OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 30, Iss. 10 — Apr. 1, 1991
  • pp: 1221–1226

Laser interferometric thermometry for substrate temperature measurement

Katherine L. Saenger and Julie Gupta  »View Author Affiliations

Applied Optics, Vol. 30, Issue 10, pp. 1221-1226 (1991)

View Full Text Article

Enhanced HTML    Acrobat PDF (746 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

Original Manuscript: January 12, 1990
Published: April 1, 1991

Katherine L. Saenger and Julie Gupta, "Laser interferometric thermometry for substrate temperature measurement," Appl. Opt. 30, 1221-1226 (1991)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited