. S. Touloukian, R. K. Kirby, R. E. Taylor, T. Y. R. Lee, Thermal Expansion—Nonmetallic Solids, Thermophysical Properties of Matter, Vol. 13 (IFI/Plenum, New York, 1977).

Luckiesh, M.

M. Luckiesh, L. L. Holladay, R. H. Sinden, “An Interference Thermometer and Dilatometer Combined,” J. Franklin Inst. 194, 251 (1922).
[CrossRef]

MacNair, D.

F. C. Nix, D. MacNair, “An Interferometric-Dilatometer with Photographic Recording,” Rev. Sci. Instrum. 12, 66–70 (1941).
[CrossRef]

Malitson, I. H.

Masuda, K.

K. Murakami, K. Takita, K. Masuda, “Measurement of Lattice Temperature During Pulsed-Laser Annealing by Time-Dependent Optical Reflectivity,” Jpn. J. Appl. Phys. 20, L867–870 (1981).
[CrossRef]

Murakami, K.

K. Murakami, K. Takita, K. Masuda, “Measurement of Lattice Temperature During Pulsed-Laser Annealing by Time-Dependent Optical Reflectivity,” Jpn. J. Appl. Phys. 20, L867–870 (1981).
[CrossRef]

Naguib, H. M.

R. A. Bond, S. Dzioba, H. M. Naguib, “Temperature Measurements of Glass Substrates During Plasma Etching,” J. Vac. Sci. Technol. 18, 335–338 (1981).
[CrossRef]

Neu, J. T.

Nix, F. C.

F. C. Nix, D. MacNair, “An Interferometric-Dilatometer with Photographic Recording,” Rev. Sci. Instrum. 12, 66–70 (1941).
[CrossRef]

Robinson, B.

G. Appleby-Hougham, B. Robinson, K. L. Saenger, C. P. Sun, “Non-Intrusive Thermometry for Transparent Thin Films by Laser Interferometric Measurement of Thermal Expansion (LIMOTEX) Using Single or Dual Beams,” IBM Tech. Discl. Bull. 30, 239–243 (1987).

Roy, R. A.

K. L. Saenger, R. A. Roy, J. Gupta, J. P. Doyle, J. J. Cuomo, “Laser Interferometric Temperature Measurement of Heated Substrates Used for High Tc Superconductor Deposition,” Mat. Res. Soc. Symp. Proc. 169, 1161–1164 (1990).
[CrossRef]

K. L. Saenger, R. A. Roy, work in progress.

Saenger, K. L.

K. L. Saenger, R. A. Roy, J. Gupta, J. P. Doyle, J. J. Cuomo, “Laser Interferometric Temperature Measurement of Heated Substrates Used for High Tc Superconductor Deposition,” Mat. Res. Soc. Symp. Proc. 169, 1161–1164 (1990).
[CrossRef]

G. Appleby-Hougham, B. Robinson, K. L. Saenger, C. P. Sun, “Non-Intrusive Thermometry for Transparent Thin Films by Laser Interferometric Measurement of Thermal Expansion (LIMOTEX) Using Single or Dual Beams,” IBM Tech. Discl. Bull. 30, 239–243 (1987).

K. L. Saenger, R. A. Roy, work in progress.

Sinden, R. H.

M. Luckiesh, L. L. Holladay, R. H. Sinden, “An Interference Thermometer and Dilatometer Combined,” J. Franklin Inst. 194, 251 (1922).
[CrossRef]

Stephens, R. E.

R. E. Stephens, I. H. Malitson, “Index of Refraction of Magnesium Oxide,” J. Res. Natl. Bur. Stand. 49, 249–252 (1952).
[CrossRef]

Strong, J.

Sun, C. P.

G. Appleby-Hougham, B. Robinson, K. L. Saenger, C. P. Sun, “Non-Intrusive Thermometry for Transparent Thin Films by Laser Interferometric Measurement of Thermal Expansion (LIMOTEX) Using Single or Dual Beams,” IBM Tech. Discl. Bull. 30, 239–243 (1987).

