Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance

Alwin Kienle; Florian K. Forster; Raimund Hibst

doi:10.1364/OL.26.001571

Optics Letters
Vol. 26,
Issue 20,
pp. 1571-1573
(2001)
•https://doi.org/10.1364/OL.26.001571

Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance

Alwin Kienle, Florian K. Forster, and Raimund Hibst

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Alwin Kienle, Florian K. Forster, and Raimund Hibst, "Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance," Opt. Lett. 26, 1571-1573 (2001)

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Abstract

Spatially resolved reflectance measurements are widely used for determination of the optical properties of biological media. However, the influence of the phase function on these measurements has not been quantified. We show that errors in the derived reduced scattering and absorption coefficients are as great as 100% for both absolute and relative spatially resolved reflectance measurements if a standard solution of the diffusion equation is used in the analysis. In addition, we investigated nonlinear regressions, using Monte Carlo simulations and an additional fitting parameter that characterizes the phase function, and found that the errors in the obtained optical coefficients were $\leq 20 %$ .

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	Coefficient
Error^a	$μ_{a, abs}$ ^b	${μ_{s, abs}}^{'}$ ^b	$μ_{a, rel}$ ^c	${μ_{s, rel}}^{'}$ ^c	$μ_{a, rel}$ ^d	${μ_{s, rel}}^{'}$ ^d
$p_{Int} (θ) (%)$	20	7	17	5	9	3
$p_{Fried} (θ) (%)$	49	19	10	8	9	9
$p_{Jacq} (θ) (%)$	31	12	13	5	4	4
$p_{Iso} (θ) (%)$	54	21	8	7	7	9
$p_{Poly} (θ) (%)$	3	6	29	16	17	12
$p_{Zee} (θ) (%)$	91	32	80	29	45	24
$p_{Rayl} (θ) (%)$	71	26	11	11	15	14
$p_{HG} (θ) (%)$	11	3	23	9	12	5

$p (θ)$	$μ_{a}$ ${(mm)}^{- 1}$	$e_{r} (%)$	${μ_{s}}^{'}$ ${(mm)}^{- 1}$	$e_{r} (%)$	$δ$	$γ_{fit}$	$γ_{th}$
$p_{Int} (θ)$	0.0090(2)	10	1.05(1)	5	0.93(1)	1.47	1.62
$p_{Fried} (θ)$	0.0080(3)	20	1.12(2)	12	0.70(3)	0.98	1.07
$p_{Jacq} (θ)$	0.0084(2)	16	1.08(2)	8	0.86(3)	1.26	1.40
$p_{Iso} (θ)$	0.0080(2)	20	1.13(2)	13	0.68(2)	0.95	1.00
$p_{Poly} (θ)$	0.0092(1)^b	8	1.06(1)^b	6	1.00(0)^b	1.80^b	2.19
$p_{Zee} (θ)$	0.0120(3)	20	0.89(1)	11	0.73(3)	1.02	0.94
$p_{Rayl} (θ)$	0.0080(4)	20	1.14(3)	14	0.55(5)	0.84	0.90
$p_{HG} (θ)$	0.0093(5)	7	1.04(3)	4	0.98(2)	1.69	1.8

	Coefficient
Error^a	$μ_{a, abs}$ ^b	${μ_{s, abs}}^{'}$ ^b	$μ_{a, rel}$ ^c	${μ_{s, rel}}^{'}$ ^c	$μ_{a, rel}$ ^d	${μ_{s, rel}}^{'}$ ^d
$p_{Int} (θ) (%)$	20	7	17	5	9	3
$p_{Fried} (θ) (%)$	49	19	10	8	9	9
$p_{Jacq} (θ) (%)$	31	12	13	5	4	4
$p_{Iso} (θ) (%)$	54	21	8	7	7	9
$p_{Poly} (θ) (%)$	3	6	29	16	17	12
$p_{Zee} (θ) (%)$	91	32	80	29	45	24
$p_{Rayl} (θ) (%)$	71	26	11	11	15	14
$p_{HG} (θ) (%)$	11	3	23	9	12	5

$p (θ)$	$μ_{a}$ ${(mm)}^{- 1}$	$e_{r} (%)$	${μ_{s}}^{'}$ ${(mm)}^{- 1}$	$e_{r} (%)$	$δ$	$γ_{fit}$	$γ_{th}$
$p_{Int} (θ)$	0.0090(2)	10	1.05(1)	5	0.93(1)	1.47	1.62
$p_{Fried} (θ)$	0.0080(3)	20	1.12(2)	12	0.70(3)	0.98	1.07
$p_{Jacq} (θ)$	0.0084(2)	16	1.08(2)	8	0.86(3)	1.26	1.40
$p_{Iso} (θ)$	0.0080(2)	20	1.13(2)	13	0.68(2)	0.95	1.00
$p_{Poly} (θ)$	0.0092(1)^b	8	1.06(1)^b	6	1.00(0)^b	1.80^b	2.19
$p_{Zee} (θ)$	0.0120(3)	20	0.89(1)	11	0.73(3)	1.02	0.94
$p_{Rayl} (θ)$	0.0080(4)	20	1.14(3)	14	0.55(5)	0.84	0.90
$p_{HG} (θ)$	0.0093(5)	7	1.04(3)	4	0.98(2)	1.69	1.8

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