Roberto Reif, Ousama A'Amar, and Irving J. Bigio, "Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media," Appl. Opt. 46, 7317-7328 (2007)
Monte Carlo simulations and experiments in tissue phantoms were used to empirically develop an analytical model that characterizes the reflectance spectrum in a turbid medium. The model extracts the optical properties (scattering and absorption coefficients) of the medium at small source-detector separations, for which the diffusion approximation is not valid. The accuracy of the model and the inversion algorithm were investigated and validated. Four fiber probe configurations were tested for which both the source and the detector fibers were tilted at a predetermined angle, with the fibers parallel to each other. This parallel-fiber geometry facilitates clinical endoscopic applications and ease of fabrication. Accurate extraction of tissue optical properties from in vivo spectral measurements could have potential applications in detecting, noninvasively and in real time, epithelial (pre)cancers.
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Values for the Coefficients a and Obtained With Monte Carlo Simulations and Experiments in Tissue Phantoms With a 0°, 15°, 30°, and 45° Fiber Probe Configuration
Fiber Tilt Angle
0°
15°
30°
45°
a
MC
1.2 × 10−5
1.1 × 10−5
1.1 × 10−5
1.0 × 10−5
Experiment
0.11
0.11
0.11
0.10
MC
0.0 × 10−5
0.0 × 10−5
0.0 × 10−5
0.0 × 10−5
Experiment
−0.04
−0.04
−0.03
−0.01
Table 2
Values for the Coefficient b Obtained With Monte Carlo Simulations and Experiments in Tissue Phantoms With a 0°, 15°, 30°, and 45° Fiber Probe Configuration
Fiber Tilt Angle
0°
15°
30°
45°
MC
μs′ = 5
0.33
0.32
0.32
0.32
μs′ = 10
0.33
0.31
0.31
0.29
μs′ = 20
0.30
0.30
0.30
0.28
Mean
0.32
0.31
0.31
0.30
Experiment
μs′ = 5.5
0.20
0.26
0.25
0.26
μs′ = 10.6
0.22
0.25
0.25
0.25
μs′ = 20.7
0.23
0.25
0.23
0.24
Mean
0.22
0.25
0.24
0.25
Table 3
Values for the Coefficient c Obtained With Monte Carlo Simulations and Experiments in Tissue Phantoms With a 0°, 15°, 30°, and 45° Fiber Probe Configuration
Fiber Tilt Angle
0°
15°
30°
45°
MC
μs′ = 5
0.21
0.21
0.21
0.20
μs′ = 10
0.21
0.22
0.21
0.19
μs′ = 20
0.20
0.20
0.20
0.19
Mean
0.21
0.21
0.21
0.19
Experiment
μs′ = 5.5
0.20
0.20
0.20
0.20
μs′ = 10.6
0.20
0.20
0.20
0.20
μs′ = 20.7
0.20
0.20
0.20
0.20
Mean
0.20
0.20
0.20
0.20
Table 4
Values for the Coefficients a, b, and c Obtained With Monte Carlo Simulations With the 0° and 45° Fiber Probe Configuration Under Different Conditionsa
A
B
C
D
E
F
G
H
Parameters
nf
1.5
1.46
1.5
1.5
1.5
1.5
1.5
1.5
nm
1.4
1.33
1.4
1.4
1.4
1.4
1.4
1.4
Separation (μm)
250
250
200
250
250
250
250
250
Phase function
HG
HG
HG
MHG
HG
HG
HG
HG
g
0.9
0.9
0.9
0.9
0.2
0.5
0.75
0.95
Tilt angle
0°
a
1.2×10−5
1.2×10−5
1.4×10−5
1.2×10−5
1.1×10−5
1.1×10−5
1.2×10−5
1.2×10−5
a0
0.0×10−5
0.0×10−5
0.0×10−5
1.5×10−5
4.8×10−5
1.7×10−5
0.0×10−5
0.0×10−5
b
0.32
0.30
0.26
0.31
0.36
0.32
0.31
0.31
c
0.21
0.21
0.21
0.21
0.20
0.20
0.20
0.19
45°
a
1.0×10−5
1.1×10−5
1.3×10−5
1.0×10−5
9.9×10−5
1.0×10−5
1.1×10−5
1.0×10−5
a0
0.0×10−5
0.0×10−5
0.0×10−5
2.1×10−5
4.0×10−5
2.0×10−5
0.0×10−5
0.0×10−5
b
0.30
0.30
0.25
0.30
0.35
0.32
0.30
0.30
c
0.19
0.20
0.20
0.20
0.20
0.21
0.21
0.21
Bold indicates the changes in the parameters referenced to the parameters described in column A. See text for details.
