Abstract

A new electro-optically modulated optical solid-state (MOSS) interferometer has been constructed for measurement of quantities related to the low-order spectral moments of line emission from optically thin radiant media such as plasmas. When Doppler broadening is dominant, the spectral moments give the Radon transform of corresponding moments of the velocity distribution function of the radiating species. The instrument, which is based on the principle of the Fourier-transform spectrometer, has high etendue and is rugged and compact. When electro-optical path-length modulation techniques are employed, the spectral information is encoded in the temporal frequency domain at harmonics of the modulation frequency and can be obtained by use of a single photodetector. Specifically, for a plasma in drifting local thermodynamic equilibrium the zeroth moment (brightness) is given by the average signal level, the first moment (shift) by the interferometric phase, and the second moment (linewidth) by the fringe visibility. To illustrate the MOSS performance, I present spectroscopic measurements of the time evolution of the plasma ion temperature and flow velocity for rf-heated discharges in the H-1 heliac, a toroidal plasma magnetic confinement at the Australian National University.

© 2002 Optical Society of America

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References

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  1. J. Howard, “Modulated Optical Solid-State spectrometer applications in plasma diagnostics,” Rev. Sci. Instrum. 70, 368–371 (1999).
    [CrossRef]
  2. J. Howard, “Optical coherence-based techniques for motional Stark effect measurements of magnetic field pitch angle,” Plasma Phys. Controlled Fusion 41, 271–284 (1999).
    [CrossRef]
  3. S. Hamberger, B. Blackwell, L. Sharp, D. Shenton, “H-1 design and construction,” Fusion Technol. 17, 123–130 (1990).
  4. J. Howard, “Vector tomography applications in plasma diagnostics,” Plasma Phys. Controlled Fusion 38, 489–503 (1996).
    [CrossRef]
  5. R. Hilliard, G. Shepherd, “Upper atmosphere temperatures from Doppler line width,” Planet. Space Sci. 14, 386–406 (1966).
    [CrossRef]
  6. G. Thuillier, M. Hersé, “Thermally stable field compensated Michelson interferometer for measurement of temperature and wind of the planetary atmospheres,” Appl. Opt. 30, 1210–1220 (1991).
    [CrossRef] [PubMed]
  7. W. Gault, S. Brown, A. Moise, D. Liang, G. Sellar, G. Shepherd, J. Wimperis, “ERWIN: an E-region wind interferometer,” Appl. Opt. 35, 2913–2922 (1996).
    [CrossRef] [PubMed]
  8. R. S. Weiss, T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
    [CrossRef]
  9. I. P. Kaminow, An Introduction to Electrooptic Devices (Academic, New York, 1974).
  10. A. P. Thorne, Spectrophysics (Chapman Hall, London, 1988).
    [CrossRef]
  11. W. Steel, Interferometry (Cambridge U. Press, Cambridge, UK, 1967).
  12. C. Michael, J. Howard, B. D. Blackwell, “The MOSS camera on H-1NF,” Rev. Sci. Instrum. 72, 1034–1037 (2001).
    [CrossRef]
  13. O. Sasaki, H. Okazaki, “Analysis of measurement accuracy in sinusoidal phase modulating interferometry,” Appl. Opt. 25, 3152–3158 (1986).
    [CrossRef] [PubMed]
  14. M. Shats, D. L. Rudakov, B. D. Blackwell, G. Borg, R. L. Dewar, J. Howard, L. Sharp, “Improved particle confinement mode in low-temperature plasma in H-1 heliac,” Phys. Rev. Lett. 77, 4190–4193 (1996).
    [CrossRef] [PubMed]

2001 (1)

C. Michael, J. Howard, B. D. Blackwell, “The MOSS camera on H-1NF,” Rev. Sci. Instrum. 72, 1034–1037 (2001).
[CrossRef]

1999 (2)

