Abstract

A grating spectrograph can be used for spectrally selective two-dimensional imaging if it is operated with a broad entrance slit. The resulting intensity distribution in its exit plane is a one-dimensional convolution of the spatial and spectral distributions of incident light. We present a dedicated deconvolution filter to reconstruct the spatial image from the spectrograph output. The algorithm is illustrated on Raman imaging of an underexpanded dry air jet. Recorded Raman images correspond to density maps convolved with the Raman spectrum of air; the latter essentially acts as a blurring function for the density map. The deconvolution filter combines the individual images recorded in the O2 and N2 Raman bands into a single image of relative air density.

© 2003 Optical Society of America

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References

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  1. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus, Cambridge, Mass., 1988).
  2. K. Kohse-Höinghaus and J. B. Jeffries, eds., Applied Combustion Diagnostics (Academic, San Diego, Calif., 2002).
  3. Ref. 2 Chap. 7.
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  8. A. Brockhinke, K. Kohse-Höinghaus, and P. Andresen, Opt. Lett. 21, 2029 (1996).
    [CrossRef] [PubMed]
  9. R. A. L. Tolboom, N. M. Sijtsema, N. J. Dam, and J. J. ter Meulen, paper AIAA-00–0956 (American Institute of Aeronautics and Astronautics, Reston, Va., 2000).
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    [CrossRef]
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    [CrossRef]
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  13. K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1996).
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  15. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, Dordrecht, The Netherlands, 1996).
    [CrossRef]

2000 (2)

G. Grünefeld, H. Schlüter, and P. Andresen, Appl. Phys. B 70, 209 (2000).

A. Ramos, B. Maté, G. Tejeda, J. M. Fernández, and S. Montero, Phys. Rev. E 62, 4940 (2000).
[CrossRef]

1999 (1)

1998 (1)

1996 (3)

Andresen, P.

G. Grünefeld, H. Schlüter, and P. Andresen, Appl. Phys. B 70, 209 (2000).

A. Brockhinke, K. Kohse-Höinghaus, and P. Andresen, Opt. Lett. 21, 2029 (1996).
[CrossRef] [PubMed]

Brockhinke, A.

A. Brockhinke, K. Kohse-Höinghaus, and P. Andresen, Opt. Lett. 21, 2029 (1996).
[CrossRef] [PubMed]

Castleman, K. R.

K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1996).

Chen, Y.

Dam, N. J.

N. M. Sijtsema, R. A. L. Tolboom, N. J. Dam, and J. J. ter Meulen, Opt. Lett. 24, 664 (1999).
[CrossRef]

R. A. L. Tolboom, N. M. Sijtsema, N. J. Dam, and J. J. ter Meulen, paper AIAA-00–0956 (American Institute of Aeronautics and Astronautics, Reston, Va., 2000).

Eckbreth, A. C.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus, Cambridge, Mass., 1988).

Engl, H. W.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, Dordrecht, The Netherlands, 1996).
[CrossRef]

Fernández, J. M.

A. Ramos, B. Maté, G. Tejeda, J. M. Fernández, and S. Montero, Phys. Rev. E 62, 4940 (2000).
[CrossRef]

Fister III, J. C.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: the Art of Scientific Computation, 2nd ed. (Cambridge University, Cambridge, England, 1992).

Grünefeld, G.

G. Grünefeld, H. Schlüter, and P. Andresen, Appl. Phys. B 70, 209 (2000).

Hanke, M.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, Dordrecht, The Netherlands, 1996).
[CrossRef]

Harris, J. M.

Kleimeyer, J. A.

Kohse-Höinghaus, K.

A. Brockhinke, K. Kohse-Höinghaus, and P. Andresen, Opt. Lett. 21, 2029 (1996).
[CrossRef] [PubMed]

Leipertz, A.

Mansour, M.

Maté, B.

A. Ramos, B. Maté, G. Tejeda, J. M. Fernández, and S. Montero, Phys. Rev. E 62, 4940 (2000).
[CrossRef]

Montero, S.

A. Ramos, B. Maté, G. Tejeda, J. M. Fernández, and S. Montero, Phys. Rev. E 62, 4940 (2000).
[CrossRef]

Neubauer, A.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, Dordrecht, The Netherlands, 1996).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: the Art of Scientific Computation, 2nd ed. (Cambridge University, Cambridge, England, 1992).

Rabenstein, F.

Ramos, A.

A. Ramos, B. Maté, G. Tejeda, J. M. Fernández, and S. Montero, Phys. Rev. E 62, 4940 (2000).
[CrossRef]

Schlüter, H.

G. Grünefeld, H. Schlüter, and P. Andresen, Appl. Phys. B 70, 209 (2000).

Sijtsema, N. M.

