Abstract

The rings of equal inclination of the double-layer interferometer disappear in their common center if a plane-parallel glass plate is rotated inside one of the interferometer gaps that is filled with a liquid. Knowledge of the ring count and the rotated angle allows the refractive indices of both the rotated plate and the liquid to be found from a new analytical formula accurate to ±0.0004. The experimental results for glass, distilled water, and methanol are fitted to the Sellmeier dispersion function to determine their quantum parameters such as the absorption wavelengths in the ultraviolet side of the spectrum and the atomic number densities contributing to these absorption bands.

© 2000 Optical Society of America

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References

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  1. M. A. Khashan, “Multiple-beam interference refractomter and comparator,” Optik 35, 421–430 (1972).
  2. M. A. Khashan, “Channeled spectrum with the double-layer interferometer,” Opt. Commun. 8, 220–221 (1973).
    [CrossRef]
  3. M. A. Khashan, “Measurement of group-velocity dispersion by double-layer interferometer,” Optik 76, 73–77 (1987).
  4. M. A. Khashan, “Phase multiplication: a new method for interference microscopy,” Opt. Acta 22, 1011–1033 (1975).
    [CrossRef]
  5. S. Tolansky, Introduction to Interferometry (Longmans, London, 1955), Chap. 12, pp. 144–146.
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975), Chap. 2, pp. 90–98, and Chap. 7, pp. 364–367.
  7. R. W. Ditchburn, Light (Blakie, London, 1967), Chap. 4, pp. 79–85, and Chap. 15, 562–571.
  8. 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]
  9. A. Y. Nassif, “Accurate measurement of refraction and dispersion of a solid by a double-layer interferometer,” Appl. Opt. 36, 779–785 (1997).
    [CrossRef] [PubMed]
  10. M. A. Khashan, A. Y. Nassif, “On the application of the Lummer–Gehrcke plate as a high-resolution spectrometer and a laser wavemeter,” Optik 104, 133–141 (1997).
  11. M. A. Khashan, “Order transformation: a new exact method for the Fabry–Perot spectrometer,” Opt. Acta 26, 873–879 (1979).
    [CrossRef]
  12. M. A. Khashan, “Application of the Fabry–Perot interferometer as a refractometer,” Opt. Acta 26, 881–888 (1979).
    [CrossRef]
  13. G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, UK, 1986), Chap. 2, 9–19.
  14. J. M. Vaughan, The Fabry–Perot Interferometer: History, Theory, Practice and Applications (Hilger, Bristol, UK, 1989), Chap. 3, 97–101.
  15. C. Candler, Modern Interferometers (Hilger and Watts, Glasgow, Scotland, UK, 1951), Chap. 5, 112–115.
  16. M. S. Shumate, “Interferometric measurement of large indices of refraction,” Appl. Opt. 5, 327–331 (1966).
    [CrossRef] [PubMed]
  17. S. De Nicola, P. Ferraro, A. Finizio, G. Pesce, G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118, 491–494 (1995).
    [CrossRef]
  18. H. Rudolph, “Photoelectric polarimeter attachment,” J. Opt. Soc. Am. 45, 50–59 (1955).
    [CrossRef]
  19. P. S. Theocaris, Moiré Fringes in Strain Analysis (Pergamon, Oxford, UK, 1969), Chap. 2, 19–30.
    [CrossRef]
  20. O. Kafri, I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1990), Chap. 1, 5–13.
  21. A. Sommerfeld, Optics (Academic, New York, 1967), Chap. 21, pp. 88–106.
  22. 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. 6e, p. 105.
  23. F. Kitayeva, A. Mazing, P. Presniakov, “Optics and Roentgen radiation,” in Tables of Physical Quantities (Atomizdat, Moscow, 1976), Chap. 31, p. 635 (in Russian).
  24. K. F. Palmer, D. Williams, “Optical properties of water in the near infrared,” J. Opt. Soc. Am. 64, 1107–1110 (1974).
    [CrossRef]

1997

M. A. Khashan, A. Y. Nassif, “On the application of the Lummer–Gehrcke plate as a high-resolution spectrometer and a laser wavemeter,” Optik 104, 133–141 (1997).

A. Y. Nassif, “Accurate measurement of refraction and dispersion of a solid by a double-layer interferometer,” Appl. Opt. 36, 779–785 (1997).
[CrossRef] [PubMed]

1995

S. De Nicola, P. Ferraro, A. Finizio, G. Pesce, G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118, 491–494 (1995).
[CrossRef]

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]

1987

M. A. Khashan, “Measurement of group-velocity dispersion by double-layer interferometer,” Optik 76, 73–77 (1987).

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]

1975

M. A. Khashan, “Phase multiplication: a new method for interference microscopy,” Opt. Acta 22, 1011–1033 (1975).
[CrossRef]

1974

1973

M. A. Khashan, “Channeled spectrum with the double-layer interferometer,” Opt. Commun. 8, 220–221 (1973).
[CrossRef]

1972

M. A. Khashan, “Multiple-beam interference refractomter and comparator,” Optik 35, 421–430 (1972).

1966

1955

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. 6e, p. 105.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975), Chap. 2, pp. 90–98, and Chap. 7, pp. 364–367.