Table 5
Mean and Standard Deviation Over 15 Measurements of the Absorption Coefficient Extracted From Experiments in Tissue Phantoms with a 0°, 15°, 30°, and 45° Fiber Probe Configuration at 610 nma
Actual μa
Actual μs′
Fiber Tilt Angle
0°
15°
30°
45°
0
9.2
0.00±0.00
0.00±0.00
0.00±0.00
0.00±0.00
17.5
0.00±0.00
0.00±0.00
0.00±0.00
0.00±0.00
0.5
9.2
0.58±0.03
0.58±0.01
0.49±0.00
0.58±0.02
17.5
0.58±0.02
0.58±0.02
0.49±0.02
0.53±0.02
2.8
9.2
2.71±0.04
3.18±0.03
2.62±0.02
2.89±0.04
17.5
2.70±0.04
3.10±0.02
2.45±0.14
2.82±0.03
8.5
9.2
7.98±0.14
8.75±0.12
8.01±0.16
8.53±0.19
17.5
8.39±0.06
8.56±0.52
8.23±0.05
8.57±0.08
Units are in cm−1.
Table 6
Mean and Standard Deviation Over 15 Measurements of the Reduced Scattering Coefficient Extracted From Experiments in Tissue Phantoms With a 0°, 15°, 30°, and 45° Fiber Probe Configuration at 610 nma
Actual μs′
Actual μa
Fiber Tilt Angle
0°
15°
30°
45°
9.2
0
8.7±0.3
8.8±0.1
9.1±0.1
9.6±0.1
0.5
9.0±0.3
9.6±0.1
9.0±0.1
9.1±0.2
2.8
8.5±0.3
9.5±0.2
9.7±0.0
9.2±0.3
8.5
9.3±0.3
9.6±0.2
9.3±0.1
8.8±0.3
17.5
0
16.9±1.1
17.4±0.5
17.4±0.2
18.3±0.6
0.5
17.4±0.9
19.0±1.0
17.3±0.2
17.3±0.9
2.8
16.4±0.7
18.4±0.4
17.6±1.1
18.3±0.4
8.5
18.5±0.4
17.1±2.0
17.2±0.2
16.4±0.4
Units are in cm−1.