N. M. Sijtsema, R. A. L. Tolboom, N. J. Dam, and J. J. ter Meulen, Opt. Lett. 24, 664 (1999).
[CrossRef]

R. A. L. Tolboom, N. M. Sijtsema, N. J. Dam, and J. J. ter Meulen, paper AIAA-00–0956 (American Institute of Aeronautics and Astronautics, Reston, Va., 2000).

Tejeda, G.

A. Ramos, B. Maté, G. Tejeda, J. M. Fernández, and S. Montero, Phys. Rev. E 62, 4940 (2000).
[CrossRef]

ter Meulen, J. J.

N. M. Sijtsema, R. A. L. Tolboom, N. J. Dam, and J. J. ter Meulen, Opt. Lett. 24, 664 (1999).
[CrossRef]

R. A. L. Tolboom, N. M. Sijtsema, N. J. Dam, and J. J. ter Meulen, paper AIAA-00–0956 (American Institute of Aeronautics and Astronautics, Reston, Va., 2000).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: the Art of Scientific Computation, 2nd ed. (Cambridge University, Cambridge, England, 1992).

Tolboom, R.

R. Tolboom, “Expanding laser diagnostics in non-seeded compressible flow research,” Ph.D. dissertation (University of Nijmegen, Nijmegen, The Netherlands, 2002), http://webdoc.ubn.kun.nl/mono/t/tolboom_r/expaladii.pdf.

Tolboom, R. A. L.

N. M. Sijtsema, R. A. L. Tolboom, N. J. Dam, and J. J. ter Meulen, Opt. Lett. 24, 664 (1999).
[CrossRef]

R. A. L. Tolboom, N. M. Sijtsema, N. J. Dam, and J. J. ter Meulen, paper AIAA-00–0956 (American Institute of Aeronautics and Astronautics, Reston, Va., 2000).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: the Art of Scientific Computation, 2nd ed. (Cambridge University, Cambridge, England, 1992).

Zimmerman, J.

Appl. Phys. B (1)

G. Grünefeld, H. Schlüter, and P. Andresen, Appl. Phys. B 70, 209 (2000).

Appl. Opt. (2)

Appl. Spectrosc. (1)

Opt. Lett. (1)

A. Brockhinke, K. Kohse-Höinghaus, and P. Andresen, Opt. Lett. 21, 2029 (1996).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. E (1)

A. Ramos, B. Maté, G. Tejeda, J. M. Fernández, and S. Montero, Phys. Rev. E 62, 4940 (2000).
[CrossRef]

Other (8)

R. A. L. Tolboom, N. M. Sijtsema, N. J. Dam, and J. J. ter Meulen, paper AIAA-00–0956 (American Institute of Aeronautics and Astronautics, Reston, Va., 2000).

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus, Cambridge, Mass., 1988).

K. Kohse-Höinghaus and J. B. Jeffries, eds., Applied Combustion Diagnostics (Academic, San Diego, Calif., 2002).

Ref. 2 Chap. 7.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: the Art of Scientific Computation, 2nd ed. (Cambridge University, Cambridge, England, 1992).

K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1996).

R. Tolboom, “Expanding laser diagnostics in non-seeded compressible flow research,” Ph.D. dissertation (University of Nijmegen, Nijmegen, The Netherlands, 2002), http://webdoc.ubn.kun.nl/mono/t/tolboom_r/expaladii.pdf.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, Dordrecht, The Netherlands, 1996).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Raw data OMAgraphs (3000 KrF excimer laser shots per image) of [a] ambient air by use of a narrow entrance slit (0.1 mm) and [b] an underexpanded dry air jet (flow vertically upward, nozzle exit just below the image) by use of a broad entrance slit (3.10 mm). Both images contain the first Stokes Raman bands of O2 and N2. The white horizontal structure is due to laser sheet inhomogeneity. The upper panels contain horizontal cross sections at the location of the white arrow.

Fig. 2
Fig. 2

Strip-by-strip deconvolution of Fig. 1[b] with the spectrum of Fig. 1[a]: [a] without data filtering and [b] with statistical data filtering. The exit labels the nozzle exit.

Equations (4)

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Ix,y;λ=Isx,yRλy;λ.
EIsx,y|Mx,y,Rλy=nInx,yPInx,y|Mx,y,Rλy.
EIsx,y|Mx,y,Rλy=nInx,yPMx,y|Inx,y,RλyPInx,yPMx,y.
E[Isx,y|Mx,y,Rλy]=M˜k=0,y1+στR˜λk=0,y2+στ2FT-1R˜λ*k,yM˜k,y1+στR˜λk,y2

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