Abstract

The argon arc plasma whose central temperature, 1.90×104K, is used as a practical example for an experiment to research the applicability of moiré deflection tomography in arc plasma flow-field diagnosis. The experimental result indicates that moiré deflection of the measured argon arc plasma is very small, even smaller than that of a common flame with the maximal temperature of nearly 1.80×103K. The refractive-index gradient in moiré deflection tomography mainly contributes to the temperature gradient in essence when the probe wavelength and pressure are certain in plasma diagnosis. The applicable temperature ranges of moiré deflection tomography in the argon arc plasma diagnosis are given with the probe wavelength 532nm at 1atm in certain measuring error requirements. In a word, the applicable temperature range of moiré deflection tomography for arc plasma diagnosis is intimately related to the probe wavelength and the practical measuring requirements.

© 2009 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2005 (1)

B. H. Kolner, P. M. Conklin, R. A. Buckles, N. K. Fontaine, and R. P. Scott, “Time-resolved pulsed-plasma characterization using broadband terahertz pulses correlated with fluorescence imaging,” Appl. Phys. Lett. 87, 151501(2005).
[CrossRef]

2004 (2)

K. Jamshidi-Ghaleh and N. Mansour, “Nonlinear refraction measurements of materials using the moiré deflectometry,” Opt. Commun. 234, 419-425 (2004).
[CrossRef]

Xue Haitao, Li Heng, and Liu Junyue, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40(8), 49-53 (2004) (in Chinese).
[CrossRef]

2003 (1)

K. Akhtar, J. E. Scharer, S. M. Tysk, and E. Kho, “Plasma interferometry at high pressures,” Rev. Sci. Instrum. 74, 996-1001 (2003).
[CrossRef]

2000 (1)

1994 (1)

1991 (2)

1988 (2)

1987 (2)

1986 (2)

S.-M. Jeng and D. R. Keefer, “Theoretical investigation of laser-sustained argon plasmas,” J. Appl. Phys. 60, 2272-2279 (1986).
[CrossRef]

J. Stricker, “Diffraction effects and special advantages in electric heterodyne moiré deflectometry,” Appl. Opt. 25, 895-902 (1986).
[CrossRef] [PubMed]

1982 (1)

J. Stricker and O. Kafri, “A new method for density gradient measurements in compressible flows,” AIAA J. 20, 820-823 (1982).
[CrossRef]

1981 (1)

1980 (1)

1975 (2)

R. J. Radley, Jr., “Two-wavelength holography for measuring plasma electron density,” Phys. Fluids 18, 175-179 (1975).
[CrossRef]

C. M. Vest, “Interferometry of strongly refracting axisymmetric phase objects,” Appl. Opt. 14, 1601-1606 (1975).
[CrossRef] [PubMed]

1970 (1)

R. A. Jeffries, “Two-wavelength holographic interferometry of partially ionized plasmas,” Phys. Fluids 13, 210-212 (1970).
[CrossRef]

1966 (1)

A. J. Alcock and S. A. Ramsden, “Two wavelength interferometry of a laser-induced spark in air,” Appl. Phys. Lett. 8, 187-188 (1966).
[CrossRef]

1964 (1)

G. D. Kahl and E. H. Wedemeyer, “Interferometric analysis of axisymmetric plasma flow,” Phys. Fluids 7, 596-601 (1964).
[CrossRef]

1959 (1)

R. A. Alpher and D. R. White, “Optical refractivity of high-temperature gases. I. Effects resulting from dissociation of diatomic gases,” Phys. Fluids 2, 153-161(1959).
[CrossRef]

Akhtar, K.

K. Akhtar, J. E. Scharer, S. M. Tysk, and E. Kho, “Plasma interferometry at high pressures,” Rev. Sci. Instrum. 74, 996-1001 (2003).
[CrossRef]

Alcock, A. J.

A. J. Alcock and S. A. Ramsden, “Two wavelength interferometry of a laser-induced spark in air,” Appl. Phys. Lett. 8, 187-188 (1966).
[CrossRef]

Allen, C. W.

