Abstract

Three-dimensional reconstruction of the electron density in a plasma can be obtained by passing multiple beams at different field angles simultaneously through a plasma and performing a tomographic reconstruction of the measured field-dependent phase profiles. A relatively simple experimental setup is proposed and simulations are carried out to verify the technique. The plasma distribution is modeled as a discrete number of phase screens, and a Zernike polynomial representation of the phase screens is used to reconstruct the plasma profile.

© 2006 Optical Society of America

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    [CrossRef]
  2. A. K. Chattopadhyay, A. Anand, and C. V. S. Rao, Rev. Sci. Instrum. 76, 063502 (2005).
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    [CrossRef]

2005

A. K. Chattopadhyay, A. Anand, and C. V. S. Rao, Rev. Sci. Instrum. 76, 063502 (2005).
[CrossRef]

2003

K. L. Baker, Rev. Sci. Instrum. 74, 5070 (2003).
[CrossRef]

2002

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

J. A. Cobble, R. P. Johnson, N. A. Kurnit, D. S. Montgomery, and J. C. Fernandez, Rev. Sci. Instrum. 73, 3813 (2002).
[CrossRef]

1996

B. Moosman, V. M. Bystritskii, C. J. Boswell, and F. J. Wessel, Rev. Sci. Instrum. 67, 170 (1996).
[CrossRef]

1993

R. S. Craxton, F. S. Turner, R. Hoefen, C. Darrow, E. F. Gabl, and G. E. Busch, Phys. Fluids B 12, 4419 (1993).
[CrossRef]

1985

G. E. Busch, Rev. Sci. Instrum. 56, 879 (1985).
[CrossRef]

R. S. Granetz and J. F. Camacho, Nucl. Fusion 25, 727 (1985).
[CrossRef]

1984

Anand, A.

A. K. Chattopadhyay, A. Anand, and C. V. S. Rao, Rev. Sci. Instrum. 76, 063502 (2005).
[CrossRef]

Baker, K. L.

K. L. Baker, Rev. Sci. Instrum. 74, 5070 (2003).
[CrossRef]

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Boswell, C. J.

B. Moosman, V. M. Bystritskii, C. J. Boswell, and F. J. Wessel, Rev. Sci. Instrum. 67, 170 (1996).
[CrossRef]

Brase, J.

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Busch, G. E.

R. S. Craxton, F. S. Turner, R. Hoefen, C. Darrow, E. F. Gabl, and G. E. Busch, Phys. Fluids B 12, 4419 (1993).
[CrossRef]

G. E. Busch, Rev. Sci. Instrum. 56, 879 (1985).
[CrossRef]

Bystritskii, V. M.

B. Moosman, V. M. Bystritskii, C. J. Boswell, and F. J. Wessel, Rev. Sci. Instrum. 67, 170 (1996).
[CrossRef]

Camacho, J. F.

R. S. Granetz and J. F. Camacho, Nucl. Fusion 25, 727 (1985).
[CrossRef]

Chattopadhyay, A. K.

A. K. Chattopadhyay, A. Anand, and C. V. S. Rao, Rev. Sci. Instrum. 76, 063502 (2005).
[CrossRef]

Chow, W. W.

Cobble, J. A.

J. A. Cobble, R. P. Johnson, N. A. Kurnit, D. S. Montgomery, and J. C. Fernandez, Rev. Sci. Instrum. 73, 3813 (2002).
[CrossRef]

Craxton, R. S.

R. S. Craxton, F. S. Turner, R. Hoefen, C. Darrow, E. F. Gabl, and G. E. Busch, Phys. Fluids B 12, 4419 (1993).
[CrossRef]

Darrow, C.

R. S. Craxton, F. S. Turner, R. Hoefen, C. Darrow, E. F. Gabl, and G. E. Busch, Phys. Fluids B 12, 4419 (1993).
[CrossRef]

Fernandez, J. C.

J. A. Cobble, R. P. Johnson, N. A. Kurnit, D. S. Montgomery, and J. C. Fernandez, Rev. Sci. Instrum. 73, 3813 (2002).
[CrossRef]

Gabl, E. F.

R. S. Craxton, F. S. Turner, R. Hoefen, C. Darrow, E. F. Gabl, and G. E. Busch, Phys. Fluids B 12, 4419 (1993).
[CrossRef]

Granetz, R. S.

R. S. Granetz and J. F. Camacho, Nucl. Fusion 25, 727 (1985).
[CrossRef]

Hoefen, R.