Takita, K.

K. Murakami, K. Takita, K. Masuda, “Measurement of Lattice Temperature During Pulsed-Laser Annealing by Time-Dependent Optical Reflectivity,” Jpn. J. Appl. Phys. 20, L867–870 (1981).
[CrossRef]

Taylor, R. E.

Y. S. Touloukian, R. K. Kirby, R. E. Taylor, T. Y. R. Lee, Thermal Expansion—Nonmetallic Solids, Thermophysical Properties of Matter, Vol. 13 (IFI/Plenum, New York, 1977).

Touloukian, Y. S.

Y. S. Touloukian, R. K. Kirby, R. E. Taylor, T. Y. R. Lee, Thermal Expansion—Nonmetallic Solids, Thermophysical Properties of Matter, Vol. 13 (IFI/Plenum, New York, 1977).

Wray, J. H.

Appl. Phys. Lett. (1)

See, for example, D. M. Hwang et al., “Microstructure of In-Situ Epitaxially Grown Superconducting Y-Ba-Cu-O Thin Films,” Appl. Phys. Lett. 54, 1702–1704 (1989); R. K. Singh, J. Narayan, A. K. Singh, J. Krishnaswamy, “In-Situ Processing of Epitaxial Y-Ba-Cu-O High Tc Superconducting Films on (100) SrTiO3 and (100) YS–ZrO2 Substrates at 500–650°C,” Appl. Phys. Lett. 54, 2271–2273 (1989).
[CrossRef]

IBM Tech. Discl. Bull. (1)

G. Appleby-Hougham, B. Robinson, K. L. Saenger, C. P. Sun, “Non-Intrusive Thermometry for Transparent Thin Films by Laser Interferometric Measurement of Thermal Expansion (LIMOTEX) Using Single or Dual Beams,” IBM Tech. Discl. Bull. 30, 239–243 (1987).

J. Franklin Inst. (1)

M. Luckiesh, L. L. Holladay, R. H. Sinden, “An Interference Thermometer and Dilatometer Combined,” J. Franklin Inst. 194, 251 (1922).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Res. Natl. Bur. Stand. (1)

R. E. Stephens, I. H. Malitson, “Index of Refraction of Magnesium Oxide,” J. Res. Natl. Bur. Stand. 49, 249–252 (1952).
[CrossRef]

J. Vac. Sci. Technol. (1)

R. A. Bond, S. Dzioba, H. M. Naguib, “Temperature Measurements of Glass Substrates During Plasma Etching,” J. Vac. Sci. Technol. 18, 335–338 (1981).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Murakami, K. Takita, K. Masuda, “Measurement of Lattice Temperature During Pulsed-Laser Annealing by Time-Dependent Optical Reflectivity,” Jpn. J. Appl. Phys. 20, L867–870 (1981).
[CrossRef]

Mat. Res. Soc. Symp. Proc. (1)

K. L. Saenger, R. A. Roy, J. Gupta, J. P. Doyle, J. J. Cuomo, “Laser Interferometric Temperature Measurement of Heated Substrates Used for High Tc Superconductor Deposition,” Mat. Res. Soc. Symp. Proc. 169, 1161–1164 (1990).
[CrossRef]

Rev. Sci. Instrum. (1)

F. C. Nix, D. MacNair, “An Interferometric-Dilatometer with Photographic Recording,” Rev. Sci. Instrum. 12, 66–70 (1941).
[CrossRef]

Other (6)

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

For clarity of notation we have taken the Fresnel reflection coefficients rj to be real. When the refractive index of the sensor’s backing material is complex, i.e., nb = nb + ikb, Eq. (1) becomesR=rf2+2rf{Re(r˜b)cosϕ−Im(r˜b)sinϕ}+|rb|21+rf2|rb|2+2rf{Re(r˜b)cosϕ+Im(r˜b)sinϕ},where Re(r˜b) and Im(r˜b) are the real and imaginary components of the complex Fresnel reflection coefficient r˜b. That is, {rfrb cosϕ} in Eq. (1) is replaced by the quantity {Re(r˜b)cosϕ+Im(r˜b)sinϕ} and rb2 is replaced by |rb|2.

