Abstract

We present a method to independently measure the refractive index and the thickness of materials having flat and parallel sides by using a combination of Michelson and Fabry–Perot interferometry techniques. The method has been used to determine refractive-index values in the infrared with uncertainties in the third decimal place and thicknesses accurate to within ±5 μm for materials at room and cryogenic temperatures.

© 2005 Optical Society of America

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References

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  1. C. A. Proctor, “Index of refraction and dispersion with the interferometer,” Phys. Rev. 24, 195–201 (1907).
  2. M. S. Shumate, “Interferometric measurement of large indices of refraction,” Appl. Opt. 5, 327–331 (1966).
    [CrossRef] [PubMed]
  3. U. Schlarb, K. Betzler, “Influence of the defect structure on the refractive indices of undoped and Mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
    [CrossRef]
  4. J. F. H. Nicholls, B. Henderson, B. H. T. Chai, “Accurate determination of the indices of refraction of nonlinear optical crystals,” Appl. Opt. 36, 8587–8594 (1997).
    [CrossRef]
  5. J. C. Brasunas, G. M. Curshman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
    [CrossRef]
  6. G. Coppala, P. Ferraro, M. Iodice, S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer,” Appl. Opt. 42, 3882–3887 (2003).
    [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 2002).
  8. G. D. Gillen, S. Guha, “Refractive-index measurements of zinc germanium diphosphide at 300 and 77 K by use of a modified Michelson interferometer,” Appl. Opt. 43, 2054–2058 (2004).
    [CrossRef] [PubMed]
  9. G. Hawkins, R. Hunneman, “The temperature-dependent spectral properties of filter substrate materials in the far-infrared (6–40 μm),” Infrared Phys. Technol. 45, 69–79 (2004).
    [CrossRef]
  10. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1998).
  11. I. S. Grigoriev, E. Z. Meilikhov, Handbook of Physical Quantities (CRC Press, Boca Raton, Fla., 1997).
  12. V. Kumar, B. S. R. Sastry, “Thermal expansion coefficient of binary semiconductors,” Cryst. Res. Technol. 36, 565–569 (2001).
    [CrossRef]

2004 (2)

G. Hawkins, R. Hunneman, “The temperature-dependent spectral properties of filter substrate materials in the far-infrared (6–40 μm),” Infrared Phys. Technol. 45, 69–79 (2004).
[CrossRef]

G. D. Gillen, S. Guha, “Refractive-index measurements of zinc germanium diphosphide at 300 and 77 K by use of a modified Michelson interferometer,” Appl. Opt. 43, 2054–2058 (2004).
[CrossRef] [PubMed]

2003 (1)

2001 (1)

V. Kumar, B. S. R. Sastry, “Thermal expansion coefficient of binary semiconductors,” Cryst. Res. Technol. 36, 565–569 (2001).
[CrossRef]

1997 (1)

1995 (1)

J. C. Brasunas, G. M. Curshman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

1994 (1)

U. Schlarb, K. Betzler, “Influence of the defect structure on the refractive indices of undoped and Mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
[CrossRef]

1966 (1)

1907 (1)

C. A. Proctor, “Index of refraction and dispersion with the interferometer,” Phys. Rev. 24, 195–201 (1907).

Betzler, K.

U. Schlarb, K. Betzler, “Influence of the defect structure on the refractive indices of undoped and Mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 2002).

Brasunas, J. C.

J. C. Brasunas, G. M. Curshman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

Chai, B. H. T.

Coppala, G.

Curshman, G. M.

J. C. Brasunas, G. M. Curshman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

De Nicola, S.

Ferraro, P.

Gillen, G. D.

Grigoriev, I. S.

I. S. Grigoriev, E. Z. Meilikhov, Handbook of Physical Quantities (CRC Press, Boca Raton, Fla., 1997).

Guha, S.

Hawkins, G.

G. Hawkins, R. Hunneman, “The temperature-dependent spectral properties of filter substrate materials in the far-infrared (6–40 μm),” Infrared Phys. Technol. 45, 69–79 (2004).
[CrossRef]

Henderson, B.

Hunneman, R.

G. Hawkins, R. Hunneman, “The temperature-dependent spectral properties of filter substrate materials in the far-infrared (6–40 μm),” Infrared Phys. Technol. 45, 69–79 (2004).
[CrossRef]

Iodice, M.

