Abstract

The particle density of ground-state chromium atoms within one cross section of an arc plasma was measured spatially resolved, and the spatial distribution of the line shape of the chromium resonance line at 427.48 nm was partly determined. The measurements were performed with a newly developed setup that combines the methods of resonance interferometry and refractive tomography. The wavelength of a dye laser was scanned over the investigated transition, and the refractive index was measured spatially and spectrally resolved by use of tomography. For each spatial point the particle density and the local line shape were calculated from the measured spectral refractivity distribution by the method of resonance interferometry. We describe the physical principles, the optical arrangement, and the numerical apparatus, and we discuss the results and further possibilities.

© 1997 Optical Society of America

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References

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    [CrossRef]
  7. T. Neger, “Optical tomography by spectral interferometry,” J. Phys. D 28, 47–54 (1995).
    [CrossRef]
  8. M Ulbel, G Pretzler, “White-light interferometric tomography for particle density determination in a free-burning arc,” J. Phys. D (to be published).
  9. G. Pretzler, “Single-shot tomography by differential interferometry,” Meas. Sci. Technol. 6, 1476–1486 (1995).
    [CrossRef]
  10. G. V. Dreiden, A. N. Zaidel’, G. V. Ostrovskaya, Yu. I. Ostrovskii, N. A. Pobedonostseva, L. V. Tanin, V. N. Filippov, E. N. Shedova, “Plasma diagnostics by resonant interferometry and holography,” Sov. J. Plasma Phys. 1, 256–267 (1975).
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    [CrossRef] [PubMed]
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  14. R. W. Ditchburn, Light, 3rd ed. (Academic, London, 1976).
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  16. A. Unsöld, Physik der Strernatmosphären (Springer-Verlag, Berlin, 1955).
  17. G. Traving, Über die Theorie der Druckverbreiterung der Spektrallinien (Braun, Karlsruhe, Germany, 1960).
  18. H. Griem, Spectral Line Broadening by Plasmas (Academic, New York, 1974).
  19. C. Haas, G. Pretzler, T. Neger, H. Jäger, “Determination of particle densities and line profiles in plasmas by resonance interferometry: A feasability study using computer simulated refractivity data,” Z. Naturforsch. A 50, 902–914 (1995).
  20. J Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Verh. Saechs. Akad. Wiss. Leipzig, Math.-Phys. Kl. 69, 292 (1917).
  21. A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications,” J. Appl. Phys. 34, 2722–2727 (1963).
    [CrossRef]
  22. G. Hounsfield, “Computerized transverse axial scanning tomography, Part I: Description of the system,” Br. J. Radiol. 46, 1016 (1973).
    [CrossRef] [PubMed]
  23. H. Barrett, W. Swindell, Radiologic Imaging (Academic, New York, 1981).
  24. R. Bracewell, “Strip integration in radio astronomy,” Aust. J. Phys. 9, 198–217 (1956).
    [CrossRef]
  25. R. Snyder, L. Hesselink, “Optical tomography for flow visualization of the density field around a revolving helicopter rotor blade,” Appl. Opt. 23, 3650–3656 (1984).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  27. L. Hesselink, “Optical tomography,” in Handbook of Flow Visualization, W.-J. Yang, ed. (Hemisphere, New York, 1989), pp. 307–329.
  28. K. Widmann, G. Pretzler, J. Woisetschläger, H. Philipp, T. Neger, H. Jäger, “Interferometric determination of the electron density in a high-pressure xenon lamp with a holographic optical element,” Appl. Opt. 35, 5896–5903 (1996).
    [CrossRef] [PubMed]
  29. G. Pretzler, H. Jäger, T. Neger, “High-accuracy differential interferometry for the investigation of phase objects,” Meas. Sci. Technol. 4, 649–658 (1993).
    [CrossRef]
  30. H. Philipp, T. Neger, H. Jäger, J. Woisetschläger, “Optical tomography of phase objects by holographic interferometry,” Measurement 10, 170–181 (1992).
    [CrossRef]
  31. G. Pujol, S. Weniger, “Broadening and shift of neutral chromium absorption lines by various perturbing gases,” J. Quant. Spectrosc. Radiat. Transfer 22, 145–153 (1979).
    [CrossRef]
  32. T Hollander, A De Leeuw, E Ter Horst, “Determination of line broadening parameters for chromium triplet lines (a7S → z7P0 transition) in a C2H2-air flame,” Spectrochim. Acta, Part B 38, 691–695 (1983).