To see this, we divide the slab into infinitesimally thin layers of thickness dz{1 + α × [T(z) − Tz=0]} with index n(z,T) = n(Tz=0){1 + β × [T(z) × Tz=0]}, where we have assumed that α and β are generally constant over the range of T(z) in the sensor. The total optical path length difference for a round trip through the slab is then simply the integral over z from 0 to L of the optical path length differences contributed by each layer, 2n(z,T)dz, This yieldsϕ=2π[2n(0)Lλ]{1+(α+β)[Tav−T(0)]},(6)where Tav≡(1/L)∫0L[T(z)]dz. After differentiation by Tav, the above equation differs from Eq. (3) only by the negligible factor of n(Tav)/n(Tz=0).

Y. S. Touloukian, R. K. Kirby, R. E. Taylor, T. Y. R. Lee, Thermal Expansion—Nonmetallic Solids, Thermophysical Properties of Matter, Vol. 13 (IFI/Plenum, New York, 1977).

K. L. Saenger, R. A. Roy, work in progress.

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

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Figures (4)

Fig. 1
Fig. 1

Interferometer schematic.

Fig. 2
Fig. 2

Calibration apparatus.

Fig. 3
Fig. 3

Calibration data (circles) and fit (line) for MgO with λ = 633 nm and L0 = 0.0635 cm.

Fig. 4
Fig. 4

Thermal coefficients vs temperature for MgO. Data (circles) and linear fit (solid line) for (α + β); literature α ≡ (1/L)(dL/dT)—dotted line; linear fit of derived β ≡ (1/n)(dn/dT) for λ = 633 nm—dashed line.

Tables (3)

Tables Icon

Table I Experimentally Determined Fitting Parameters Relating Fringes to Temperature (25–870°C) via Eq. (5) or (6) for λ = 633 nm; the Quantity (ΔT/fringe)|25°C is the Room Temperature Degrees per Fringe Calibration for a 0.1-cm Thick Sensor

Tables Icon

Table II Thermal Expansion Fitting ParametersaAm and Room Temperature Refractive Indices at 633 nm for Some Optically Transparent Sensor Materials

Tables Icon

Table III Measured and Literature Values of Thermal Coefficients, α = (1/L)(dL/dT) and β ≡ (1/n)(dn/dT) at Room Temperature (25°C) and 800°C for Several Materials; the Wavelength is 633 nm

Equations (9)

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R = r f 2 + 2 r f r b cos ( ϕ ) + r b 2 1 + 2 r f r b cos ( ϕ ) + r f 2 r b 2 .
ϕ = 2 π λ ( 2 n L )
d ϕ d T = 2 π λ 2 n L ( α + β ) ,
Δ T / fringe = ( d ϕ / d T 2 π ) 1 = λ 2 n L ( α + β ) .
Δ F ( T ; T 0 ) = L 0 [ a 1 ( T T 0 ) + a 2 ( T T 0 ) 2 + a 3 ( T T 0 ) 3 ] ,
T ( Δ F ) T 0 = b 1 ( Δ F / L 0 ) + b 2 ( Δ F / L 0 ) 2 + b 3 ( Δ F / L 0 ) 3 + b 4 ( Δ F / L 0 ) 4 ,
α + β = λ 2 n 0 L 0 [ Δ T fringe ] 1 = λ 2 n 0 L 0 [ d Δ F ( T ; T 0 ) d T ] = λ 2 n 0 [ a 1 + 2 a 2 ( T T 0 ) + 3 a 3 ( T T 0 ) 2 ] .
α ( T K ) = A 1 + 2 A 2 T K + 3 A 3 T K 2 ,
ϕ=2π[2n(0)Lλ]{1+(α+β)[TavT(0)]},

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