C. W. Allen, Astrophysical Quantities (Athlone, 1963).

Alpher, R. A.

R. A. Alpher and D. R. White, “Optical refractivity of high-temperature gases. I. Effects resulting from dissociation of diatomic gases,” Phys. Fluids 2, 153-161(1959).
[CrossRef]

Anzhi, He

Chen Yunyun, Song Yang, He Anzhi, and Li Zhenhua, “Temperature and density distribution measurement of flame by using of moiré deflection tomography,” Acta Optica Sinca (to be published).

Bar-Ziv, E.

Bergström, H.

Brinkman, E. A.

Buckles, R. A.

B. H. Kolner, P. M. Conklin, R. A. Buckles, N. K. Fontaine, and R. P. Scott, “Time-resolved pulsed-plasma characterization using broadband terahertz pulses correlated with fluorescence imaging,” Appl. Phys. Lett. 87, 151501(2005).
[CrossRef]

Byer, R. L.

Conklin, P. M.

B. H. Kolner, P. M. Conklin, R. A. Buckles, N. K. Fontaine, and R. P. Scott, “Time-resolved pulsed-plasma characterization using broadband terahertz pulses correlated with fluorescence imaging,” Appl. Phys. Lett. 87, 151501(2005).
[CrossRef]

Faris, G. W.

Fontaine, N. K.

B. H. Kolner, P. M. Conklin, R. A. Buckles, N. K. Fontaine, and R. P. Scott, “Time-resolved pulsed-plasma characterization using broadband terahertz pulses correlated with fluorescence imaging,” Appl. Phys. Lett. 87, 151501(2005).
[CrossRef]

Glatt, I.

Haitao, Xue

Xue Haitao, Li Heng, and Liu Junyue, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40(8), 49-53 (2004) (in Chinese).
[CrossRef]

He, An-Zhi

Heng, Li

Xue Haitao, Li Heng, and Liu Junyue, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40(8), 49-53 (2004) (in Chinese).
[CrossRef]

Hesselink, L.

Jamshidi-Ghaleh, K.

K. Jamshidi-Ghaleh and N. Mansour, “Nonlinear refraction measurements of materials using the moiré deflectometry,” Opt. Commun. 234, 419-425 (2004).
[CrossRef]

Jeffries, J. B.

Jeffries, R. A.

R. A. Jeffries, “Two-wavelength holographic interferometry of partially ionized plasmas,” Phys. Fluids 13, 210-212 (1970).
[CrossRef]

Jeng, S.-M.

S.-M. Jeng and D. R. Keefer, “Theoretical investigation of laser-sustained argon plasmas,” J. Appl. Phys. 60, 2272-2279 (1986).
[CrossRef]

Junyue, Liu

Xue Haitao, Li Heng, and Liu Junyue, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40(8), 49-53 (2004) (in Chinese).
[CrossRef]

Kafri, O.

Kahl, G. D.

G. D. Kahl and E. H. Wedemeyer, “Interferometric analysis of axisymmetric plasma flow,” Phys. Fluids 7, 596-601 (1964).
[CrossRef]

Keefer, D. R.

S.-M. Jeng and D. R. Keefer, “Theoretical investigation of laser-sustained argon plasmas,” J. Appl. Phys. 60, 2272-2279 (1986).
[CrossRef]

Keren, E.

Kho, E.

K. Akhtar, J. E. Scharer, S. M. Tysk, and E. Kho, “Plasma interferometry at high pressures,” Rev. Sci. Instrum. 74, 996-1001 (2003).
[CrossRef]

Kolner, B. H.

B. H. Kolner, P. M. Conklin, R. A. Buckles, N. K. Fontaine, and R. P. Scott, “Time-resolved pulsed-plasma characterization using broadband terahertz pulses correlated with fluorescence imaging,” Appl. Phys. Lett. 87, 151501(2005).
[CrossRef]

Mansour, N.