1996 (1)

1995 (4)

J. E. Millerd, N. J. Brock, M. S. Brown, P. A. DeBarber, “Real-time resonant holography using bacteriorhodopsin thin films,” Opt. Lett. 20, 626–628 (1995).
[CrossRef] [PubMed]

T. Neger, “Optical tomography by spectral interferometry,” J. Phys. D 28, 47–54 (1995).
[CrossRef]

G. Pretzler, “Single-shot tomography by differential interferometry,” Meas. Sci. Technol. 6, 1476–1486 (1995).
[CrossRef]

C. Haas, G. Pretzler, T. Neger, H. Jäger, “Determination of particle densities and line profiles in plasmas by resonance interferometry: A feasability study using computer simulated refractivity data,” Z. Naturforsch. A 50, 902–914 (1995).

1993 (1)

G. Pretzler, H. Jäger, T. Neger, “High-accuracy differential interferometry for the investigation of phase objects,” Meas. Sci. Technol. 4, 649–658 (1993).
[CrossRef]

1992 (1)

H. Philipp, T. Neger, H. Jäger, J. Woisetschläger, “Optical tomography of phase objects by holographic interferometry,” Measurement 10, 170–181 (1992).
[CrossRef]

1991 (1)

J. Woisetschläger, H. Jäger, H. Philipp, G. Pfeifer, T. Neger, “Tomographic investigation of the particle density distribution of sodium atoms in a glow discharge using heterodyne holographic interferometry,” Phys. Lett. A 152, 42–46 (1991).
[CrossRef]

1987 (1)

1986 (2)

G. W. Faris, R. L. Byer, “Quantitative optical tomographic imaging of a supersonic jet,” Opt. Lett. 11, 413–415 (1986).
[CrossRef] [PubMed]

R. Koslover, R. McWilliams, “Measurement of multidimensional ion velocity distributions by optical tomography,” Rev. Sci. Instrum. 57, 2441–2448 (1986).
[CrossRef]

1984 (2)

1983 (2)

T Hollander, A De Leeuw, E Ter Horst, “Determination of line broadening parameters for chromium triplet lines (a7S → z7P0 transition) in a C2H2-air flame,” Spectrochim. Acta, Part B 38, 691–695 (1983).

E. Kügler, D. Bershader, “Recent high-resolution resonant refractivity studies of a sodium-seeded flame,” Exp. Fluids 1, 1–9 (1983).
[CrossRef]

1979 (1)

G. Pujol, S. Weniger, “Broadening and shift of neutral chromium absorption lines by various perturbing gases,” J. Quant. Spectrosc. Radiat. Transfer 22, 145–153 (1979).
[CrossRef]

1975 (1)

G. V. Dreiden, A. N. Zaidel’, G. V. Ostrovskaya, Yu. I. Ostrovskii, N. A. Pobedonostseva, L. V. Tanin, V. N. Filippov, E. N. Shedova, “Plasma diagnostics by resonant interferometry and holography,” Sov. J. Plasma Phys. 1, 256–267 (1975).

