Abstract

The band spacing of the fringes of equal chromatic order of a thin Fabry–Perot interferometer is compared when this interferometer contains air, a solid, or a liquid. This comparison enables the dispersion of the group velocity of light in these media to be known accurately to 2.4 parts in one thousand. The Sellmeier dispersion function is used to deduce the refractive indices with the same degree of accuracy. The order-transformation method is used to find the exact order values from the roughly known optical thickness. The exact order values for air and the sample are used to find the refractive index accurately to approximately 3 × 10-5. A least-squares fitting of the accurate experimental data to the Sellmeier dispersion function enables the coefficients of the latter to be more precisely defined for solids such as glass and mica and for liquids such as glycerin and distilled water. The atomic parameters such as the density of states and the absorption wavelengths in the ultraviolet region of the spectrum for the given samples are deduced from the more precisely found Sellmeier coefficients.

© 1997 Optical Society of America

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References

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  1. S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Dover, New York, 1970), Chap. 8, p. 96.
  2. O. Svelto, Principles of Lasers, 2nd ed. (Plenum, New York, 1982), Chap. 4, p. 107.
    [CrossRef]
  3. M. A. Khashan, “Application of the Fabry-Perot interferometer as a refractometer,” Opt. Acta 26, 881–888 (1979).
    [CrossRef]
  4. T. S. Izumitani, Optical Glass, Translation Series (American Institute of Physics, New York, 1986), Chap. 5, p. 149.
  5. H. H. Karow, Fabrication Method for Precision Optics (Wiley, New York, 1993), Chap. 1, p. 3.
  6. A. N. Winchell, H. Winchell, Elements of Optical Mineralogy, 1st ed. (Wiley Eastern Private, New Delhi, 1968), Chap. 10, pp. 365–378.
  7. S. S. Ballard, J. S. Browder, J. F. Ebersole, “Optics,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6b, p. 105.
  8. H. M. Dobbins, E. R. Peck, “Change of refractive index of water as a function of temperature,” J. Opt. Soc. Am. 63, 318–320 (1973).
    [CrossRef]
  9. W. M. M. Yunus, “Temperature dependence of refractive index and absorption of NaCl, MgCl2, and Na2SO4 solutions as major components in natural seawater,” Appl. Opt. 31, 2963–2964 (1992).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. B. Richerzhagen, “Interferometer for measuring the absolute refractive index of liquid water as a function of temperature at 1.064 µm,” Appl. Opt. 35, 1850–1853 (1996).
    [CrossRef]
  14. A. Sommerfeld, Optics (Academic, New York, 1967), Chap. 3, p. 105.
  15. L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960), Chap. 4, p. 96.
  16. M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson interferometer,” Optik (Stuttgart) 64, 285–297 (1983).
  17. B. J. Tompson, “Coherence requirements,” in Optical Transforms, H. S. Lipson, ed. (Academic, London, 1972), Chap. 2, pp. 27–69.
  18. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1978), Chap. 2, p. 6.
  19. M. A. Khashan, “Order transformation: a new exact method for the Fabry-Perot spectrometer,” Opt. Acta 26, 873–879 (1979).
    [CrossRef]
  20. M. M. Abdel-Rahman, “Studies on interference refractometry,” Ph.D. dissertation (Ain Shams University, Cairo, Egypt, 1981).
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    [CrossRef]
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    [CrossRef] [PubMed]
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  25. M. A. Khashan, A. Y. Nassif, “Measurement of birefringence, dispersion and line splitting for biaxial crystals by double-layer interferometer,” J. Mod. Opt. 36, 785–796 (1989).
    [CrossRef]

1996

B. Richerzhagen, “Interferometer for measuring the absolute refractive index of liquid water as a function of temperature at 1.064 µm,” Appl. Opt. 35, 1850–1853 (1996).
[CrossRef]

P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566–1573 (1996).
[CrossRef] [PubMed]

1994

K. P. Birch, M. J. Downs, “Correction to the updated Edlen equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

1993

1992

1989

M. A. Khashan, A. Y. Nassif, “Measurement of birefringence, dispersion and line splitting for biaxial crystals by double-layer interferometer,” J. Mod. Opt. 36, 785–796 (1989).
[CrossRef]

1983

M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson interferometer,” Optik (Stuttgart) 64, 285–297 (1983).