R. S. Craxton, F. S. Turner, R. Hoefen, C. Darrow, E. F. Gabl, and G. E. Busch, Phys. Fluids B 12, 4419 (1993).
[CrossRef]

Johnson, R. P.

J. A. Cobble, R. P. Johnson, N. A. Kurnit, D. S. Montgomery, and J. C. Fernandez, Rev. Sci. Instrum. 73, 3813 (2002).
[CrossRef]

Kartz, M.

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Kolmogorov, A. N.

A. N. Kolmogorov, in Turbulence, Classic Papers on Statistical Theory, S.K.Friedlander and L.Topper, eds. (Interscience, 1961).

Kurnit, N. A.

J. A. Cobble, R. P. Johnson, N. A. Kurnit, D. S. Montgomery, and J. C. Fernandez, Rev. Sci. Instrum. 73, 3813 (2002).
[CrossRef]

Lawrence, G. N.

Montgomery, D. S.

J. A. Cobble, R. P. Johnson, N. A. Kurnit, D. S. Montgomery, and J. C. Fernandez, Rev. Sci. Instrum. 73, 3813 (2002).
[CrossRef]

Moosman, B.

B. Moosman, V. M. Bystritskii, C. J. Boswell, and F. J. Wessel, Rev. Sci. Instrum. 67, 170 (1996).
[CrossRef]

Olivier, S. S.

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Rao, C. V.

A. K. Chattopadhyay, A. Anand, and C. V. S. Rao, Rev. Sci. Instrum. 76, 063502 (2005).
[CrossRef]

Sawvel, B.

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Tucker, J.

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Turner, F. S.

R. S. Craxton, F. S. Turner, R. Hoefen, C. Darrow, E. F. Gabl, and G. E. Busch, Phys. Fluids B 12, 4419 (1993).
[CrossRef]

Wessel, F. J.

B. Moosman, V. M. Bystritskii, C. J. Boswell, and F. J. Wessel, Rev. Sci. Instrum. 67, 170 (1996).
[CrossRef]

Nucl. Fusion

R. S. Granetz and J. F. Camacho, Nucl. Fusion 25, 727 (1985).
[CrossRef]

Opt. Lett.

Phys. Fluids B

R. S. Craxton, F. S. Turner, R. Hoefen, C. Darrow, E. F. Gabl, and G. E. Busch, Phys. Fluids B 12, 4419 (1993).
[CrossRef]

Rev. Sci. Instrum.

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

K. L. Baker, Rev. Sci. Instrum. 74, 5070 (2003).
[CrossRef]

A. K. Chattopadhyay, A. Anand, and C. V. S. Rao, Rev. Sci. Instrum. 76, 063502 (2005).
[CrossRef]

G. E. Busch, Rev. Sci. Instrum. 56, 879 (1985).
[CrossRef]

B. Moosman, V. M. Bystritskii, C. J. Boswell, and F. J. Wessel, Rev. Sci. Instrum. 67, 170 (1996).
[CrossRef]

J. A. Cobble, R. P. Johnson, N. A. Kurnit, D. S. Montgomery, and J. C. Fernandez, Rev. Sci. Instrum. 73, 3813 (2002).
[CrossRef]

Other

A. N. Kolmogorov, in Turbulence, Classic Papers on Statistical Theory, S.K.Friedlander and L.Topper, eds. (Interscience, 1961).

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Figures (3)

Fig. 1
Fig. 1

Experimental setups for the three-dimensional tomographic reconstruction of the electron density in high-density plasmas. a, Setup using a cyclical interferometer; b, alternative system obtained with a Shack–Hartmann wavefront sensor. In both cases two crossed transmission gratings are used to generate nine beams at different field angles to probe the plasma and enable a tomographic reconstruction of the three-dimensional electron-density profile. A low pitch lenslet array is used in both cases to collimate the separate beams and reimage the plane of the plasma onto the wavefront detector.

Fig. 2
Fig. 2

Tomographic reconstruction results of comparing the reconstructed phase profiles with the phase profiles placed on the phase screens that represent the plasma. Top row, applied phase; middle row, reconstructed phase at each of the three planes in the plasma. Bottom row, difference in phase between the applied and the reconstructed phases at each of the planes that represent the plasma.

Fig. 3
Fig. 3

Variance in phase between applied and reconstructed phases at each of the three screens that represent the plasma.

Equations (1)

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n e = 1.5 exp [ ( z 750 μ m ) 2 ] exp [ ( x 1.34 mm ) 2 ] ( 15 + Kol. Tur. ) ,

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