1973 (1)

G. Hounsfield, “Computerized transverse axial scanning tomography, Part I: Description of the system,” Br. J. Radiol. 46, 1016 (1973).
[CrossRef] [PubMed]

1966 (1)

1963 (1)

A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications,” J. Appl. Phys. 34, 2722–2727 (1963).
[CrossRef]

1956 (1)

R. Bracewell, “Strip integration in radio astronomy,” Aust. J. Phys. 9, 198–217 (1956).
[CrossRef]

1917 (1)

J Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Verh. Saechs. Akad. Wiss. Leipzig, Math.-Phys. Kl. 69, 292 (1917).

Barrett, H.

H. Barrett, W. Swindell, Radiologic Imaging (Academic, New York, 1981).

Bennett, K. E.

Bershader, D.

E. Kügler, D. Bershader, “Recent high-resolution resonant refractivity studies of a sodium-seeded flame,” Exp. Fluids 1, 1–9 (1983).
[CrossRef]

Bracewell, R.

R. Bracewell, “Strip integration in radio astronomy,” Aust. J. Phys. 9, 198–217 (1956).
[CrossRef]

Brock, N. J.

Brown, M. S.

Byer, R. L.

Cormack, A. M.

A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications,” J. Appl. Phys. 34, 2722–2727 (1963).
[CrossRef]

De Leeuw, A

T Hollander, A De Leeuw, E Ter Horst, “Determination of line broadening parameters for chromium triplet lines (a7S → z7P0 transition) in a C2H2-air flame,” Spectrochim. Acta, Part B 38, 691–695 (1983).

DeBarber, P. A.

Ditchburn, R. W.

R. W. Ditchburn, Light, 3rd ed. (Academic, London, 1976).

Dreiden, G. V.

G. V. Dreiden, A. N. Zaidel’, G. V. Ostrovskaya, Yu. I. Ostrovskii, N. A. Pobedonostseva, L. V. Tanin, V. N. Filippov, E. N. Shedova, “Plasma diagnostics by resonant interferometry and holography,” Sov. J. Plasma Phys. 1, 256–267 (1975).

Faris, G. W.

Filippov, V. N.

G. V. Dreiden, A. N. Zaidel’, G. V. Ostrovskaya, Yu. I. Ostrovskii, N. A. Pobedonostseva, L. V. Tanin, V. N. Filippov, E. N. Shedova, “Plasma diagnostics by resonant interferometry and holography,” Sov. J. Plasma Phys. 1, 256–267 (1975).

Griem, H.

H. Griem, Spectral Line Broadening by Plasmas (Academic, New York, 1974).

H. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964).

Haas, C.

C. Haas, G. Pretzler, T. Neger, H. Jäger, “Determination of particle densities and line profiles in plasmas by resonance interferometry: A feasability study using computer simulated refractivity data,” Z. Naturforsch. A 50, 902–914 (1995).

Herman, G. T.

G. T. Herman, Image Reconstruction from Projections (Academic, New York, 1980).

Hesselink, L.

R. Snyder, L. Hesselink, “Optical tomography for flow visualization of the density field around a revolving helicopter rotor blade,” Appl. Opt. 23, 3650–3656 (1984).
[CrossRef] [PubMed]

L. Hesselink, “Optical tomography,” in Handbook of Flow Visualization, W.-J. Yang, ed. (Hemisphere, New York, 1989), pp. 307–329.

Hollander, T

T Hollander, A De Leeuw, E Ter Horst, “Determination of line broadening parameters for chromium triplet lines (a7S → z7P0 transition) in a C2H2-air flame,” Spectrochim. Acta, Part B 38, 691–695 (1983).

Hounsfield, G.

G. Hounsfield, “Computerized transverse axial scanning tomography, Part I: Description of the system,” Br. J. Radiol. 46, 1016 (1973).
[CrossRef] [PubMed]

Jäger, H.

K. Widmann, G. Pretzler, J. Woisetschläger, H. Philipp, T. Neger, H. Jäger, “Interferometric determination of the electron density in a high-pressure xenon lamp with a holographic optical element,” Appl. Opt. 35, 5896–5903 (1996).
[CrossRef] [PubMed]

C. Haas, G. Pretzler, T. Neger, H. Jäger, “Determination of particle densities and line profiles in plasmas by resonance interferometry: A feasability study using computer simulated refractivity data,” Z. Naturforsch. A 50, 902–914 (1995).

