Abstract

Three Monte Carlo programs were developed which keep track of the status of polarization of light traveling through mono-disperse solutions of micro-spheres. These programs were described in detail in our previous article [1]. This paper illustrates a series of Monte Carlo simulations that model common experiments of light transmission and reflection of scattering media. Furthermore the codes were expanded to model light propagating through poly-disperse solutions of micro-spheres of different radii distributions.

© 2005 Optical Society of America

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References

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  18. The experimental data gently provided by Dr. Cameron.

Appl. Opt. (6)

Comput. Methods Programs Biomed. (1)

L. Whang, S.L. Jacques, amd L. Zheng, "MCML- Monte Carlo modeling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146, (1995).
[CrossRef]

J. Opt. Soc. Am. A. (1)

J. He, A Karlsson, J. Swartling, S. Anderson-Engles, "Light scattering by multiple red blood cells," J. Opt. Soc. Am. A. 21, 1953-1961, (2004).
[CrossRef]

J.Quant.Spectrosc. Radiat. Transfer. (1)

K.F. Evans and G.L. Stephens, "A new polarized atmospheric radiative transfer model," J.Quant.Spectrosc. Radiat. Transfer. 46, 413-423, (1991).
[CrossRef]

Lasers Surg. Med. (1)

S. L. Jacques, R. J. Roman, K. Lee, "Imaging superficial tissues with polarized light," Lasers Surg. Med. 26, 119-129, (2000).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Opt. Letters (1)

G. Yao, L-H. Wang, "Two-dimensional depth-resolved Muller matrix characterization of biological tissue by optical coherence tomography," Opt. Letters 24, 537-539, (1999).
[CrossRef]

Other (2)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, the art of Scientific Computing, (Cambridge University Press, 1992).

The experimental data gently provided by Dr. Cameron.

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Figures (14)

Fig. 1.
Fig. 1.

Experimental set-up for back-reflected Mueller matrix measurements.

Fig. 2.
Fig. 2.

Comparison of Mueller matrix results for light backscattered from solutions of micro-spheres. The image on the left is an experimental result of Cameron et al. the image on the right is the Mueller matrix obtained with our Monte Carlo programs. (The left-hand image was gently provided by Dr. Cameron.)

Fig. 3.
Fig. 3.

Experimental apparatus. We studied backscattering from a solution of micro-spheres (diameter 2μm) when the polarized illumination is at an angle of 30°.

Fig. 4.
Fig. 4.

Experimental results (left) and Monte Carlo simulation (right) of the first 9 of elements of the 16 element of Mueller matrix. The micro-spheres diameter was 2μm and index of refraction 1.59. The micro-spheres were in a water media with index of refraction equal to 1.33. Each image is 4x4 cm. Light was incident at an angle θ from the normal. m1 1 values are in between 0 and 0.1 all other element were in between -.01 and 0.1; only positive values are shown in these images to enhance contrast.

Fig. 5.
Fig. 5.

Experimental setup, top view. Polarized images of light scattered by a micro-spheres solution were acquired with a digital camera. Laser light (632.8nm) was polarized and the scattered light was passed through an analyzer whose orientation was either parallel or perpendicular to the incident beam.

Fig. 6.
Fig. 6.

Top image is the experimental results obtained with polarizer and analyzer oriented parallel to each other, the bottom image is the Monte Carlo simulation.

Fig. 7.
Fig. 7.

Comparison of exittance for experiment (line) and Monte Carlo results (void circles) for parallel image. This intensity profile corresponds to the centerline of the axis of irradiation.

Fig. 8.
Fig. 8.

Top image is the experimental results obtained with the polarizer oriented parallel to the optical table and analyzer oriented perpendicular to the optical table, the bottom image is the corresponding Monte Carlo simulation. Both images were normalized by the maximum value of the parallel image.

Fig. 9.
Fig. 9.

Transmission experiment. The incident beam is polarized parallel to the optical table and an analyzer in front of the detector selects the status of polarization of light transmitted through the cuvette.

Fig. 10.
Fig. 10.

Experimental results and Monte Carlo simulations (black circles and squares) for a mono-disperse solution of micro-spheres. Diameter of micro-spheres was 482 nm, light wavelength was 543 nm. The back line is the heuristic model applied to the Monte Carlo data

Fig. 11.
Fig. 11.

Experimental results and Monte Carlo simulations (black circles and squares) for a mono-disperse solution of micro-spheres. Diameter was 0.308 μm, light wavelength was 0.543 μm.

Fig. 12.
Fig. 12.

A photon scattering in a poly-disperse solution of micro-spheres

Fig. 13.
Fig. 13.

Total transmittance and reflectance geometry; the reference plane for the incident polarized beam was the plane of the x and y unit vectors.

Fig. 14.
Fig. 14.

Degree of polarization for poly-disperse solutions of micro-spheres and mono-disperse solutions of identical anisotropy.

Tables (2)

Tables Icon

Table 1. Results of total reflectance from a solution of poly-disperse modified gamma distribution of spheres. Comparison of Adding Doubling code by Evans and Monte Carlo simulations

Tables Icon

Table 2. Results of total transmission through a solution of poly-disperse modified gamma distribution of spheres. Comparison of Adding Doubling code by Evans and Monte Carlo simulations

Equations (1)

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N ( r ) = a r α exp ( b r γ )

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