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Original Articles

Reconstruction of a combination of the absorption and scattering coefficients with a discrete ordinates method consistent with the source–detector system

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Pages 81-101 | Received 11 Jan 2002, Accepted 20 May 2003, Published online: 13 Oct 2011

Figures & data

FIGURE 1 Schematical representation of the influx boundary.

FIGURE 1 Schematical representation of the influx boundary.

FIGURE 2 Pixel mesh generated by a particular external source j.

FIGURE 2 Pixel mesh generated by a particular external source j.

FIGURE 3 Domain partition consistent with parallel beams of radiation, and corresponding rotated coordinate system.

FIGURE 3 Domain partition consistent with parallel beams of radiation, and corresponding rotated coordinate system.

FIGURE 4 Rotational symmetry for the coefficients of matrix C.

FIGURE 4 Rotational symmetry for the coefficients of matrix C.

FIGURE 5 Domain partition considering 2J = 16 sources and 2M = 12 strips for each source.

FIGURE 5 Domain partition considering 2J = 16 sources and 2M = 12 strips for each source.

FIGURE 6 Rotated pixel Knj, mjj and representation of radiation intensities for the discontinuous Galerkin finite element method.

FIGURE 6 Rotated pixel Knj, mjj and representation of radiation intensities for the discontinuous Galerkin finite element method.

FIGURE 7 Configuration 1.

FIGURE 7 Configuration 1.

FIGURE 8 Solution of the direct radiative transfer problem for configuration 1 with 2J=12 and 2M = 20. Radiation originated at source j = 1 is coming into the medium only through the strip n1= 10.

FIGURE 8 Solution of the direct radiative transfer problem for configuration 1 with 2J=12 and 2M = 20. Radiation originated at source j = 1 is coming into the medium only through the strip n1 = 10.

FIGURE 9 Reconstructed values for the combination of absorption and scattering coefficients. Test case 1 with configuration 1. α1 = β1 = 10.

FIGURE 9 Reconstructed values for the combination of absorption and scattering coefficients. Test case 1 with configuration 1. α1 = β1 = 10.

FIGURE 10 Reconstructed values for the combination of absorption and scattering coefficients. Test case 2 with configuration 1. α11=12.5.

FIGURE 10 Reconstructed values for the combination of absorption and scattering coefficients. Test case 2 with configuration 1. α1=β1=12.5.

FIGURE 11 Configuration 2.

FIGURE 11 Configuration 2.

FIGURE 12 Solution of the direct radiative transfer problem for configuration 2 with 2J = 12 and 2M = 20. Radiation originated at source j = 1 is coming into the medium only through the strip n1 = 10.

FIGURE 12 Solution of the direct radiative transfer problem for configuration 2 with 2J = 12 and 2M = 20. Radiation originated at source j = 1 is coming into the medium only through the strip n1 = 10.

FIGURE 13 Reconstructed values for the combination of absorption and scattering coefficients. Test case 1 with configuration 2. α1= 10, β1= 1, α2 = 1, β2 = 10.

FIGURE 13 Reconstructed values for the combination of absorption and scattering coefficients. Test case 1 with configuration 2. α1 = 10, β1 = 1, α2 = 1, β2 = 10.

FIGURE 14 Reconstructed values for the combination of absorption and scattering coefficients. Test case 2 with configuration 2. α1=12.5, β1= 1, α2 = 1, β2 = 20.

FIGURE 14 Reconstructed values for the combination of absorption and scattering coefficients. Test case 2 with configuration 2. α1=12.5, β1 = 1, α2 = 1, β2 = 20.

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