Optical properties of turbid media with specularly reflecting boundaries: applications to biological problems

R. P. Hemenger

doi:10.1364/AO.16.002007

Optical properties of turbid media with specularly reflecting boundaries: applications to biological problems

R. P. Hemenger

Applied Optics
Vol. 16,
Issue 7,
pp. 2007-2012
(1977)
•https://doi.org/10.1364/AO.16.002007

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R. P. Hemenger, "Optical properties of turbid media with specularly reflecting boundaries: applications to biological problems," Appl. Opt. 16, 2007-2012 (1977)

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History
- Original Manuscript: December 20, 1976
- Published: July 1, 1977

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Abstract

The optical properties of turbid media are formulated in terms of the diffusion equation approximation to linear transport theory. In particular the important effects of specular reflection at bounding surfaces are accurately accounted for by means of explicit boundary conditions at these surfaces. Applications of these results to two problems of biological interest are made. In one a simple multiple scattering model of a leaf is shown to account well for its measured optical properties. In another a method is proposed for finding accurate absorption spectra of pigment-containing cells.

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	N =1.0			N =1.5
γ_S/γ	Exact^a	Approx.^b	Error(%)	Exact^a	Approx.^b	Error(%)
1.000	1.000	1.000	0.0	1.000	1.000	0
0.999	0.913	0.912	0.1	0.841	0.847	0.7
0.995	0.817	0.815	0.2	0.691	0.700	1.3
0.990	0.753	0.751	0.3	0.602	0.612	1.7
0.975	0.641	0.638	0.5	0.469	0.476	1.5
0.950	0.536	0.531	0.9	0.361	0.364	0.8
0.925	0.467	0.460	1.5	0.301	0.297	1.3
0.900	0.415	0.406	2.2	0.260	0.251	3.5
0.800	0.285	0.267	6.3	0.172	0.146	15.1

	N =1.0				N =1.5
γ_S/γ	Exacta	Approx.^b	Error(%)	Exact^a	Approx.^b	Error(%)
1.000	1.000	1.000	0	1.000	1.000	0
0.999	0.894	0.893	0.1	0.811	0.817	0.7
0.995	0.779	0.780	0.1	0.639	0.650	1.7
0.990	0.703	0.705	0.3	0.542	0.555	2.4
0.975	0.573	0.580	1.2	0.400	0.413	3.3
0.950	0.456	0.464	1.8	0.294	0.301	2.4
0.925	0.381	0.390	2.4	0.236	0.238	0.8
0.900	0.327	0.336	2.8	0.198	0.195	1.5
0.800	0.200	0.203	1.5	0.121	0.103	14.9

${\bar{μ}}_{o}$	γ_S/γ	Exact^a	Approx.^b	Error(%)
	1.00	1.000	1.000	0
	0.99	0.665	0.670	0.8
0.50	0.95	0.404	0.415	2.7
	0.90	0.278	0.287	3.2
	0.80	0.162	0.161	0.6
	1.00	1.000	1.000	0
	0.99	0.559	0.572	2.3
0.75	0.95	0.277	0.296	6.9
	0.90	0.166	0.178	6.6
	0.80	0.082	0.082	0
	1.00	1.000	1.000	0
	0.99	0.440	0.460	4.6
0.875	0.95	0.168	0.186	10.7
	0.90	0.087	0.093	6.9
	0.80	0.038	0.034	10.5

	N =1.0			N =1.5
γ_S/γ	Exact^a	Approx.^b	Error(%)	Exact^a	Approx.^b	Error(%)
1.000	1.000	1.000	0.0	1.000	1.000	0
0.999	0.913	0.912	0.1	0.841	0.847	0.7
0.995	0.817	0.815	0.2	0.691	0.700	1.3
0.990	0.753	0.751	0.3	0.602	0.612	1.7
0.975	0.641	0.638	0.5	0.469	0.476	1.5
0.950	0.536	0.531	0.9	0.361	0.364	0.8
0.925	0.467	0.460	1.5	0.301	0.297	1.3
0.900	0.415	0.406	2.2	0.260	0.251	3.5
0.800	0.285	0.267	6.3	0.172	0.146	15.1

	N =1.0				N =1.5
γ_S/γ	Exacta	Approx.^b	Error(%)	Exact^a	Approx.^b	Error(%)
1.000	1.000	1.000	0	1.000	1.000	0
0.999	0.894	0.893	0.1	0.811	0.817	0.7
0.995	0.779	0.780	0.1	0.639	0.650	1.7
0.990	0.703	0.705	0.3	0.542	0.555	2.4
0.975	0.573	0.580	1.2	0.400	0.413	3.3
0.950	0.456	0.464	1.8	0.294	0.301	2.4
0.925	0.381	0.390	2.4	0.236	0.238	0.8
0.900	0.327	0.336	2.8	0.198	0.195	1.5
0.800	0.200	0.203	1.5	0.121	0.103	14.9

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