1979

M. A. Khashan, “Order transformation: a new exact method for the Fabry-Perot spectrometer,” Opt. Acta 26, 873–879 (1979).
[CrossRef]

M. A. Khashan, “Application of the Fabry-Perot interferometer as a refractometer,” Opt. Acta 26, 881–888 (1979).
[CrossRef]

1973

Abdel-Rahman, M. M.

M. M. Abdel-Rahman, “Studies on interference refractometry,” Ph.D. dissertation (Ain Shams University, Cairo, Egypt, 1981).

Ballard, S. S.

S. S. Ballard, J. S. Browder, J. F. Ebersole, “Optics,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6b, p. 105.

Birch, K. P.

K. P. Birch, M. J. Downs, “Correction to the updated Edlen equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1975), Chap. 13, p. 621.

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1978), Chap. 2, p. 6.

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960), Chap. 4, p. 96.

Browder, J. S.

S. S. Ballard, J. S. Browder, J. F. Ebersole, “Optics,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6b, p. 105.

Chylek, P.

Ciddor, P. E.

Ditchburn, R. W.

R. W. Ditchburn, Light (Blackie, London, 1967), Chap. 15, p. 553.

Dobbins, H. M.

Downs, M. J.

K. P. Birch, M. J. Downs, “Correction to the updated Edlen equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Ebersole, J. F.

S. S. Ballard, J. S. Browder, J. F. Ebersole, “Optics,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6b, p. 105.

Izumitani, T. S.

T. S. Izumitani, Optical Glass, Translation Series (American Institute of Physics, New York, 1986), Chap. 5, p. 149.

Karow, H. H.

H. H. Karow, Fabrication Method for Precision Optics (Wiley, New York, 1993), Chap. 1, p. 3.

Khashan, M. A.

M. A. Khashan, A. Y. Nassif, “Measurement of birefringence, dispersion and line splitting for biaxial crystals by double-layer interferometer,” J. Mod. Opt. 36, 785–796 (1989).
[CrossRef]

M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson interferometer,” Optik (Stuttgart) 64, 285–297 (1983).

M. A. Khashan, “Application of the Fabry-Perot interferometer as a refractometer,” Opt. Acta 26, 881–888 (1979).
[CrossRef]

M. A. Khashan, “Order transformation: a new exact method for the Fabry-Perot spectrometer,” Opt. Acta 26, 873–879 (1979).
[CrossRef]

Kou, L.

Labrie, D.

Lu, W.

Nassif, A. Y.

M. A. Khashan, A. Y. Nassif, “Measurement of birefringence, dispersion and line splitting for biaxial crystals by double-layer interferometer,” J. Mod. Opt. 36, 785–796 (1989).
[CrossRef]

Nemoto, S.

Peck, E. R.

Richerzhagen, B.

B. Richerzhagen, “Interferometer for measuring the absolute refractive index of liquid water as a function of temperature at 1.064 µm,” Appl. Opt. 35, 1850–1853 (1996).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, Optics (Academic, New York, 1967), Chap. 3, p. 105.

Svelto, O.

O. Svelto, Principles of Lasers, 2nd ed. (Plenum, New York, 1982), Chap. 4, p. 107.
[CrossRef]

Tolansky, S.

S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Dover, New York, 1970), Chap. 8, p. 96.

Tompson, B. J.

B. J. Tompson, “Coherence requirements,” in Optical Transforms, H. S. Lipson, ed. (Academic, London, 1972), Chap. 2, pp. 27–69.

Winchell, A. N.

A. N. Winchell, H. Winchell, Elements of Optical Mineralogy, 1st ed. (Wiley Eastern Private, New Delhi, 1968), Chap. 10, pp. 365–378.

Winchell, H.

A. N. Winchell, H. Winchell, Elements of Optical Mineralogy, 1st ed. (Wiley Eastern Private, New Delhi, 1968), Chap. 10, pp. 365–378.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1975), Chap. 13, p. 621.

Worek, W. M.

Yunus, W. M. M.

Appl. Opt.

J. Mod. Opt.

M. A. Khashan, A. Y. Nassif, “Measurement of birefringence, dispersion and line splitting for biaxial crystals by double-layer interferometer,” J. Mod. Opt. 36, 785–796 (1989).
[CrossRef]

J. Opt. Soc. Am.

Metrologia

K. P. Birch, M. J. Downs, “Correction to the updated Edlen equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Opt. Acta

M. A. Khashan, “Order transformation: a new exact method for the Fabry-Perot spectrometer,” Opt. Acta 26, 873–879 (1979).
[CrossRef]

M. A. Khashan, “Application of the Fabry-Perot interferometer as a refractometer,” Opt. Acta 26, 881–888 (1979).
[CrossRef]

Optik (Stuttgart)

M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson interferometer,” Optik (Stuttgart) 64, 285–297 (1983).

