Abstract

A laser interferometric measurement technique that uses a Mach–Zehnder interferometer is developed. This technique permits studies of the physical processes that involve a change in the refractive index with temperature to a high degree of accuracy. A theoretical derivation has been formulated to permit computation of the refractive index of transparent materials. The technique is particularly useful in studying slight changes in refractive index of various gases, solutions over a considerable region, and flow patterns in wind tunnels.

© 1994 Optical Society of America

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References

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  1. K. B. Newbound, “Refractive indices of water vapor and carbon dioxide at low pressure,” J. Opt. Soc. Am. 39, 835–840 (1949).
    [CrossRef]
  2. D. E. McCarthy, “Refractive index measurements of silver bromide in the infrared,” Appl. Opt. 12, 409 (1973).
    [CrossRef] [PubMed]
  3. J. H. Shaw, “Thin film infrared channel spectra,” Appl. Opt. 13, 2465–2467 (1974).
    [CrossRef] [PubMed]
  4. M. A. Khashan, “Channelled spectrum with the double-layer interferometer,” Opt. Commun. 8, 220–221 (1973).
    [CrossRef]
  5. M. A. Khashan, “Measurement of group-velocity dispersion by double-layer interferometer,” Optik (Stuttgart) 76, 73–77 (1987).
  6. A. J. T. Holmes, J. R. Cozens, “Interferometric measurements of the gas density distribution in the dark space of an abnormal glow discharge in xenon,” J. Phys. D 8, 400–404 (1975).
    [CrossRef]
  7. M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson interferometer,” Optik (Stuttgart) 64, 285–297 (1983).
  8. N. Barakat, A. M. Hamed, F. Sharaf, “Study of thermal source using two-beam interference,” Opt. Laser Technol. 24, 23–26 (1992).
    [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1965), Chap. 7, p. 312.
  10. F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics, 1st ed. (Prentice-Hall, Englewood Cliffs, N.J., 1987), Chap. 14, p. 285.
  11. H. El-Kashef, G. E. Hassan, “New development of Mach–Zehnder interferometer for laser frequency selection and tuning,” J. Mod. Opt. 39, 43–47 (1992).
    [CrossRef]
  12. H. El-Kashef, “New high interferometric quality dye laser jet nozzle,” Opt. Commun. 100, 141–146 (1993).
    [CrossRef]
  13. H. El-Kashef, G. E. Hassan, “Stability conditions of the dye-laser circulation system,” Acta Phys. Slovaca 42, 305–309 (1992).
  14. H. El-Kashef, G. E. Hassan, “Computerized technique for high precision laser beam transformation,” Bulg. J. Phys. 18, 337–340 (1991).
  15. A. G. Bathelt, R. Viskanta, “Heat transfer and interface motion during melting and solidification around a finned heat source/sink,” J. Heat Transfer 103, 720–726 (1981).
    [CrossRef]

1993 (1)

H. El-Kashef, “New high interferometric quality dye laser jet nozzle,” Opt. Commun. 100, 141–146 (1993).
[CrossRef]

1992 (3)

H. El-Kashef, G. E. Hassan, “Stability conditions of the dye-laser circulation system,” Acta Phys. Slovaca 42, 305–309 (1992).

N. Barakat, A. M. Hamed, F. Sharaf, “Study of thermal source using two-beam interference,” Opt. Laser Technol. 24, 23–26 (1992).
[CrossRef]

H. El-Kashef, G. E. Hassan, “New development of Mach–Zehnder interferometer for laser frequency selection and tuning,” J. Mod. Opt. 39, 43–47 (1992).
[CrossRef]

1991 (1)

H. El-Kashef, G. E. Hassan, “Computerized technique for high precision laser beam transformation,” Bulg. J. Phys. 18, 337–340 (1991).

1987 (1)

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

1983 (1)

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

1981 (1)

A. G. Bathelt, R. Viskanta, “Heat transfer and interface motion during melting and solidification around a finned heat source/sink,” J. Heat Transfer 103, 720–726 (1981).
[CrossRef]

1975 (1)

A. J. T. Holmes, J. R. Cozens, “Interferometric measurements of the gas density distribution in the dark space of an abnormal glow discharge in xenon,” J. Phys. D 8, 400–404 (1975).
[CrossRef]

1974 (1)

1973 (2)

D. E. McCarthy, “Refractive index measurements of silver bromide in the infrared,” Appl. Opt. 12, 409 (1973).
[CrossRef] [PubMed]

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

1949 (1)

Barakat, N.

N. Barakat, A. M. Hamed, F. Sharaf, “Study of thermal source using two-beam interference,” Opt. Laser Technol. 24, 23–26 (1992).
[CrossRef]

Bathelt, A. G.

A. G. Bathelt, R. Viskanta, “Heat transfer and interface motion during melting and solidification around a finned heat source/sink,” J. Heat Transfer 103, 720–726 (1981).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1965), Chap. 7, p. 312.

Cozens, J. R.

A. J. T. Holmes, J. R. Cozens, “Interferometric measurements of the gas density distribution in the dark space of an abnormal glow discharge in xenon,” J. Phys. D 8, 400–404 (1975).
[CrossRef]

El-Kashef, H.