K. Jamshidi-Ghaleh and N. Mansour, “Nonlinear refraction measurements of materials using the moiré deflectometry,” Opt. Commun. 234, 419-425 (2004).
[CrossRef]

Matulka, R. D.

R. D. Matulka, “The application of holographic interferometry to the determination of asymmetric three-dimensional density field in free jet flow,” AD-A174610 (1970).

Meier, G. E. A.

Middendorf, P.

Ni, Xiao-Wu

Obermeier, F.

Radley, R. J.

R. J. Radley, Jr., “Two-wavelength holography for measuring plasma electron density,” Phys. Fluids 18, 175-179 (1975).
[CrossRef]

Ramsden, S. A.

A. J. Alcock and S. A. Ramsden, “Two wavelength interferometry of a laser-induced spark in air,” Appl. Phys. Lett. 8, 187-188 (1966).
[CrossRef]

Scharer, J. E.

K. Akhtar, J. E. Scharer, S. M. Tysk, and E. Kho, “Plasma interferometry at high pressures,” Rev. Sci. Instrum. 74, 996-1001 (2003).
[CrossRef]

Scott, R. P.

B. H. Kolner, P. M. Conklin, R. A. Buckles, N. K. Fontaine, and R. P. Scott, “Time-resolved pulsed-plasma characterization using broadband terahertz pulses correlated with fluorescence imaging,” Appl. Phys. Lett. 87, 151501(2005).
[CrossRef]

Snyder, R.

Söller, C.

Stricker, J.

J. Stricker, “Diffraction effects and special advantages in electric heterodyne moiré deflectometry,” Appl. Opt. 25, 895-902 (1986).
[CrossRef] [PubMed]

J. Stricker and O. Kafri, “A new method for density gradient measurements in compressible flows,” AIAA J. 20, 820-823 (1982).
[CrossRef]

Tysk, S. M.

K. Akhtar, J. E. Scharer, S. M. Tysk, and E. Kho, “Plasma interferometry at high pressures,” Rev. Sci. Instrum. 74, 996-1001 (2003).
[CrossRef]

Vest, C. M.

Wedemeyer, E. H.

G. D. Kahl and E. H. Wedemeyer, “Interferometric analysis of axisymmetric plasma flow,” Phys. Fluids 7, 596-601 (1964).
[CrossRef]

Weinberg, F. J.

F. J. Weinberg, Optics of Flames (Butterworths, 1963), Chap. 2, p. 23.

Wenhua, Z.

G. Zengyuan and Z. Wenhua, Arc and Thermal Plasma (Science, 1986), Chap. 2, p. 52.

Wenskus, R.

White, D. R.

R. A. Alpher and D. R. White, “Optical refractivity of high-temperature gases. I. Effects resulting from dissociation of diatomic gases,” Phys. Fluids 2, 153-161(1959).
[CrossRef]

Yan, Da-Peng

Yang, Song

Chen Yunyun, Song Yang, He Anzhi, and Li Zhenhua, “Temperature and density distribution measurement of flame by using of moiré deflection tomography,” Acta Optica Sinca (to be published).

You-Ming, J.

J. You-Ming and F. You-San, The Physical Basis of Low Temperature Plasma (Tsinghua University, 1983).

You-San, F.

J. You-Ming and F. You-San, The Physical Basis of Low Temperature Plasma (Tsinghua University, 1983).

Yunyun, Chen

Chen Yunyun, Song Yang, He Anzhi, and Li Zhenhua, “Temperature and density distribution measurement of flame by using of moiré deflection tomography,” Acta Optica Sinca (to be published).

Zengyuan, G.

G. Zengyuan and Z. Wenhua, Arc and Thermal Plasma (Science, 1986), Chap. 2, p. 52.

Zhenhua, Li

Chen Yunyun, Song Yang, He Anzhi, and Li Zhenhua, “Temperature and density distribution measurement of flame by using of moiré deflection tomography,” Acta Optica Sinca (to be published).