Other

B. J. Tompson, “Coherence requirements,” in Optical Transforms, H. S. Lipson, ed. (Academic, London, 1972), Chap. 2, pp. 27–69.

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1978), Chap. 2, p. 6.

M. M. Abdel-Rahman, “Studies on interference refractometry,” Ph.D. dissertation (Ain Shams University, Cairo, Egypt, 1981).

T. S. Izumitani, Optical Glass, Translation Series (American Institute of Physics, New York, 1986), Chap. 5, p. 149.

H. H. Karow, Fabrication Method for Precision Optics (Wiley, New York, 1993), Chap. 1, p. 3.

A. N. Winchell, H. Winchell, Elements of Optical Mineralogy, 1st ed. (Wiley Eastern Private, New Delhi, 1968), Chap. 10, pp. 365–378.

S. S. Ballard, J. S. Browder, J. F. Ebersole, “Optics,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6b, p. 105.

A. Sommerfeld, Optics (Academic, New York, 1967), Chap. 3, p. 105.

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960), Chap. 4, p. 96.

S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Dover, New York, 1970), Chap. 8, p. 96.

O. Svelto, Principles of Lasers, 2nd ed. (Plenum, New York, 1982), Chap. 4, p. 107.
[CrossRef]

R. W. Ditchburn, Light (Blackie, London, 1967), Chap. 15, p. 553.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1975), Chap. 13, p. 621.

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Figures (5)

Fig. 1
Fig. 1

Setup to photograph spectra channeled with a thin FPI containing a liquid or a solid sample together with air. The definitions of the optical components are given in the text.

Fig. 2
Fig. 2

Spectra channeled with a thin FPI filled with air together with (a) glass, (b) glycerin, (c) water, (d) mica.

Fig. 3
Fig. 3

Dispersion of nG (filled circles) and n (curved lines) for glass (upper) and glycerin (lower). The dispersion curves are calculated by Eq. (9) for nG and Eq. (6) for n so as to fit the experimental points.

Fig. 4
Fig. 4

Fit of the Sellmeier function (curves) so as to find accurate refractive-indices n of four samples (filled circles). The Sellmeier coefficients are given in Table 3 to an accuracy of approximately 3 × 10-5.

Fig. 5
Fig. 5

Dispersion of the mica birefringence. The experimental results (filled circles) are fit to the dispersion formula of Eq. (29) (curved line).

Tables (3)

Tables Icon

Table 1 Values of nG and n for Four Different Samplesa

Tables Icon

Table 2 Application of the Order-Transformation Method to Find the Accurate Order Values for Air and Glycerin

Tables Icon

Table 3 Accurate Atomic Parameters of the Sellmeier Dispersion Functiona

Equations (30)

Equations on this page are rendered with MathJax. Learn more.

n2-1=2aikλ2/λ2-λik2.
aik=r0/2πNfikλik2,
r0=e2/m0c2.
Ψik=lnλ/λik,
n2-1=aik1+coth Ψik.
n2-b=aUV1+coth ΨUV+aIR1+coth ΨIR,
b=1+2amn
G=1-λ/ndn/dλ.
n2G2-b=aUV1+coth ΨUVcoth ΨUV+aIR×1+coth ΨIRcoth ΨIR.
2nLσ+τ=p,
Δσ=1/2nGL.
nG/naGa=Δxa/Δx.
nG=Δxa/Δx.
nL=p-τλ/2.
2n1σ1-n2σ2L+τ1-τ2=m,
2nGL+dτ/dσ=m/Δσ,
p1=q1/Gm-Δτ+τ1,
p2=q2/Gm-Δτ+τ2.
q1=σ1/σ1-σ2,  q2=σ2/σ1-σ2.
δq=qδλ/λ+2δλ/Δλ.
pc=qm/G.
δpc=pcδm/m2+δq/q2+δG/G21/2.
n1-n2=p1λ1-p2λ2/2L
n1-n2=n1-Gλ1-λ2/λ,
Δσa=1/2naGaL,
n=nap-τ/pa-τa.
τ=1/πarctan2niks/ni2-ns2-ks2
δn=n2δε/pa2+2δε/p2+δna/na21/2.
no-ne=1/2n1+coth ΨUVΔaUV+Δb.
Δa/a=2Δλ/λ+ΔN/N.

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