Kumar, V.

V. Kumar, B. S. R. Sastry, “Thermal expansion coefficient of binary semiconductors,” Cryst. Res. Technol. 36, 565–569 (2001).
[CrossRef]

Meilikhov, E. Z.

I. S. Grigoriev, E. Z. Meilikhov, Handbook of Physical Quantities (CRC Press, Boca Raton, Fla., 1997).

Nicholls, J. F. H.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1998).

Proctor, C. A.

C. A. Proctor, “Index of refraction and dispersion with the interferometer,” Phys. Rev. 24, 195–201 (1907).

Sastry, B. S. R.

V. Kumar, B. S. R. Sastry, “Thermal expansion coefficient of binary semiconductors,” Cryst. Res. Technol. 36, 565–569 (2001).
[CrossRef]

Schlarb, U.

U. Schlarb, K. Betzler, “Influence of the defect structure on the refractive indices of undoped and Mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
[CrossRef]

Shumate, M. S.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 2002).

Appl. Opt. (4)

Cryst. Res. Technol. (1)

V. Kumar, B. S. R. Sastry, “Thermal expansion coefficient of binary semiconductors,” Cryst. Res. Technol. 36, 565–569 (2001).
[CrossRef]

Infrared Phys. Technol. (1)

G. Hawkins, R. Hunneman, “The temperature-dependent spectral properties of filter substrate materials in the far-infrared (6–40 μm),” Infrared Phys. Technol. 45, 69–79 (2004).
[CrossRef]

Opt. Eng. (1)

J. C. Brasunas, G. M. Curshman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

Phys. Rev. (1)

C. A. Proctor, “Index of refraction and dispersion with the interferometer,” Phys. Rev. 24, 195–201 (1907).

Phys. Rev. B (1)

U. Schlarb, K. Betzler, “Influence of the defect structure on the refractive indices of undoped and Mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 2002).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1998).

I. S. Grigoriev, E. Z. Meilikhov, Handbook of Physical Quantities (CRC Press, Boca Raton, Fla., 1997).

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Figures (2)

Fig. 1
Fig. 1

Experimental setup for Michelson interferometry and Fabry–Perot etalon interferometry, where S is the sample, VC is the vacuum chamber, BS is the beam splitter, and D is the detector. For Fabry–Perot etalon experiments, the reference beam is blocked at position 1.

Fig. 2
Fig. 2

Observed relative intensity fluctuations at the detector for (a) Michelson interferometry and (b) Fabry–Perot interferometry for a ZnSe window at 296 K and having a thickness of 4 mm. The intensity spike at 0 deg is due to the reflected beam at normal incidence.

Tables (3)

Tables Icon

Table 1 Temperature-Dependent Refractive-Index Results for GaAs, Ge, Si, and ZnSe

Tables Icon

Table 2 Temperature-Dependent Thickness Results for GaAs, Ge, Si, and ZnSe

Tables Icon

Table 3 Calculated Average Thermo-Optic Coefficients for Ge and ZnSe over the Temperature Ranges of 93 to 296 K and 97 to 296 K, Respectively

Equations (8)

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I t = [ ( 1 - r 2 ) 2 1 + r 4 - 2 r 2 cos ϕ f ] I o ,
ϕ f ( θ ) = 4 π n d λ cos θ t = 4 π d λ n 2 - sin 2 θ ,
I = I r + I s + 2 I r I 2 cos ϕ m ,
ϕ m ( θ ) = [ 4 π d λ ( n 2 - sin 2 θ + 1 - cos θ ) ] .
ϕ m ( θ ) - ϕ f ( θ ) = 4 π d λ ( 1 - cos θ ) ,
I t = [ ( 1 - r 2 ) 2 1 + r 4 - 2 r 2 cos ϕ f ] 2 I o .
ϕ m ( θ ) = m m ( θ ) π = 4 π d g λ [ n t 2 - sin 2 ( θ - θ o ) + 1 - cos ( θ - θ o ) ] + ϕ o ,
ϕ f ( θ ) = m f ( θ ) π = 4 π d g λ n t 2 - sin 2 ( θ - θ o ) + ϕ o ,

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