J. Howard, “Modulated Optical Solid-State spectrometer applications in plasma diagnostics,” Rev. Sci. Instrum. 70, 368–371 (1999).
[CrossRef]

J. Howard, “Optical coherence-based techniques for motional Stark effect measurements of magnetic field pitch angle,” Plasma Phys. Controlled Fusion 41, 271–284 (1999).
[CrossRef]

1996 (3)

J. Howard, “Vector tomography applications in plasma diagnostics,” Plasma Phys. Controlled Fusion 38, 489–503 (1996).
[CrossRef]

W. Gault, S. Brown, A. Moise, D. Liang, G. Sellar, G. Shepherd, J. Wimperis, “ERWIN: an E-region wind interferometer,” Appl. Opt. 35, 2913–2922 (1996).
[CrossRef] [PubMed]

M. Shats, D. L. Rudakov, B. D. Blackwell, G. Borg, R. L. Dewar, J. Howard, L. Sharp, “Improved particle confinement mode in low-temperature plasma in H-1 heliac,” Phys. Rev. Lett. 77, 4190–4193 (1996).
[CrossRef] [PubMed]

1991 (1)

1990 (1)

S. Hamberger, B. Blackwell, L. Sharp, D. Shenton, “H-1 design and construction,” Fusion Technol. 17, 123–130 (1990).

1986 (1)

1985 (1)

R. S. Weiss, T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

1966 (1)

R. Hilliard, G. Shepherd, “Upper atmosphere temperatures from Doppler line width,” Planet. Space Sci. 14, 386–406 (1966).
[CrossRef]

Blackwell, B.

S. Hamberger, B. Blackwell, L. Sharp, D. Shenton, “H-1 design and construction,” Fusion Technol. 17, 123–130 (1990).

Blackwell, B. D.

C. Michael, J. Howard, B. D. Blackwell, “The MOSS camera on H-1NF,” Rev. Sci. Instrum. 72, 1034–1037 (2001).
[CrossRef]

M. Shats, D. L. Rudakov, B. D. Blackwell, G. Borg, R. L. Dewar, J. Howard, L. Sharp, “Improved particle confinement mode in low-temperature plasma in H-1 heliac,” Phys. Rev. Lett. 77, 4190–4193 (1996).
[CrossRef] [PubMed]

Borg, G.

M. Shats, D. L. Rudakov, B. D. Blackwell, G. Borg, R. L. Dewar, J. Howard, L. Sharp, “Improved particle confinement mode in low-temperature plasma in H-1 heliac,” Phys. Rev. Lett. 77, 4190–4193 (1996).
[CrossRef] [PubMed]

Brown, S.

Dewar, R. L.

M. Shats, D. L. Rudakov, B. D. Blackwell, G. Borg, R. L. Dewar, J. Howard, L. Sharp, “Improved particle confinement mode in low-temperature plasma in H-1 heliac,” Phys. Rev. Lett. 77, 4190–4193 (1996).
[CrossRef] [PubMed]

Gault, W.

Gaylord, T. K.

R. S. Weiss, T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

Hamberger, S.

S. Hamberger, B. Blackwell, L. Sharp, D. Shenton, “H-1 design and construction,” Fusion Technol. 17, 123–130 (1990).

Hersé, M.

Hilliard, R.

R. Hilliard, G. Shepherd, “Upper atmosphere temperatures from Doppler line width,” Planet. Space Sci. 14, 386–406 (1966).
[CrossRef]

Howard, J.