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. 6e, p. 105.

De Nicola, S.

S. De Nicola, P. Ferraro, A. Finizio, G. Pesce, G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118, 491–494 (1995).
[CrossRef]

Ditchburn, R. W.

R. W. Ditchburn, Light (Blakie, London, 1967), Chap. 4, pp. 79–85, and Chap. 15, 562–571.

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. 6e, p. 105.

Ferraro, P.

S. De Nicola, P. Ferraro, A. Finizio, G. Pesce, G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118, 491–494 (1995).
[CrossRef]

Finizio, A.

S. De Nicola, P. Ferraro, A. Finizio, G. Pesce, G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118, 491–494 (1995).
[CrossRef]

Glatt, I.

O. Kafri, I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1990), Chap. 1, 5–13.

Hernandez, G.

G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, UK, 1986), Chap. 2, 9–19.

Kafri, O.

O. Kafri, I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1990), Chap. 1, 5–13.

Khashan, M. A.

M. A. Khashan, A. Y. Nassif, “On the application of the Lummer–Gehrcke plate as a high-resolution spectrometer and a laser wavemeter,” Optik 104, 133–141 (1997).

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, “Measurement of group-velocity dispersion by double-layer interferometer,” Optik 76, 73–77 (1987).

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]

M. A. Khashan, “Phase multiplication: a new method for interference microscopy,” Opt. Acta 22, 1011–1033 (1975).
[CrossRef]

M. A. Khashan, “Channeled spectrum with the double-layer interferometer,” Opt. Commun. 8, 220–221 (1973).
[CrossRef]

M. A. Khashan, “Multiple-beam interference refractomter and comparator,” Optik 35, 421–430 (1972).

Kitayeva, F.

F. Kitayeva, A. Mazing, P. Presniakov, “Optics and Roentgen radiation,” in Tables of Physical Quantities (Atomizdat, Moscow, 1976), Chap. 31, p. 635 (in Russian).

Mazing, A.

F. Kitayeva, A. Mazing, P. Presniakov, “Optics and Roentgen radiation,” in Tables of Physical Quantities (Atomizdat, Moscow, 1976), Chap. 31, p. 635 (in Russian).

Nassif, A. Y.

M. A. Khashan, A. Y. Nassif, “On the application of the Lummer–Gehrcke plate as a high-resolution spectrometer and a laser wavemeter,” Optik 104, 133–141 (1997).

A. Y. Nassif, “Accurate measurement of refraction and dispersion of a solid by a double-layer interferometer,” Appl. Opt. 36, 779–785 (1997).
[CrossRef] [PubMed]

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]

Palmer, K. F.

Pesce, G.

S. De Nicola, P. Ferraro, A. Finizio, G. Pesce, G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118, 491–494 (1995).
[CrossRef]

Pierattini, G.

S. De Nicola, P. Ferraro, A. Finizio, G. Pesce, G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118, 491–494 (1995).
[CrossRef]

Presniakov, P.

F. Kitayeva, A. Mazing, P. Presniakov, “Optics and Roentgen radiation,” in Tables of Physical Quantities (Atomizdat, Moscow, 1976), Chap. 31, p. 635 (in Russian).

Rudolph, H.

Shumate, M. S.

Sommerfeld, A.

A. Sommerfeld, Optics (Academic, New York, 1967), Chap. 21, pp. 88–106.

Theocaris, P. S.

P. S. Theocaris, Moiré Fringes in Strain Analysis (Pergamon, Oxford, UK, 1969), Chap. 2, 19–30.
[CrossRef]

Tolansky, S.

S. Tolansky, Introduction to Interferometry (Longmans, London, 1955), Chap. 12, pp. 144–146.

Vaughan, J. M.

J. M. Vaughan, The Fabry–Perot Interferometer: History, Theory, Practice and Applications (Hilger, Bristol, UK, 1989), Chap. 3, 97–101.

Williams, D.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975), Chap. 2, pp. 90–98, and Chap. 7, pp. 364–367.

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.

Opt. Acta

M. A. Khashan, “Phase multiplication: a new method for interference microscopy,” Opt. Acta 22, 1011–1033 (1975).
[CrossRef]

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]

Opt. Commun.

M. A. Khashan, “Channeled spectrum with the double-layer interferometer,” Opt. Commun. 8, 220–221 (1973).
[CrossRef]

S. De Nicola, P. Ferraro, A. Finizio, G. Pesce, G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118, 491–494 (1995).
[CrossRef]

Optik

M. A. Khashan, “Multiple-beam interference refractomter and comparator,” Optik 35, 421–430 (1972).

M. A. Khashan, “Measurement of group-velocity dispersion by double-layer interferometer,” Optik 76, 73–77 (1987).

M. A. Khashan, A. Y. Nassif, “On the application of the Lummer–Gehrcke plate as a high-resolution spectrometer and a laser wavemeter,” Optik 104, 133–141 (1997).