G. Pretzler, H. Jäger, T. Neger, “High-accuracy differential interferometry for the investigation of phase objects,” Meas. Sci. Technol. 4, 649–658 (1993).
[CrossRef]

H. Philipp, T. Neger, H. Jäger, J. Woisetschläger, “Optical tomography of phase objects by holographic interferometry,” Measurement 10, 170–181 (1992).
[CrossRef]

J. Woisetschläger, H. Jäger, H. Philipp, G. Pfeifer, T. Neger, “Tomographic investigation of the particle density distribution of sodium atoms in a glow discharge using heterodyne holographic interferometry,” Phys. Lett. A 152, 42–46 (1991).
[CrossRef]

Koslover, R.

R. Koslover, R. McWilliams, “Measurement of multidimensional ion velocity distributions by optical tomography,” Rev. Sci. Instrum. 57, 2441–2448 (1986).
[CrossRef]

Kügler, E.

E. Kügler, D. Bershader, “Recent high-resolution resonant refractivity studies of a sodium-seeded flame,” Exp. Fluids 1, 1–9 (1983).
[CrossRef]

Maldonado, C. D.

McWilliams, R.

R. Koslover, R. McWilliams, “Measurement of multidimensional ion velocity distributions by optical tomography,” Rev. Sci. Instrum. 57, 2441–2448 (1986).
[CrossRef]

Millerd, J. E.

Neger, T.

K. Widmann, G. Pretzler, J. Woisetschläger, H. Philipp, T. Neger, H. Jäger, “Interferometric determination of the electron density in a high-pressure xenon lamp with a holographic optical element,” Appl. Opt. 35, 5896–5903 (1996).
[CrossRef] [PubMed]

C. Haas, G. Pretzler, T. Neger, H. Jäger, “Determination of particle densities and line profiles in plasmas by resonance interferometry: A feasability study using computer simulated refractivity data,” Z. Naturforsch. A 50, 902–914 (1995).

T. Neger, “Optical tomography by spectral interferometry,” J. Phys. D 28, 47–54 (1995).
[CrossRef]

G. Pretzler, H. Jäger, T. Neger, “High-accuracy differential interferometry for the investigation of phase objects,” Meas. Sci. Technol. 4, 649–658 (1993).
[CrossRef]

H. Philipp, T. Neger, H. Jäger, J. Woisetschläger, “Optical tomography of phase objects by holographic interferometry,” Measurement 10, 170–181 (1992).
[CrossRef]

J. Woisetschläger, H. Jäger, H. Philipp, G. Pfeifer, T. Neger, “Tomographic investigation of the particle density distribution of sodium atoms in a glow discharge using heterodyne holographic interferometry,” Phys. Lett. A 152, 42–46 (1991).
[CrossRef]

Olsen, H. N.

Ostrovskaya, G. V.

G. V. Dreiden, A. N. Zaidel’, G. V. Ostrovskaya, Yu. I. Ostrovskii, N. A. Pobedonostseva, L. V. Tanin, V. N. Filippov, E. N. Shedova, “Plasma diagnostics by resonant interferometry and holography,” Sov. J. Plasma Phys. 1, 256–267 (1975).

Ostrovskii, Yu. I.

G. V. Dreiden, A. N. Zaidel’, G. V. Ostrovskaya, Yu. I. Ostrovskii, N. A. Pobedonostseva, L. V. Tanin, V. N. Filippov, E. N. Shedova, “Plasma diagnostics by resonant interferometry and holography,” Sov. J. Plasma Phys. 1, 256–267 (1975).

Pfeifer, G.