H. El-Kashef, “New high interferometric quality dye laser jet nozzle,” Opt. Commun. 100, 141–146 (1993).
[CrossRef]

H. El-Kashef, G. E. Hassan, “Stability conditions of the dye-laser circulation system,” Acta Phys. Slovaca 42, 305–309 (1992).

H. El-Kashef, G. E. Hassan, “New development of Mach–Zehnder interferometer for laser frequency selection and tuning,” J. Mod. Opt. 39, 43–47 (1992).
[CrossRef]

H. El-Kashef, G. E. Hassan, “Computerized technique for high precision laser beam transformation,” Bulg. J. Phys. 18, 337–340 (1991).

Hamed, A. M.

N. Barakat, A. M. Hamed, F. Sharaf, “Study of thermal source using two-beam interference,” Opt. Laser Technol. 24, 23–26 (1992).
[CrossRef]

Hassan, G. E.

H. El-Kashef, G. E. Hassan, “Stability conditions of the dye-laser circulation system,” Acta Phys. Slovaca 42, 305–309 (1992).

H. El-Kashef, G. E. Hassan, “New development of Mach–Zehnder interferometer for laser frequency selection and tuning,” J. Mod. Opt. 39, 43–47 (1992).
[CrossRef]

H. El-Kashef, G. E. Hassan, “Computerized technique for high precision laser beam transformation,” Bulg. J. Phys. 18, 337–340 (1991).

Holmes, A. J. T.

A. J. T. Holmes, J. R. Cozens, “Interferometric measurements of the gas density distribution in the dark space of an abnormal glow discharge in xenon,” J. Phys. D 8, 400–404 (1975).
[CrossRef]

Khashan, M. A.

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

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

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

McCarthy, D. E.

Newbound, K. B.

Pedrotti, F. L.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics, 1st ed. (Prentice-Hall, Englewood Cliffs, N.J., 1987), Chap. 14, p. 285.

Pedrotti, L. S.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics, 1st ed. (Prentice-Hall, Englewood Cliffs, N.J., 1987), Chap. 14, p. 285.

Sharaf, F.

N. Barakat, A. M. Hamed, F. Sharaf, “Study of thermal source using two-beam interference,” Opt. Laser Technol. 24, 23–26 (1992).
[CrossRef]

Shaw, J. H.

Viskanta, R.

A. G. Bathelt, R. Viskanta, “Heat transfer and interface motion during melting and solidification around a finned heat source/sink,” J. Heat Transfer 103, 720–726 (1981).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1965), Chap. 7, p. 312.

Acta Phys. Slovaca (1)

H. El-Kashef, G. E. Hassan, “Stability conditions of the dye-laser circulation system,” Acta Phys. Slovaca 42, 305–309 (1992).

Appl. Opt. (2)

Bulg. J. Phys. (1)

H. El-Kashef, G. E. Hassan, “Computerized technique for high precision laser beam transformation,” Bulg. J. Phys. 18, 337–340 (1991).

J. Heat Transfer (1)

A. G. Bathelt, R. Viskanta, “Heat transfer and interface motion during melting and solidification around a finned heat source/sink,” J. Heat Transfer 103, 720–726 (1981).
[CrossRef]

J. Mod. Opt. (1)

H. El-Kashef, G. E. Hassan, “New development of Mach–Zehnder interferometer for laser frequency selection and tuning,” J. Mod. Opt. 39, 43–47 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. D (1)

A. J. T. Holmes, J. R. Cozens, “Interferometric measurements of the gas density distribution in the dark space of an abnormal glow discharge in xenon,” J. Phys. D 8, 400–404 (1975).
[CrossRef]

Opt. Commun. (2)

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

H. El-Kashef, “New high interferometric quality dye laser jet nozzle,” Opt. Commun. 100, 141–146 (1993).
[CrossRef]

Opt. Laser Technol. (1)

N. Barakat, A. M. Hamed, F. Sharaf, “Study of thermal source using two-beam interference,” Opt. Laser Technol. 24, 23–26 (1992).
[CrossRef]

Optik (Stuttgart) (2)

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

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

Other (2)

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1965), Chap. 7, p. 312.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics, 1st ed. (Prentice-Hall, Englewood Cliffs, N.J., 1987), Chap. 14, p. 285.

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Figures (5)

Fig. 1
Fig. 1

Mach–Zehnder optical circuit: HR, high reflectivity (=100%).

Fig. 2
Fig. 2

Graphic representation of Eq. (3).

Fig. 3
Fig. 3

One of the recorded interferograms of the fringe pattern.

Fig. 4
Fig. 4

Thickness fluctuations (nm) as a function of flow velocity (m/s).

Fig. 5
Fig. 5

Thermal coefficient of the index of refraction dn/dT: (a) water, (b) ethylene glycol, (c) paraffin wax, (d) water and ethylene glycol (1:1).

Equations (5)

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N λ = t ( n 2 - sin 2 θ ) 1 / 2 - t cos θ - n t + t ,
( n 2 - sin 2 θ ) 1 / 2 = N λ t + cos θ + n - 1 ,
1 sin 2 θ / 2 = [ 2 t λ n ( n - 1 ) ] 1 N + 2 n .
n 2 t - n 1 t = N λ , ( n 2 - n 1 ) t = N λ ,
Δ n = N λ / t .

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