Acta Optica Sinca (1)

Chen Yunyun, Song Yang, He Anzhi, and Li Zhenhua, “Temperature and density distribution measurement of flame by using of moiré deflection tomography,” Acta Optica Sinca (to be published).

AIAA J. (1)

J. Stricker and O. Kafri, “A new method for density gradient measurements in compressible flows,” AIAA J. 20, 820-823 (1982).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. Lett. (2)

B. H. Kolner, P. M. Conklin, R. A. Buckles, N. K. Fontaine, and R. P. Scott, “Time-resolved pulsed-plasma characterization using broadband terahertz pulses correlated with fluorescence imaging,” Appl. Phys. Lett. 87, 151501(2005).
[CrossRef]

A. J. Alcock and S. A. Ramsden, “Two wavelength interferometry of a laser-induced spark in air,” Appl. Phys. Lett. 8, 187-188 (1966).
[CrossRef]

Chin. J. Mech. Eng. (1)

Xue Haitao, Li Heng, and Liu Junyue, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40(8), 49-53 (2004) (in Chinese).
[CrossRef]

J. Appl. Phys. (1)

S.-M. Jeng and D. R. Keefer, “Theoretical investigation of laser-sustained argon plasmas,” J. Appl. Phys. 60, 2272-2279 (1986).
[CrossRef]

Opt. Commun. (1)

K. Jamshidi-Ghaleh and N. Mansour, “Nonlinear refraction measurements of materials using the moiré deflectometry,” Opt. Commun. 234, 419-425 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Fluids (4)

R. A. Jeffries, “Two-wavelength holographic interferometry of partially ionized plasmas,” Phys. Fluids 13, 210-212 (1970).
[CrossRef]

R. J. Radley, Jr., “Two-wavelength holography for measuring plasma electron density,” Phys. Fluids 18, 175-179 (1975).
[CrossRef]

G. D. Kahl and E. H. Wedemeyer, “Interferometric analysis of axisymmetric plasma flow,” Phys. Fluids 7, 596-601 (1964).
[CrossRef]

R. A. Alpher and D. R. White, “Optical refractivity of high-temperature gases. I. Effects resulting from dissociation of diatomic gases,” Phys. Fluids 2, 153-161(1959).
[CrossRef]

Rev. Sci. Instrum. (1)

K. Akhtar, J. E. Scharer, S. M. Tysk, and E. Kho, “Plasma interferometry at high pressures,” Rev. Sci. Instrum. 74, 996-1001 (2003).
[CrossRef]

Other (5)

R. D. Matulka, “The application of holographic interferometry to the determination of asymmetric three-dimensional density field in free jet flow,” AD-A174610 (1970).

G. Zengyuan and Z. Wenhua, Arc and Thermal Plasma (Science, 1986), Chap. 2, p. 52.

C. W. Allen, Astrophysical Quantities (Athlone, 1963).

F. J. Weinberg, Optics of Flames (Butterworths, 1963), Chap. 2, p. 23.

J. You-Ming and F. You-San, The Physical Basis of Low Temperature Plasma (Tsinghua University, 1983).

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Figures (10)

Fig. 1
Fig. 1

Moiré deflection tomography experimental system.

Fig. 2
Fig. 2

Measured argon arc plasma of the experiment.

Fig. 3
Fig. 3

(a) Deflected moiré fringes of the measured argon arc plasma. (b) Paralleled reference fringes.

Fig. 4
Fig. 4

(a) Moiré fringes of the measured flame. (b) Measured flame.

Fig. 5
Fig. 5

Dependence of the refractive index on temperature with the probe wavelength 532 nm at 1 atm .

Fig. 6
Fig. 6

Dependence of the electron number density on temperature at 1 atm .

Fig. 7
Fig. 7

Relation between the electron number density gradient and temperature at 1 atm .

Fig. 8
Fig. 8

Dependence of the refractive-index gradient on temperature.

Fig. 9
Fig. 9

Applicable temperature ranges of moiré deflection tomography in certain measuring errors with the probe wavelength 532 nm .

