Abstract

We report the use of a tunable differential interferometer for optical tomography. This interferometer has several advantages over other methods for phase measurements in optical tomography, including good stability, variable sensitivity, and the elimination of fringe ambiguity. Quantitative images of the gas concentrations in subsonic jets of methane and oxygen issuing into air are presented, with absolute accuracies better than 3.5% and 4.5%, respectively.

© 1989 Optical Society of America

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References

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  1. H. M. Hertz, “Experimental Determination of 2-D Flame Temperature Fields by Interferometric Tomography,” Opt. Commun. 54, 131–136 (1985).
    [CrossRef]
  2. G. W. Faris, R. L. Byer, “Quantitative Three-Dimensional Optical Tomographic Imaging of Supersonic Flows,” Science 238, 1700–1702 (1987).
    [CrossRef] [PubMed]
  3. R. Snyder, L. Hesselink, “Measurement of Mixing Fluid Flows with Optical Tomography,” Opt. Lett. 13, 87–89 (1988).
    [CrossRef] [PubMed]
  4. G. W. Faris, R. L. Byer, “Quantitative Optical Tomographic Imaging of a Supersonic Jet,” Opt. Lett. 11, 413–415 (1986).
    [CrossRef] [PubMed]
  5. S. R. Ray, H. G. Semerjian, “High-Speed Laser Tomographic Measurements in Fluctuating Flames,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper TUB4.
  6. H. M. Hertz, G. W. Faris, Emission Tomography, “of Flame Radicals,” Opt. Lett. 13, 351–353 (1988).
    [CrossRef] [PubMed]
  7. S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983).
  8. M. Francon, Optical Interferometry (Academic, New York, 1966) Chap. 7.
  9. G. W. Faris, R. L. Byer, “Three-Dimensional Beam Deflection Optical Tomography of a Supersonic Jet,” Appl. Opt. 27, 5202–5212 (1988).
    [CrossRef] [PubMed]
  10. K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181–194 (1981).
    [CrossRef]
  11. G. W. Faris, R. L. Byer, “Beam-Deflection Optical Tomography of a Flame,” Opt. Lett. 12, 155–157 (1987).
    [CrossRef] [PubMed]
  12. H. M. Hertz, “Kerr Effect Tomography for Nonintrusive Spatially Resolved Measurements of Asymmetric Electric Field Distributions,” Appl. Opt. 25, 914–921 (1986).
    [CrossRef] [PubMed]
  13. J. Bartels et al., Eds., Landolt-Bornstein: Zahlenwerte und Funktionnen, Vol. 2 (Springer-Verlag, Heidelberg, 1962).
  14. B. Edlén, “The Refractive Index of Air,” Metrologia 2, 71–80 (1966).
    [CrossRef]
  15. H. H. Barrett, W. Swindell, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89–107 (1977).
    [CrossRef]

1988 (3)

1987 (2)

G. W. Faris, R. L. Byer, “Beam-Deflection Optical Tomography of a Flame,” Opt. Lett. 12, 155–157 (1987).
[CrossRef] [PubMed]

G. W. Faris, R. L. Byer, “Quantitative Three-Dimensional Optical Tomographic Imaging of Supersonic Flows,” Science 238, 1700–1702 (1987).
[CrossRef] [PubMed]

1986 (2)

1985 (1)

H. M. Hertz, “Experimental Determination of 2-D Flame Temperature Fields by Interferometric Tomography,” Opt. Commun. 54, 131–136 (1985).
[CrossRef]

1981 (1)

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181–194 (1981).
[CrossRef]

1977 (1)

H. H. Barrett, W. Swindell, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89–107 (1977).
[CrossRef]

1966 (1)

B. Edlén, “The Refractive Index of Air,” Metrologia 2, 71–80 (1966).
[CrossRef]

Barrett, H. H.

H. H. Barrett, W. Swindell, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89–107 (1977).
[CrossRef]

Byer, R. L.

Deans, S. R.

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983).

Edlén, B.

B. Edlén, “The Refractive Index of Air,” Metrologia 2, 71–80 (1966).
[CrossRef]

Faris, G. W.

Francon, M.

M. Francon, Optical Interferometry (Academic, New York, 1966) Chap. 7.

Hertz, H. M.

Hesselink, L.

Kirchartz, K. R.

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181–194 (1981).
[CrossRef]

Muller, U.

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181–194 (1981).
[CrossRef]

Oertel, H.

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181–194 (1981).
[CrossRef]

Ray, S. R.

S. R. Ray, H. G. Semerjian, “High-Speed Laser Tomographic Measurements in Fluctuating Flames,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper TUB4.

Semerjian, H. G.

S. R. Ray, H. G. Semerjian, “High-Speed Laser Tomographic Measurements in Fluctuating Flames,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper TUB4.

Snyder, R.

Swindell, W.

H. H. Barrett, W. Swindell, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89–107 (1977).
[CrossRef]

Tomography, Emission

Zierep, J.

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181–194 (1981).
[CrossRef]

Acta Mech. (1)

K. R. Kirchartz, U. Muller, H. Oertel, J. Zierep, “Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container,” Acta Mech. 40, 181–194 (1981).
[CrossRef]

Appl. Opt. (2)

Metrologia (1)

B. Edlén, “The Refractive Index of Air,” Metrologia 2, 71–80 (1966).
[CrossRef]

Opt. Commun. (1)

H. M. Hertz, “Experimental Determination of 2-D Flame Temperature Fields by Interferometric Tomography,” Opt. Commun. 54, 131–136 (1985).
[CrossRef]

Opt. Lett. (4)

Proc. IEEE (1)

H. H. Barrett, W. Swindell, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89–107 (1977).
[CrossRef]

Science (1)

G. W. Faris, R. L. Byer, “Quantitative Three-Dimensional Optical Tomographic Imaging of Supersonic Flows,” Science 238, 1700–1702 (1987).
[CrossRef] [PubMed]

Other (4)

S. R. Ray, H. G. Semerjian, “High-Speed Laser Tomographic Measurements in Fluctuating Flames,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper TUB4.

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983).

M. Francon, Optical Interferometry (Academic, New York, 1966) Chap. 7.

J. Bartels et al., Eds., Landolt-Bornstein: Zahlenwerte und Funktionnen, Vol. 2 (Springer-Verlag, Heidelberg, 1962).

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Figures (5)

Fig. 1
Fig. 1

Experimental arrangement for the tunable differential interferometer.

Fig. 2
Fig. 2

Typical projection measurements for the differential interferometer: (a) signal (Isig), reference (Iref), and incident intensity (I0) curves; (b) differential projection, calculated from the curves in (a); (c) projection, resulting from the integration of the curve in (b).

Fig. 3
Fig. 3

Tomographic reconstruction of the concentration of methane in a subsonic asymmetric jet into air; the pixel size is 160 × 160 μm.

Fig. 4
Fig. 4

(a) Tomographic reconstruction of a cylindrical methane jet; the pixel size is 160 × 160 μm. (b) Section through the center of the reconstruction in (a).

Fig. 5
Fig. 5

Tomographic reconstruction of the oxygen concentration in an asymmetric jet into air; the pixel size is 115 × 115 μm.

Equations (2)

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I ( x ) = I 0 ( x ) sin 2 { ½ [ ϕ θ + ϕ err ( x ) + ϕ sig ( x ) ] } ,
ϕ sig ( x ) = 2 sin 1 [ I sig ( x ) I 0 ( x ) ] 1 / 2 2 sin 1 [ I ref ( x ) I 0 ( x ) ] 1 / 2 .

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