Other

S. Tolansky, Introduction to Interferometry (Longmans, London, 1955), Chap. 12, pp. 144–146.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975), Chap. 2, pp. 90–98, and Chap. 7, pp. 364–367.

R. W. Ditchburn, Light (Blakie, London, 1967), Chap. 4, pp. 79–85, and Chap. 15, 562–571.

G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, UK, 1986), Chap. 2, 9–19.

J. M. Vaughan, The Fabry–Perot Interferometer: History, Theory, Practice and Applications (Hilger, Bristol, UK, 1989), Chap. 3, 97–101.

C. Candler, Modern Interferometers (Hilger and Watts, Glasgow, Scotland, UK, 1951), Chap. 5, 112–115.

P. S. Theocaris, Moiré Fringes in Strain Analysis (Pergamon, Oxford, UK, 1969), Chap. 2, 19–30.
[CrossRef]

O. Kafri, I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1990), Chap. 1, 5–13.

A. Sommerfeld, Optics (Academic, New York, 1967), Chap. 21, pp. 88–106.

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. 6e, p. 105.

F. Kitayeva, A. Mazing, P. Presniakov, “Optics and Roentgen radiation,” in Tables of Physical Quantities (Atomizdat, Moscow, 1976), Chap. 31, p. 635 (in Russian).

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Figures (6)

Fig. 1
Fig. 1

(a) Double-layer interferometer assembled from three glass plates whose plane faces are silvered to serve as three mirrors (dense lines) separating two wide gaps in tandem. (b) On the calculation of the optical path length of an axial ray refracted through a rotatable plate, P, associated with a rotating system of Cartesian coordinates.

Fig. 2
Fig. 2

Schematic diagram of a setup to produce and observe the rings of equal inclination of a double-layer interferometer via a constant-deviation prism spectroscope of moderate dispersion and resolution. The optical elements and their functions are defined in the text.

Fig. 3
Fig. 3

Photograph of rings of equal inclination produced by the double-layer interferometer and recorded in the focal plane of a constant-deviation prism spectrograph separating the Cd, Na, and Hg broad lines, whose wavelengths decrease from left to right. The rings of Hg yellow doublet (to the left) overlap because a spectrograph slit of 1-mm width was used.

Fig. 4
Fig. 4

Plots of sin2 θ versus the order change, Δk, for a glass plate (K8) having a thickness of 4.005 mm and rotating in air inside one of the DLI gaps at a temperature of 26 °C.

Fig. 5
Fig. 5

Plots of sin2 θ versus the order change, Δk, for distilled water in which a glass plate is rotated at 26 °C temperature inside one of the DLI gaps.

Fig. 6
Fig. 6

Dispersion of glass BaLK, glass K8, methanol, and distilled water at 26 °C temperature. The open symbols represent the experimental data, and the solid curves represent the Sellmeier functions that are fitted to these data by a least-squares process.

Tables (1)

Tables Icon

Table 1 Dependence on the Wavelength of the Refractive Indices of Two Solid Samples, K8 and BaLK Glasses, and Two Liquids, Distilled Water and Methanol, at 26 °C Temperaturea

Equations (37)

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2D+n cos θ-n cos θt=kλ,
D=nl-nolo
2n cos θ-n cos θt=kλ.
2nt cos θ=pλ  2nt cos θ=pλ,
k=p-p.
nt sin2 θ=jλ,
n2t/nsin2 θ=jλ.
cos θ=p/po,  cos θ=p/po,
po=2nt/λ,  po=2nt/λ,
ko=po-po=2n-nt/λ,
j=po-p,  j=po-p,
2n-n1-n/2nsin2 θt=kλ.
sin2 θ=AΔk,
A=nλ/nn-nt.
n=n/1-λ/ntA,
n=n/21+1-4λ/ntA1/2.
δn=n/λδλ2+n/naδna2+n/tδt2+n/AδA21/2.
δA/A=δΔk/Δk2+2δθ/tan θ21/2
δn=n/λδλ2+n/nδn2+n/tδt2+n/AδA21/2
S=q1λ1/2=q2λ2/2,
q1=λ2/λ2-λ1,  q2=λ1/λ2-λ1.
m=n-nt/S.
ko1=mq1,  ko2=mq2
δko/ko=δm/m2+δq/q21/2.
δq/q=2δλ/Δλ2+δλ/λ21/2.
n=na+koλ/2t,
δn=δna2+koδλ/2t2+λδko/2t2+koλδt/2t221/2.
n=n-koλ/2t.
n2=1+j=i+1 aijλ/λij2-1/λ/λij-λij/λ2+1/Qij2.
aij=reNfijλij2/π,
re=e2/mec2=2.818×10-13 cm,
Qij=λij/δλij.
n2=A+B/λ2+C/λ4+.
n2=1+Σaij/1-λij/λ2
A=1+Σaij,  B=Σaijλij2,  C=Σaijλij4.
n2=aij/1-λij/λ2+b.
b=1+Σaij,

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