J. Woisetschläger, H. Jäger, H. Philipp, G. Pfeifer, T. Neger, “Tomographic investigation of the particle density distribution of sodium atoms in a glow discharge using heterodyne holographic interferometry,” Phys. Lett. A 152, 42–46 (1991).
[CrossRef]

Philipp, H.

K. Widmann, G. Pretzler, J. Woisetschläger, H. Philipp, T. Neger, H. Jäger, “Interferometric determination of the electron density in a high-pressure xenon lamp with a holographic optical element,” Appl. Opt. 35, 5896–5903 (1996).
[CrossRef] [PubMed]

H. Philipp, T. Neger, H. Jäger, J. Woisetschläger, “Optical tomography of phase objects by holographic interferometry,” Measurement 10, 170–181 (1992).
[CrossRef]

J. Woisetschläger, H. Jäger, H. Philipp, G. Pfeifer, T. Neger, “Tomographic investigation of the particle density distribution of sodium atoms in a glow discharge using heterodyne holographic interferometry,” Phys. Lett. A 152, 42–46 (1991).
[CrossRef]

Pobedonostseva, N. A.

G. V. Dreiden, A. N. Zaidel’, G. V. Ostrovskaya, Yu. I. Ostrovskii, N. A. Pobedonostseva, L. V. Tanin, V. N. Filippov, E. N. Shedova, “Plasma diagnostics by resonant interferometry and holography,” Sov. J. Plasma Phys. 1, 256–267 (1975).

Pretzler, G

M Ulbel, G Pretzler, “White-light interferometric tomography for particle density determination in a free-burning arc,” J. Phys. D (to be published).

Pretzler, G.

K. Widmann, G. Pretzler, J. Woisetschläger, H. Philipp, T. Neger, H. Jäger, “Interferometric determination of the electron density in a high-pressure xenon lamp with a holographic optical element,” Appl. Opt. 35, 5896–5903 (1996).
[CrossRef] [PubMed]

C. Haas, G. Pretzler, T. Neger, H. Jäger, “Determination of particle densities and line profiles in plasmas by resonance interferometry: A feasability study using computer simulated refractivity data,” Z. Naturforsch. A 50, 902–914 (1995).

G. Pretzler, “Single-shot tomography by differential interferometry,” Meas. Sci. Technol. 6, 1476–1486 (1995).
[CrossRef]

G. Pretzler, H. Jäger, T. Neger, “High-accuracy differential interferometry for the investigation of phase objects,” Meas. Sci. Technol. 4, 649–658 (1993).
[CrossRef]

Pujol, G.

G. Pujol, S. Weniger, “Broadening and shift of neutral chromium absorption lines by various perturbing gases,” J. Quant. Spectrosc. Radiat. Transfer 22, 145–153 (1979).
[CrossRef]

Radon, J

J Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Verh. Saechs. Akad. Wiss. Leipzig, Math.-Phys. Kl. 69, 292 (1917).

Shedova, E. N.

G. V. Dreiden, A. N. Zaidel’, G. V. Ostrovskaya, Yu. I. Ostrovskii, N. A. Pobedonostseva, L. V. Tanin, V. N. Filippov, E. N. Shedova, “Plasma diagnostics by resonant interferometry and holography,” Sov. J. Plasma Phys. 1, 256–267 (1975).

Snyder, R.

Swindell, W.

H. Barrett, W. Swindell, Radiologic Imaging (Academic, New York, 1981).

Tanin, L. V.

G. V. Dreiden, A. N. Zaidel’, G. V. Ostrovskaya, Yu. I. Ostrovskii, N. A. Pobedonostseva, L. V. Tanin, V. N. Filippov, E. N. Shedova, “Plasma diagnostics by resonant interferometry and holography,” Sov. J. Plasma Phys. 1, 256–267 (1975).

Ter Horst, E

T Hollander, A De Leeuw, E Ter Horst, “Determination of line broadening parameters for chromium triplet lines (a7S → z7P0 transition) in a C2H2-air flame,” Spectrochim. Acta, Part B 38, 691–695 (1983).