C. Michael, J. Howard, B. D. Blackwell, “The MOSS camera on H-1NF,” Rev. Sci. Instrum. 72, 1034–1037 (2001).
[CrossRef]

J. Howard, “Modulated Optical Solid-State spectrometer applications in plasma diagnostics,” Rev. Sci. Instrum. 70, 368–371 (1999).
[CrossRef]

J. Howard, “Optical coherence-based techniques for motional Stark effect measurements of magnetic field pitch angle,” Plasma Phys. Controlled Fusion 41, 271–284 (1999).
[CrossRef]

J. Howard, “Vector tomography applications in plasma diagnostics,” Plasma Phys. Controlled Fusion 38, 489–503 (1996).
[CrossRef]

M. Shats, D. L. Rudakov, B. D. Blackwell, G. Borg, R. L. Dewar, J. Howard, L. Sharp, “Improved particle confinement mode in low-temperature plasma in H-1 heliac,” Phys. Rev. Lett. 77, 4190–4193 (1996).
[CrossRef] [PubMed]

Kaminow, I. P.

I. P. Kaminow, An Introduction to Electrooptic Devices (Academic, New York, 1974).

Liang, D.

Michael, C.

C. Michael, J. Howard, B. D. Blackwell, “The MOSS camera on H-1NF,” Rev. Sci. Instrum. 72, 1034–1037 (2001).
[CrossRef]

Moise, A.

Okazaki, H.

Rudakov, D. L.

M. Shats, D. L. Rudakov, B. D. Blackwell, G. Borg, R. L. Dewar, J. Howard, L. Sharp, “Improved particle confinement mode in low-temperature plasma in H-1 heliac,” Phys. Rev. Lett. 77, 4190–4193 (1996).
[CrossRef] [PubMed]

Sasaki, O.

Sellar, G.

Sharp, L.

M. Shats, D. L. Rudakov, B. D. Blackwell, G. Borg, R. L. Dewar, J. Howard, L. Sharp, “Improved particle confinement mode in low-temperature plasma in H-1 heliac,” Phys. Rev. Lett. 77, 4190–4193 (1996).
[CrossRef] [PubMed]

S. Hamberger, B. Blackwell, L. Sharp, D. Shenton, “H-1 design and construction,” Fusion Technol. 17, 123–130 (1990).

Shats, M.

M. Shats, D. L. Rudakov, B. D. Blackwell, G. Borg, R. L. Dewar, J. Howard, L. Sharp, “Improved particle confinement mode in low-temperature plasma in H-1 heliac,” Phys. Rev. Lett. 77, 4190–4193 (1996).
[CrossRef] [PubMed]

Shenton, D.

S. Hamberger, B. Blackwell, L. Sharp, D. Shenton, “H-1 design and construction,” Fusion Technol. 17, 123–130 (1990).

Shepherd, G.

W. Gault, S. Brown, A. Moise, D. Liang, G. Sellar, G. Shepherd, J. Wimperis, “ERWIN: an E-region wind interferometer,” Appl. Opt. 35, 2913–2922 (1996).
[CrossRef] [PubMed]

R. Hilliard, G. Shepherd, “Upper atmosphere temperatures from Doppler line width,” Planet. Space Sci. 14, 386–406 (1966).
[CrossRef]

Steel, W.

W. Steel, Interferometry (Cambridge U. Press, Cambridge, UK, 1967).

Thorne, A. P.

A. P. Thorne, Spectrophysics (Chapman Hall, London, 1988).
[CrossRef]

Thuillier, G.

Weiss, R. S.

R. S. Weiss, T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

Wimperis, J.

Appl. Opt. (3)

Appl. Phys. A (1)

R. S. Weiss, T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

Fusion Technol. (1)

S. Hamberger, B. Blackwell, L. Sharp, D. Shenton, “H-1 design and construction,” Fusion Technol. 17, 123–130 (1990).

Phys. Rev. Lett. (1)

M. Shats, D. L. Rudakov, B. D. Blackwell, G. Borg, R. L. Dewar, J. Howard, L. Sharp, “Improved particle confinement mode in low-temperature plasma in H-1 heliac,” Phys. Rev. Lett. 77, 4190–4193 (1996).
[CrossRef] [PubMed]

Planet. Space Sci. (1)

