Manabu Machida, Yoko Hoshi, Keiichiro Kagawa, and Kazuki Takada, "Decay behavior and optical parameter identification for spatial-frequency domain imaging by the radiative transport equation," J. Opt. Soc. Am. A 37, 2020-2031 (2020)
The decay behavior of specific intensity is studied for spatial-frequency domain imaging (SFDI). It is shown using the radiative transport equation that the decay is given by a superposition of different decay modes, and the decay rates of these modes are determined by spatial frequencies and Case’s eigenvalues. This explains why SFDI can focus on shallow regions. The fact that light with nonzero spatial frequency rapidly decays makes it possible to exclusively extract optical properties of the top layer of a layered medium. We determine optical properties of the top layer of a solid phantom. This measurement is verified with different layered media of numerical phantoms.
Tyler B. Rice, Soren D. Konecky, Amaan Mazhar, David J. Cuccia, Anthony J. Durkin, Bernard Choi, and Bruce J. Tromberg J. Opt. Soc. Am. A 28(10) 2108-2114 (2011)
References
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In the top layer, ${\mu _{a,1}} = 0.01$, 0.02, or 0.03 (${\rm{m}}{{\rm{m}}^{- 1}}$). In the bottom layer, ${\mu _{a,3}} = 0.01$, 0.02, or 0.03 (${\rm{m}}{{\rm{m}}^{- 1}}$).
Table 4.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.01
—
1.8
—
RTE
0.0084
0.16
1.8
0.021
DA1
0.0060
0.40
1.8
0.018
DA2
0.015
0.53
1.5
0.18
Table 5.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.01
—
1.8
—
RTE
0.0085
0.15
1.8
0.021
DA1
0.0060
0.40
1.8
0.018
DA2
0.015
0.53
1.5
0.18
Table 6.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.01
—
1.8
—
RTE
0.0085
0.15
1.8
0.022
DA1
0.0060
0.40
1.8
0.018
DA2
0.015
0.54
1.5
0.18
Table 7.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.02
—
1.8
—
RTE
0.016
0.20
1.8
0.0015
DA1
0.012
0.39
1.9
0.053
DA2
0.026
0.31
1.5
0.19
Table 8.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.02
—
1.8
—
RTE
0.016
0.20
1.8
0.0013
DA1
0.012
0.39
1.9
0.053
DA2
0.026
0.31
1.5
0.19
Table 9.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.02
—
1.8
—
RTE
0.016
0.20
1.8
0.0012
DA1
0.012
0.39
1.9
0.053
DA2
0.026
0.32
1.5
0.19
Table 10.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.03
—
1.8
—
RTE
0.023
0.25
1.8
0.026
DA1
0.017
0.42
2.0
0.088
DA2
0.036
0.21
1.5
0.18
Table 11.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.03
—
1.8
—
RTE
0.023
0.25
1.8
0.026
DA1
0.017
0.42
2.0
0.088
DA2
0.036
0.21
1.5
0.18
Table 12.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.03
—
1.8
—
RTE
0.023
0.25
1.8
0.026
DA1
0.017
0.42
2.0
0.088
DA2
0.036
0.21
1.5
0.18
Tables (12)
Table 1.
Reconstructed and () of the Top Layer of the Two-Layer Medium by RTE for in the Bottom Layer
Error
Error
True
0.02
—
1.0
—
RTE
0.0079
0.60
1.1
0.14
Table 2.
Reconstructed and () of the Top Layer of the Two-Layer Medium by RTE for in the Bottom Layer
In the top layer, ${\mu _{a,1}} = 0.01$, 0.02, or 0.03 (${\rm{m}}{{\rm{m}}^{- 1}}$). In the bottom layer, ${\mu _{a,3}} = 0.01$, 0.02, or 0.03 (${\rm{m}}{{\rm{m}}^{- 1}}$).
Table 4.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.01
—
1.8
—
RTE
0.0084
0.16
1.8
0.021
DA1
0.0060
0.40
1.8
0.018
DA2
0.015
0.53
1.5
0.18
Table 5.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.01
—
1.8
—
RTE
0.0085
0.15
1.8
0.021
DA1
0.0060
0.40
1.8
0.018
DA2
0.015
0.53
1.5
0.18
Table 6.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.01
—
1.8
—
RTE
0.0085
0.15
1.8
0.022
DA1
0.0060
0.40
1.8
0.018
DA2
0.015
0.54
1.5
0.18
Table 7.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.02
—
1.8
—
RTE
0.016
0.20
1.8
0.0015
DA1
0.012
0.39
1.9
0.053
DA2
0.026
0.31
1.5
0.19
Table 8.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.02
—
1.8
—
RTE
0.016
0.20
1.8
0.0013
DA1
0.012
0.39
1.9
0.053
DA2
0.026
0.31
1.5
0.19
Table 9.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.02
—
1.8
—
RTE
0.016
0.20
1.8
0.0012
DA1
0.012
0.39
1.9
0.053
DA2
0.026
0.32
1.5
0.19
Table 10.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.03
—
1.8
—
RTE
0.023
0.25
1.8
0.026
DA1
0.017
0.42
2.0
0.088
DA2
0.036
0.21
1.5
0.18
Table 11.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer
Error
Error
True
0.03
—
1.8
—
RTE
0.023
0.25
1.8
0.026
DA1
0.017
0.42
2.0
0.088
DA2
0.036
0.21
1.5
0.18
Table 12.
Reconstructed and () by RTE, DA1, and DA2 When in the Top Layer and in the Bottom Layer