Thorne, A.

A. Thorne, Spectrophysics (Chapman Hall, London, 1974).

Traving, G.

G. Traving, Über die Theorie der Druckverbreiterung der Spektrallinien (Braun, Karlsruhe, Germany, 1960).

Ulbel, M

M Ulbel, G Pretzler, “White-light interferometric tomography for particle density determination in a free-burning arc,” J. Phys. D (to be published).

Unsöld, A.

A. Unsöld, Physik der Strernatmosphären (Springer-Verlag, Berlin, 1955).

Weniger, S.

G. Pujol, S. Weniger, “Broadening and shift of neutral chromium absorption lines by various perturbing gases,” J. Quant. Spectrosc. Radiat. Transfer 22, 145–153 (1979).
[CrossRef]

Widmann, K.

Woisetschläger, J.

K. Widmann, G. Pretzler, J. Woisetschläger, H. Philipp, T. Neger, H. Jäger, “Interferometric determination of the electron density in a high-pressure xenon lamp with a holographic optical element,” Appl. Opt. 35, 5896–5903 (1996).
[CrossRef] [PubMed]

H. Philipp, T. Neger, H. Jäger, J. Woisetschläger, “Optical tomography of phase objects by holographic interferometry,” Measurement 10, 170–181 (1992).
[CrossRef]

J. Woisetschläger, H. Jäger, H. Philipp, G. Pfeifer, T. Neger, “Tomographic investigation of the particle density distribution of sodium atoms in a glow discharge using heterodyne holographic interferometry,” Phys. Lett. A 152, 42–46 (1991).
[CrossRef]

Zaidel’, A. N.

G. V. Dreiden, A. N. Zaidel’, G. V. Ostrovskaya, Yu. I. Ostrovskii, N. A. Pobedonostseva, L. V. Tanin, V. N. Filippov, E. N. Shedova, “Plasma diagnostics by resonant interferometry and holography,” Sov. J. Plasma Phys. 1, 256–267 (1975).

Appl. Opt. (3)

Aust. J. Phys. (1)

R. Bracewell, “Strip integration in radio astronomy,” Aust. J. Phys. 9, 198–217 (1956).
[CrossRef]

Ber. Verh. Saechs. Akad. Wiss. Leipzig, Math.-Phys. Kl. (1)

J Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Verh. Saechs. Akad. Wiss. Leipzig, Math.-Phys. Kl. 69, 292 (1917).

Br. J. Radiol. (1)

G. Hounsfield, “Computerized transverse axial scanning tomography, Part I: Description of the system,” Br. J. Radiol. 46, 1016 (1973).
[CrossRef] [PubMed]

Exp. Fluids (1)

E. Kügler, D. Bershader, “Recent high-resolution resonant refractivity studies of a sodium-seeded flame,” Exp. Fluids 1, 1–9 (1983).
[CrossRef]

J. Appl. Phys. (1)

A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications,” J. Appl. Phys. 34, 2722–2727 (1963).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. D (1)

T. Neger, “Optical tomography by spectral interferometry,” J. Phys. D 28, 47–54 (1995).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

G. Pujol, S. Weniger, “Broadening and shift of neutral chromium absorption lines by various perturbing gases,” J. Quant. Spectrosc. Radiat. Transfer 22, 145–153 (1979).
[CrossRef]

Meas. Sci. Technol. (2)

G. Pretzler, H. Jäger, T. Neger, “High-accuracy differential interferometry for the investigation of phase objects,” Meas. Sci. Technol. 4, 649–658 (1993).
[CrossRef]

G. Pretzler, “Single-shot tomography by differential interferometry,” Meas. Sci. Technol. 6, 1476–1486 (1995).
[CrossRef]

Measurement (1)

H. Philipp, T. Neger, H. Jäger, J. Woisetschläger, “Optical tomography of phase objects by holographic interferometry,” Measurement 10, 170–181 (1992).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

