Analysis of simulated and experimental backscattered images of turbid media in linearly polarized light: estimation of the anisotropy factor

Julie Falconet; Raphaël Sablong; Emmanuel Perrin; Franck Jaillon; Hervé Saint-Jalmes

doi:10.1364/AO.47.005811

Applied Optics
Vol. 47,
Issue 31,
pp. 5811-5820
(2008)
•https://doi.org/10.1364/AO.47.005811

Analysis of simulated and experimental backscattered images of turbid media in linearly polarized light: estimation of the anisotropy factor

Julie Falconet, Raphaël Sablong, Emmanuel Perrin, Franck Jaillon, and Hervé Saint-Jalmes

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Julie Falconet, Raphaël Sablong, Emmanuel Perrin, Franck Jaillon, and Hervé Saint-Jalmes, "Analysis of simulated and experimental backscattered images of turbid media in linearly polarized light: estimation of the anisotropy factor," Appl. Opt. 47, 5811-5820 (2008)

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- Medical Optics and Biotechnology
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About this Article
History
- Original Manuscript: March 31, 2008
- Revised Manuscript: September 18, 2008
- Manuscript Accepted: September 24, 2008
- Published: October 24, 2008
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 4, Iss. 1

Abstract

Optical characterization of biological tissues is of real interest to improve medical diagnosis, in particular in the detection of precancerous tissues. We propose a new, noninvasive method allowing the estimation of the anisotropy factor. This method is based on the image analysis of the Q element of the Stokes vector backscattered from the turbid medium. These Q-element images show specific patterns depending on g. Therefore the use of Fourier descriptors (FDs) on simulated data to discriminate the specific geometrical features of the Q element enabled us to determine a linear relation between the anisotropy factor and six FDs. This method was applied on experimental data obtained with calibrated solutions. The anisotropy factor was estimated with a maximum relative error of 13%.

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	Theoretical g	Pixel Size ( $μm$ )	Estimated g	Relative Error (%)	Mean Relative Error (%)
1	0.68		0.720	5.9
2	0.72		0.706	2.0
3	0.74		0.739	0.2
4	0.77		0.766	1.0
5	0.82	35	0.817	0.4	1.6
6	0.84		0.835	0.7
7	0.86		0.875	1.8
8	0.88		0.878	0.5
9	0.92		0.937	1.9
10	0.77	23	0.763	1.0
11	0.77	29	0.764	0.9	0.8
12	0.77	39	0.772	0.3

g	Spheres’ Diameter ( $μm$ )	Concentration (%)	$μ_{s}$ ( ${cm}^{- 1}$ )	$μ_{s}^{'}$ ( ${cm}^{- 1}$ )
0.61	0.298	0.5	47.8	18.9
0.69	0.336	0.5	58.1	18.2
0.75	0.442	0.5	88.4	21.8
0.82	0.520	0.5	106.3	19.5
0.88	0.741	0.5	150.1	17.8
0.90	0.82	0.6	194.2	20.1
0.92	1.01	0.6	217.7	18.3

Theoretical g	Mean Estimated g	Mean Relative Error (%)	Max. Relative Error (%)
0.61	0.646	6.0	13.1
0.69	0.669	4.2	8.4
0.75	0.692	7.8	11.2
0.82	0.788	4.4	8.7
0.88	0.852	3.1	7.5
0.90	0.8991	1.6	3.3
0.92	0.950	4.2	8.4
		4.5	13.1

Mean Theoretical g	Theoretical Standard Deviation (Due to Sphere Diameter Variability)	Mean Estimated g	Standard Deviation of Estimates	Mean Absolute Error	t value 1	t value 2
0.61	0.015	0.646	0.021	0.036	5.42	$- 1.39$
0.69	^b	0.669	0.029	0.021	$- 2.29$	^b
0.75	0.005	0.692	0.022	0.058	$- 8.34$	2.57
0.82	0.025	0.788	0.029	0.032	$- 3.49$	0.84
0.88	0.010	0.852	0.018	0.028	$- 4.92$	1.36
0.90	0.017	0.8991	0.018	0.001	$- 0.16$	0.04
0.92	^b	0.950	0.031	0.030	3.06	^b

	Theoretical g	Pixel Size ( $μm$ )	Estimated g	Relative Error (%)	Mean Relative Error (%)
1	0.68		0.720	5.9
2	0.72		0.706	2.0
3	0.74		0.739	0.2
4	0.77		0.766	1.0
5	0.82	35	0.817	0.4	1.6
6	0.84		0.835	0.7
7	0.86		0.875	1.8
8	0.88		0.878	0.5
9	0.92		0.937	1.9
10	0.77	23	0.763	1.0
11	0.77	29	0.764	0.9	0.8
12	0.77	39	0.772	0.3

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Applied Optics