R. Hilliard, G. Shepherd, “Upper atmosphere temperatures from Doppler line width,” Planet. Space Sci. 14, 386–406 (1966).
[CrossRef]

Plasma Phys. Controlled Fusion (2)

J. Howard, “Vector tomography applications in plasma diagnostics,” Plasma Phys. Controlled Fusion 38, 489–503 (1996).
[CrossRef]

J. Howard, “Optical coherence-based techniques for motional Stark effect measurements of magnetic field pitch angle,” Plasma Phys. Controlled Fusion 41, 271–284 (1999).
[CrossRef]

Rev. Sci. Instrum. (2)

J. Howard, “Modulated Optical Solid-State spectrometer applications in plasma diagnostics,” Rev. Sci. Instrum. 70, 368–371 (1999).
[CrossRef]

C. Michael, J. Howard, B. D. Blackwell, “The MOSS camera on H-1NF,” Rev. Sci. Instrum. 72, 1034–1037 (2001).
[CrossRef]

Other (3)

I. P. Kaminow, An Introduction to Electrooptic Devices (Academic, New York, 1974).

A. P. Thorne, Spectrophysics (Chapman Hall, London, 1988).
[CrossRef]

W. Steel, Interferometry (Cambridge U. Press, Cambridge, UK, 1967).

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Figures (14)

Fig. 1
Fig. 1

Geometry for tomography of some two-dimensional scalar function O showing the relationship between unit vector and the viewing line L(p, θ) at impact parameter p and angle θ.

Fig. 2
Fig. 2

Simulated interferograms showing the effect on the interferogram phase of a change in line-center frequency (exaggerated for clarity). The dashed vertical line corresponds to the delay introduced by the birefringent crystal, and the bold section is the portion of the interferogram swept by the electro-optic modulation. The fringe contrast also varies with changes in the temperature of the emitting species.

Fig. 3
Fig. 3

Optical layout for the modulated solid-state spectrometer. EO, electro-optic.

Fig. 4
Fig. 4

Overlay of plasma spectrum in the vicinity of the 488-nm ArII line and the MOSS spectral response function. The interferogram is apodized by the narrow-bandpass interference filter that is used to isolate the spectral line from the plasma background. The period of the interferogram is inversely proportional to the MOSS interferometer delay (in this case, the crystal thickness is 24 mm) and is chosen to be comparable with the Doppler-broadened width of the emission line.

Fig. 5
Fig. 5

Plot of the wavelength dependence of the birefringence for LiNbO3 obtained by the Sellmeier equations. The dashed curve is the monochromatic birefringence, and the solid curve shows the calculated effective birefringence brought about by inclusion of the refractive-index dispersion. The filled squares are measurements obtained as discussed in the text.

Fig. 6
Fig. 6

Dependence of the scaling functions k T (r) and k υ(r) relating the fractional light noise and the relative uncertainty in the inferred temperature T S and drift velocity υ D as a function of the normalized temperature r = T S /T C .

Fig. 7
Fig. 7

Measured interferogram contrast modulation for the two σ components of the Zeeman split triplet versus magnetic field strength. The beat period of the respective interferograms is a measure of the MOSS delay dispersion. The theoretical curve based on the calculated delay dispersion (κ = 1.6) for LiNbO3 crystals is a reasonable match to the measurements.

Fig. 8
Fig. 8

Plot showing the MOSS calibration data obtained at 632.8 nm. (a) The high-voltage (HV) signal (triangle-wave plus sine-wave modulation) applied to the LiNbO3 plate. (b) The modulated signal at the polarizer transmit port. Demodulated quantities (solid curves, transmit port; dashed curves, reflect port): (c) laser light intensity, (d) instrument contrast, (e) phase offset.

Fig. 9
Fig. 9

Photograph of the dual MOSS spectrometer with major components labeled.