J. Woisetschläger, H. Jäger, H. Philipp, G. Pfeifer, T. Neger, “Tomographic investigation of the particle density distribution of sodium atoms in a glow discharge using heterodyne holographic interferometry,” Phys. Lett. A 152, 42–46 (1991).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Koslover, R. McWilliams, “Measurement of multidimensional ion velocity distributions by optical tomography,” Rev. Sci. Instrum. 57, 2441–2448 (1986).
[CrossRef]

Sov. J. Plasma Phys. (1)

G. V. Dreiden, A. N. Zaidel’, G. V. Ostrovskaya, Yu. I. Ostrovskii, N. A. Pobedonostseva, L. V. Tanin, V. N. Filippov, E. N. Shedova, “Plasma diagnostics by resonant interferometry and holography,” Sov. J. Plasma Phys. 1, 256–267 (1975).

Spectrochim. Acta, Part B (1)

T Hollander, A De Leeuw, E Ter Horst, “Determination of line broadening parameters for chromium triplet lines (a7S → z7P0 transition) in a C2H2-air flame,” Spectrochim. Acta, Part B 38, 691–695 (1983).

Z. Naturforsch. A (1)

C. Haas, G. Pretzler, T. Neger, H. Jäger, “Determination of particle densities and line profiles in plasmas by resonance interferometry: A feasability study using computer simulated refractivity data,” Z. Naturforsch. A 50, 902–914 (1995).

Other (10)

H. Barrett, W. Swindell, Radiologic Imaging (Academic, New York, 1981).

G. T. Herman, Image Reconstruction from Projections (Academic, New York, 1980).

M Ulbel, G Pretzler, “White-light interferometric tomography for particle density determination in a free-burning arc,” J. Phys. D (to be published).

A. Thorne, Spectrophysics (Chapman Hall, London, 1974).

R. W. Ditchburn, Light, 3rd ed. (Academic, London, 1976).

H. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964).

A. Unsöld, Physik der Strernatmosphären (Springer-Verlag, Berlin, 1955).

G. Traving, Über die Theorie der Druckverbreiterung der Spektrallinien (Braun, Karlsruhe, Germany, 1960).

H. Griem, Spectral Line Broadening by Plasmas (Academic, New York, 1974).

L. Hesselink, “Optical tomography,” in Handbook of Flow Visualization, W.-J. Yang, ed. (Hemisphere, New York, 1989), pp. 307–329.

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Figures (7)

Fig. 1
Fig. 1

Spectral profiles of (a) the refractivity n − 1 and (b) the extinction coefficient κ (Voigt profiles) for different ratios of the linewidths: δνL/δνD = 0.1 (dashed, Doppler dominated), 1.0 (solid, Voigt profile), and 10.0 (dotted, Lorentz dominated).

Fig. 2
Fig. 2

Principle of optical tomography: The quantity f(r, φ) is arbitrarily distributed in the x, y plane. For determining the spatial distribution of f, integral projections h(l, Θi) are measured for many directions Θi. (Here two directions are shown.)

Fig. 3
Fig. 3

Experimental setup9: LS1, dye laser; LS2, argon-ion laser; BS, beam splitter; BE, beam expander; CL, cylindrical lens; MG, mirror gallery; O, investigation object (carbon arc); HOE, holographic optical coupling element; D, diaphragm; S, screen; DI, differential interferometer; and C, CCD camera. Components with index 1 (HOE and differential interferometer) are used for dye-laser light only, components with index 2 and dashed light paths are for argon-ion laser light only, and the rest of the arrangement is used together by light from both lasers.