Fig. 10
Fig. 10

Applicable temperature ranges of moiré deflection tomography in certain measuring errors with the probe wavelength 808 nm .

Equations (23)

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ϕ x ( x , y ) = 1 n 0 0 L n ( x , y , z ) x d z ,
( n 1 ) a = 1 L ( A + B λ 2 ) N a ,
( n 1 ) e 1 2 N e e 2 λ 2 2 π m e c 2 = 4.46 × 10 14 λ 2 N e ( λ : cm , N e : cm 3 ) ,
n 1 = ( n 1 ) a + ( n 1 ) i + ( n 1 ) e = 1 L ( A + B λ 2 ) N a + 0.67 1 L ( A + B λ 2 ) N i 4.46 × 10 14 λ 2 N e = 1 L ( A + B λ 2 ) ( N a + 0.67 N i ) 4.46 × 10 14 λ 2 N e ,
d n d T = 1 L · ( A + B λ 2 ) · ( d N a d T + 0.67 d N i d T ) 4.46 × 10 14 λ 2 · d N e d T .
n 1 = 1.05959 × 10 23 · ( N a + 0.67 N i ) 1.2623 × 10 22 · N e ,
d n d T = 1.05959 × 10 23 · ( d N a d T + 0.67 d N i d T ) 1.2623 × 10 22 · d N e d T .
Δ T = Δ n d n d T | T .
e = Δ T T = Δ n / d n d T | T T = Δ n d n d T | T · T .
N 1 N e N a = 2 Z 1 Z 0 ( 2 π κ T m e h 2 ) 3 / 2 exp ( E 1 κ T ) ,
N 2 N e N 1 = 2 Z 2 Z 1 ( 2 π κ T m e h 2 ) 3 / 2 exp ( E 2 κ T ) ,
2 Z 1 Z 0 ( 2 π κ T m e h 2 ) 3 / 2 exp ( E 1 κ T ) = C Z 1 Z 0 T 3 / 2 exp ( E 1 κ T ) = K 1 ,
2 Z 2 Z 1 ( 2 π κ T m e h 2 ) 3 / 2 exp ( E 2 κ T ) = C Z 2 Z 1 T 3 / 2 exp ( E 2 κ T ) = K 2 ,
N 1 + 2 N 2 = N e ,
P = N t κ T = ( N a + N i + N e ) κ T = ( N a + N 1 + N 2 + N e ) κ T .
N e 3 + 2 K N e 2 1 + ( 3 K 1 K 2 K 1 N t ) N e 2 K 1 K 2 N t = 0.
N 1 = N e 2 N e + 2 K 2 ,
N 2 = K 2 N 1 N e ,
N a = N 1 N e K 1 .
d N e d T = ( 2 K 1 K 2 + K 1 N e ) d N t d T + ( 2 K 2 N t 3 K 2 N e + N t N e 2 N e 2 ) d K 1 d T + ( 2 K 1 N t 3 K 1 N e ) d K 2 d T 3 N e 2 + 4 K 1 N e + 3 K 1 K 2 K 1 N t .
d N a d T = N 1 K 1 d N e d T + K 1 N e d N 1 d T N 1 N e d K 1 d T K 1 2 ,
d N i d T = d ( N 1 + N 2 ) d T = d N 1 d T + d N 2 d T .
d n d T = 1 L · ( A + B λ 2 ) · ( N 1 K 1 d N e d T + K 1 N e d N 1 d T N 1 N e d K 1 d T K 1 2 + 0.67 × ( d N 1 d T + d N 2 d T ) ) 4.46 × 10 14 λ 2 · ( 2 K 1 K 2 + K 1 N e ) d N t d T + ( 2 K 2 N t 3 K 2 N e + N t N e 2 N e 2 ) d K 1 d T + ( 2 K 1 N t 3 K 1 N e ) d K 2 d T 3 N e 2 + 4 K 1 N e + 3 K 1 K 2 K 1 N t .

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