Tables (6)
Table 1
Values for the Coefficients a and Obtained With Monte Carlo Simulations and Experiments in Tissue Phantoms With a 0°, 15°, 30°, and 45° Fiber Probe Configuration
Fiber Tilt Angle
0°
15°
30°
45°
a
MC
1.2 × 10−5
1.1 × 10−5
1.1 × 10−5
1.0 × 10−5
Experiment
0.11
0.11
0.11
0.10
MC
0.0 × 10−5
0.0 × 10−5
0.0 × 10−5
0.0 × 10−5
Experiment
−0.04
−0.04
−0.03
−0.01
Table 2
Values for the Coefficient b Obtained With Monte Carlo Simulations and Experiments in Tissue Phantoms With a 0°, 15°, 30°, and 45° Fiber Probe Configuration
Fiber Tilt Angle
0°
15°
30°
45°
MC
μs′ = 5
0.33
0.32
0.32
0.32
μs′ = 10
0.33
0.31
0.31
0.29
μs′ = 20
0.30
0.30
0.30
0.28
Mean
0.32
0.31
0.31
0.30
Experiment
μs′ = 5.5
0.20
0.26
0.25
0.26
μs′ = 10.6
0.22
0.25
0.25
0.25
μs′ = 20.7
0.23
0.25
0.23
0.24
Mean
0.22
0.25
0.24
0.25
Table 3
Values for the Coefficient c Obtained With Monte Carlo Simulations and Experiments in Tissue Phantoms With a 0°, 15°, 30°, and 45° Fiber Probe Configuration
Fiber Tilt Angle
0°
15°
30°
45°
MC
μs′ = 5
0.21
0.21
0.21
0.20
μs′ = 10
0.21
0.22
0.21
0.19
μs′ = 20
0.20
0.20
0.20
0.19
Mean
0.21
0.21
0.21
0.19
Experiment
μs′ = 5.5
0.20
0.20
0.20
0.20
μs′ = 10.6
0.20
0.20
0.20
0.20
μs′ = 20.7
0.20
0.20
0.20
0.20
Mean
0.20
0.20
0.20
0.20
Table 4
Values for the Coefficients a, b, and c Obtained With Monte Carlo Simulations With the 0° and 45° Fiber Probe Configuration Under Different Conditionsa
A
B
C
D
E
F
G
H
Parameters
nf
1.5
1.46
1.5
1.5
1.5
1.5
1.5
1.5
nm
1.4
1.33
1.4
1.4
1.4
1.4
1.4
1.4
Separation (μm)
250
250
200
250
250
250
250
250
Phase function
HG
HG
HG
MHG
HG
HG
HG
HG
g
0.9
0.9
0.9
0.9
0.2
0.5
0.75
0.95
Tilt angle
0°
a
1.2×10−5
1.2×10−5
1.4×10−5
1.2×10−5
1.1×10−5
1.1×10−5
1.2×10−5
1.2×10−5
a0
0.0×10−5
0.0×10−5
0.0×10−5
1.5×10−5
4.8×10−5
1.7×10−5
0.0×10−5
0.0×10−5
b
0.32
0.30
0.26
0.31
0.36
0.32
0.31
0.31
c
0.21
0.21
0.21
0.21
0.20
0.20
0.20
0.19
45°
a
1.0×10−5
1.1×10−5
1.3×10−5
1.0×10−5
9.9×10−5
1.0×10−5
1.1×10−5
1.0×10−5
a0
0.0×10−5
0.0×10−5
0.0×10−5
2.1×10−5
4.0×10−5
2.0×10−5
0.0×10−5
0.0×10−5
b
0.30
0.30
0.25
0.30
0.35
0.32
0.30
0.30
c
0.19
0.20
0.20
0.20
0.20
0.21
0.21
0.21
Bold indicates the changes in the parameters referenced to the parameters described in column A. See text for details.
Table 5
Mean and Standard Deviation Over 15 Measurements of the Absorption Coefficient Extracted From Experiments in Tissue Phantoms with a 0°, 15°, 30°, and 45° Fiber Probe Configuration at 610 nma
Actual μa
Actual μs′
Fiber Tilt Angle
0°
15°
30°
45°
0
9.2
0.00±0.00
0.00±0.00
0.00±0.00
0.00±0.00
17.5
0.00±0.00
0.00±0.00
0.00±0.00
0.00±0.00
0.5
9.2
0.58±0.03
0.58±0.01
0.49±0.00
0.58±0.02
17.5
0.58±0.02
0.58±0.02
0.49±0.02
0.53±0.02
2.8
9.2
2.71±0.04
3.18±0.03
2.62±0.02
2.89±0.04
17.5
2.70±0.04
3.10±0.02
2.45±0.14
2.82±0.03
8.5
9.2
7.98±0.14
8.75±0.12
8.01±0.16
8.53±0.19
17.5
8.39±0.06
8.56±0.52
8.23±0.05
8.57±0.08
Units are in cm−1.
Table 6
Mean and Standard Deviation Over 15 Measurements of the Reduced Scattering Coefficient Extracted From Experiments in Tissue Phantoms With a 0°, 15°, 30°, and 45° Fiber Probe Configuration at 610 nma