Fig. 4
Fig. 4

Tomographic interferograms recorded with the dye laser at three different laser frequencies ν. Each of the eight horizontal strips represents one tomographic projection of the object, and the vertical fringes constitute the interferometric reference fringe system (installed for accurate interferogram evaluation, e.g., see Ref. 29). Variations of the spatial frequency of these fringes represent the interferometric information. Note that plasma self-radiation is negligible (owing to the HOE’s in Fig. 3), although cw lasers were used to take the interferograms. (a) Δν = |ν − ν0| ≈ 0.5(δνV) (where ν0 is the central transition frequency and δνV is the transition linewidth), the plasma is optically thick, there is total absorption by the chromium atoms, and evaluation is impossible. (b) Δν ≈ 8(δνV), the plasma is optically thin, but Δν is too large, and no effect of the chromium atoms is detectable by the differential interferometer. (c) Δν ≈ 2(δνV), and the plasma is partly optically thick. A shift of the reference fringes can be observed especially at the edges of the absorption region.

Fig. 5
Fig. 5

Spatial distribution of the line shape of the Cr i transition at 427.480 nm within a free-burning arc discharge: (a) distribution of the Lorentz width δνL and (b) distribution of the Doppler width δνD. At the top is a contour plot; at the bottom is the section of the plot between the two arrows. In the cross-hatched areas the obtained results were judged unreliable (the calculated fitting error was larger than 25% or the difference from all neighboring points was larger than a factor of 2); elsewhere the statistical errors are between 5 and 20% of the maximum value.

Fig. 6
Fig. 6

Spatial distribution of the chromium ground-state particle density within a free-burning arc discharge (current I ≈ 6 A). At the top is a contour plot; at the bottom is the section of the plot between the two arrows. The statistical errors are between 2 and 8% of the maximum value.

Fig. 7
Fig. 7

Fit of the Voigt refractivity profile equation (2) to measured data: (a) spatial point (x = 18 mm, y = 18 mm) (see Figs. 5 and 6) where fit results have statistical errors smaller than 15%; (b) spatial point (x = 12 mm, y = 15 mm) where fit results of δνL and δνD have statistical errors of Δδν > 50%. The solid curve represents the calculated result, and the dashed curve represents the refractivity profile for the same particle density but at a half-width broader by a factor of 10. Note that the two curves coincide in the region of the measured points. The measurement error is Δn = 0.2 × 10−5 (size of the points), the other deviations are caused by temporal fluctuations of the arc plasma.

Equations (15)

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δ ν D = 2 ν 0 c ( 2 ln 2 k B T M ) 1 / 2 ,
n ( ν ) - 1 = e 2 ( π ln 2 ) 1 / 2 8 π 2 m e 0 f i k ν 0 N i δ ν D Im [ W ( z ) ] ,
κ ( ν ) = e 2 ( π ln 2 ) 1 / 2 8 π 2 m e 0 f i k ν 0 N i δ ν D Re [ W ( z ) ] ,
W ( z ) = exp ( - z 2 ) [ 1 + 2 i π 0 z exp ( t 2 ) d t ] ,
z = x + i y ,
x = ( ln 2 ) 1 / 2 2 ( ν 0 - ν ) δ ν D ,
y = ( ln 2 ) 1 / 2 δ ν L δ ν D .
n ( ν ) - 1 = e 2 8 π 2 0 m e N i f i k ( ν 0 2 - ν 2 ) ,
f ( r , φ ) = 1 2 π 2 0 π [ 0 1 r sin ( Θ - φ ) - l h ( l , Θ ) l d l ] d Θ .
I ( l , Θ ) = I 0 ( l , Θ ) exp [ 4 π λ L κ ( r , φ ) d p ]
h ( l , Θ ) = ln [ I ( l , Θ ) I 0 ( l , Θ ) ] = 4 π λ L κ ( r , φ ) d p
h ( l , Θ ) = 2 π λ L [ n ( r , φ ) - n 0 ] d p ,
f ( r , φ ) = 2 π λ [ n ( r , φ ) - n 0 ] .
T = 1 8 ln 2 M k B ( δ ν D c ν 0 ) 2 3500 K ,
α = δ ν L δ ν D ( ln 2 ) 1 / 2 ,

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