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1.
Figure 5

Figure 5. Experimental schematic and spatially resolved reflectance. From: Photon diffusion near the point-of-entry in anisotropically scattering turbid media.

(a) Schematic of the experimental setup. The expanded incident laser beam passes through a 20/80 beamsplitter and is delivered to the scattering sample through an objective. Light scattered from the sample is collected by the same objective and is reflected by a beamsplitter toward the imaging CCD. (b) Experimentally collected spatially resolved reflectance.

Edward Vitkin, et al. Nat Commun. ;2:587-587.
2.
Figure 1

Figure 1. Semi-infinite turbid medium geometry. From: Photon diffusion near the point-of-entry in anisotropically scattering turbid media.

The medium is illuminated with a narrow collimated beam. In addition to unscattered photons, low-angle scattered photons are also shown. Any point along the beam can be a source of a single large angle turn, which is followed by low-angle scattered photons propagating toward the surface. The large angle turn is described by the phase function, providing phase function correction. Here .

Edward Vitkin, et al. Nat Commun. ;2:587-587.
3.
Figure 6

Figure 6. Comparison with the experiment. From: Photon diffusion near the point-of-entry in anisotropically scattering turbid media.

Red circles - experiment, the bars on the experimental points show the range of measurements. Black dashed line - standard diffusion approximation (DA), blue dashed line - PFC diffusion theory. Inset: Expanded view of the critical region near the point-of-entry to show the range of measurements more clearly. The PFC diffusion theory demonstrates excellent agreement with the experiment while the DA deviates significantly near the POE.

Edward Vitkin, et al. Nat Commun. ;2:587-587.
4.
Figure 7

Figure 7. Evaluation of the contribution of the neglected integral term. From: Photon diffusion near the point-of-entry in anisotropically scattering turbid media.

(a) Angles between vectors s, s′, and jd. The vector s defines the z′. The vectors s and jd(r) define the (y′, z′) plane. (b) Contributions of the neglected integral term, PFC term, and diffuse reflectance term to the reflectance. Black line - radially dependent diffuse reflectance Rd(ρ), blue line - contribution of the PFC term Rp(ρ), red line - contribution of the neglected integral term ΔRp. The contribution of the neglected integral term, ΔRp(ρ), is less than 4% of Rp(ρ) for . The contribution of ΔRp(ρ) is less than 7% of Rd(ρ) for . The calculations are performed for Henyey-Greenstein phase function, g=0.9 and .

Edward Vitkin, et al. Nat Commun. ;2:587-587.
5.
Figure 4

Figure 4. Comparison of the PFC for internal fluence rate with Monte Carlo simulations. From: Photon diffusion near the point-of-entry in anisotropically scattering turbid media.

The phase function correction to the fluence rate within the medium (solid lines) is calculated for the Henyey-Greenstein phase function with g=0.9. The Monte Carlo data (circles) are obtained taking the difference in the fluence rate from a simulation with isotropic scattering (g=0) and a simulation with g=0.9. In all cases, The depth values corresponding to the colors black, green, red, blue and magenta are 0.01, 0.06, 0.1, 0.24 and 0.5 respectively.

Edward Vitkin, et al. Nat Commun. ;2:587-587.
6.
Figure 2

Figure 2. Sensitivity to the form of the phase function and comparison to other light transport approximations. From: Photon diffusion near the point-of-entry in anisotropically scattering turbid media.

(a) Dimensionless reflectance for Henyey-Greenstein (H-G) and Mie phase functions with g=0.95 and . Blue lines and circles - Henyey-Greenstein phase function, red lines and circles - Mie phase function, where lines are for PFC diffusion theory and circles are for Monte Carlo simulations. Black dashed line - the standard diffusion approximation (DA). (b) Comparison of PFC diffusion theory with the standard diffusion approximation, the P3 and δ-P1 approximations and Monte Carlo simulations for the Henyey-Greenstein phase function with g=0.95 and . The error plot shows the percentage error ((RRMC)/RMC·100%), between each of the approximations, R, and Monte Carlo simulation, RMC.

Edward Vitkin, et al. Nat Commun. ;2:587-587.
7.
Figure 3

Figure 3. Effects of absorption and anisotropy factor g. From: Photon diffusion near the point-of-entry in anisotropically scattering turbid media.

Dimensionless reflectance for the PFC diffusion theory compared with Monte Carlo simulations (MC) and the standard diffusion theory (DA) for the case of the Henyey-Greenstein phase function with different absorptions; (a) blue lines and circles - g=0.9 and relatively weak absorption (), red lines and circles - g=0.9 and relatively high absorption (). Dashed lines - standard diffusion approximation, solid lines - PFC diffusion theory, circles - Monte Carlo simulations. Though the standard diffusion theory gives significant errors for the PFC diffusion approximation does not suffer from this problem and agrees with the Monte Carlo simulations for all distances; (b) effect of different anisotropy factors g. Red represents g=0 and blue represents g=0.9. The PFC diffusion theory (solid lines) agrees with Monte Carlo simulations (circles) for all distances, while the standard diffusion theory (black dashed line) does not have any dependence on the anisotropy factor g. (Note that the standard diffusion theory and the PFC diffusion theory curves exactly overlap for g=0.) Inset: the separate contributions of the diffuse reflectance (black line) and PFC reflectance (blue line) and their asymptotic behavior (dashed lines).

Edward Vitkin, et al. Nat Commun. ;2:587-587.

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