Fig. 10
Fig. 10

Plot of fringe contrast versus FTS phase delay for a uniform plasma with ion temperatures 5, 10, 15, … , 40 eV. The vertical lines correspond to the delays introduced by 25- and 40-mm LiNbO3 cells at 488 nm. Note particularly the wide dynamic range for sensitivity to temperature changes.

Fig. 11
Fig. 11

Schematic view of the plasma region scanned by the solid-state spectrometer.

Fig. 12
Fig. 12

Plot showing plasma parameters for a discharge that dithers between regimes of poor and high confinement. (a) The line-of-sight averaged electron number density, (b) the absorbed rf power, (c) the plasma light intensity, (d) ion temperature, (e) toroidal flow velocity.

Fig. 13
Fig. 13

Plot showing detailed comparison of data extracted from the dual MOSS system. Solid curves, T C = 14-eV cell; dashed curves, T C = 36-eV cell. (a) The extracted light intensities, (b) ion temperatures, (c) toroidal flow speeds.

Fig. 14
Fig. 14

Comparison of perpendicular and parallel ion pressure for nominally identical discharges. (a) Superposition of electron density traces (solid curve, parallel; dashed curve, perpendicular), (b) ion pressure, (c) pressure anisotropy. See text for discussion.

Equations (40)

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eξ; lˆ=L gr, ξ; lˆdl,
gr, ξ; lˆ= fr, υ-υDδξ-υ·lˆdυ
Gr, ϕlˆgr, ξ; lˆ=expiϕυD·lˆG0r, ϕ.
S±ϕ=μ021±γϕ; lˆexpiϕ,
γϕ; lˆ=1μ0- eξ; lˆexpiϕξdξ.
I0rG0r, 0= gr, ξ; lˆdξ.
|γϕ; lˆ|=1μ0L G0r, ϕdl.
G0r, ϕ=I0rexp-ϕ2υth2/4=I0rexp-TSr/TC,
kTC=12 mSυC2,
υC=2cϕ.
|γϕ; lˆ|=1μ0L I0rexp-TSr/TCdl,
δϕϕ=1μ0|γ|L G0r, ϕυD · dl,
ϕ=ϕ0+ϕ1 sin Ωt
S±ϕ=μ01±γ˜c cosϕ1 sin Ωtγ˜q sinϕ1 sin Ωt,
ϕ0=k0BL=2πν0τ02πN,
ϕ1=πLVδλ0d,
ϕξ=ϕ0+κϕ0ξ,
κ=1+ν0B0Bν
nE2λ=4.5820+0.099169/λ2-0.04443-0.021950λ2,nO2λ=4.9048+0.11768/λ2-0.04750-0.027169λ2,
S±=I0±I0ζ cosϕ01+κυD+ϕ1 sinΩt,
RCν0Δν=πNeff,
ϕϕ01-θi22nOcos2 ψnO-sin2 ψnE,
γI=1-Ω2N212n4+exp-iϕ01-BΩ8πn3+,
TITCΩ2N212n4,
αTmaxϕSTS=-I0TC ζ.
dI0I0=ζdTSTC.
dTSTS=kTrdI0I0,
αυmaxϕSυD=I0ζκϕ.
dυDυth=kυrdI0I0.
S=I081+ζ cos2πν+τ++I081+ζ cosπν-τ-=I041+ζ cosκϕ0ξBcos ϕ0,
ΔνB=geB4πme
S±f=f±n J2nϕ1Cf-2nfm±i n J2n+1ϕ1Qf-2n+1fm,
f=I0,Cf=I0γc,Qf=I0γq
S±kfΠ ffm S±f+kfm.
S±2k+1=±I0γqJ2k+1,S±2k=±I0γcJ2k k>0,S±0=I0±I0γcJ0.
γ|γ|=Q2+C21/2/I0,
ϕ=arctanQ/C,
Qt=Sodd/kK J2k+1,
Ct=Seven/kK J2k,
I0t=S0+J0Ct.

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