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Liquid phantom for investigating light propagation through layered diffusive media

S. Del Bianco, F. Martelli, F. Cignini, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu

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Abstract

A liquid phantom for investigating light propagation through layered diffusive media is described. The diffusive medium is an aqueous suspension of calibrated scatterers and absorbers. A thin membrane separates layers with different optical properties. Experiments showed that a material with scattering properties should be used for the membrane to avoid the perturbation due to the guided propagation that occurs through a transparent layer. Examples of measurements on a three-layered medium are reported both in the cw and in the time domain.

©2004 Optical Society of America

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Figures (7)
Fig. 1.
Fig. 1. View of the proposed phantom.

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Fig. 2.
Fig. 2. MC time resolved reflectance for a homogeneous medium and for the same medium with a transparent membrane of different thickness, scl , at a depth of 5 mm. The results are shown for two values of the source-receiver separation: ρ = 20 and 50 mm. The diffusive medium has μs ' = 1 mm-1, μa =0.01 mm-1, and refractive index n 1 = 1.33. The refractive index of the membrane is n 2 = 1.5.

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Fig. 3.
Fig. 3. Examples of perturbation due to three different transparent membranes on multidistance (ρ = 10, 20, 30, 40 mm) measurements of time resolved reflectance. The figure reports the results for the homogeneous medium (μs ' =1.00±0.03 mm-1 and μa = 0.01±0.0005 mm-1) with (red curves) and without (black curves) the membrane. For all measurements the membrane was at a depth of 4.5 mm.

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Fig. 4.
Fig. 4. Examples of perturbation due to three different membranes of similar thickness but of different material, on measurements of CW reflectance. The figure reports the relative perturbation (R - R hom)/ R hom as a function of the depth of the membrane. Measurements have been repeated for three values of absorption for a diffusive medium with μs ' =1.0±0.05mm-1. The blue, green, red, and black curves refer to source-receiver distances ρ = 10, 20, 30, and 40 mm, respectively.

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Fig. 5.
Fig. 5. Effect of a clear layer on measurements of time resolved reflectance. The three-layered medium has the first and the third layer (thickness 4.5 and 51 mm, respectively) with the same optical properties: μ s1 ' = μ s3 ' = 1.0 mm-1 and μ a1 = μ a3 = 0.01 mm-1. The figure shows the comparison between measurements for the homogeneous medium and for the layered medium with μ s2 ' = 0.1 mm-1 and μ a2 = 0.003 mm-1. The thickness of the second layer was 4.5 mm. The results for ρ = 20 and 40 mm are reported together with predictions of MC simulations.

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Fig. 6.
Fig. 6. Time resolved mean path followed by received photons inside the second layer of a medium having: thickness of the first, second, and third layer 4.5, 4.5, and 51 mm respectively; μ s1 ' = μ s3 ' = 1.00 mm-1, μ s2 ' = 1.05 mm-1, μ a1 = μ a3 = 0.01 mm-1 and μ a2 = 0003 mm-1. The results are reported for measurements at ρ = 10, 20, 30, and 40 mm together with the prediction of the diffusion equation.

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Fig. 7.
Fig. 7. Perturbation due to an absorbing inhomogeneity (volume = 1.1 ml, μsi ' = 5.7 mm-1 and μai = 0.012 mm-1) immersed into the third layer of a medium having: thickness of the first, second, and third layer 11, 3, and 46 mm respectively; μ s1 ' = 1.7 mm-1, μ s3 ' = 5.7 mm-1, μ a1 = μ a2 = μ a3 = 0.0003 mm-1. Results are shown for four values of μ s2 ' . The source and the receiver are at x = -20 and +20 mm respectively. The perturbation is reported as a function of the x-coordinate of the centre of the inhomogeneity for two values of the depth: 22 mm (red curve) and 25 mm (black curve) within the third layer.

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Equations (1)

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〈 l 2 〉 ( t ) = 1 Δ μ a 2 ln R ( ρ , μ a 2 , t ) R ( ρ , μ a 2 + Δ μ a 2 , t ) .
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