Bottom layer absorption coefficients extraction from two-layer phantoms based on crossover point in diffuse reflectance

Abstract. Significance: Numerous optical imaging and spectroscopy techniques are used to study the tissue-optical properties; the majority of them are limited in information regarding the penetration depth. A simple, safe, easily applicable diagnostic technique is required to get deeper tissue information in a multilayer structure. Aim: A fiber-based diffuse reflectance (DR) technique is used to extract and quantify the bottom layer absorption coefficients in two-layer (2L) tissue-mimicking solid phantoms. We determine the Indian black ink concentrations in a deep-hidden layer that is sandwiched between agar and silicone-based phantom layers. Approach: A fiber-based DR experiment was performed to study the optical properties of the tissue at higher penetration depth, with different fiber core diameters and a constant numerical aperture (0.5 NA). The optimal core diameter of the fiber was chosen by measuring solid phantoms. In 2L phantoms, the thickness of the top layer was kept 5.5 mm with a constant absorption and reduced scattering coefficients (μa  =  0.045  mm  −  1 and μs  ′    =  2.622  mm  −  1), whereas the absorption coefficients of the bottom layers were varied from 0.014 to 0.037  mm  −  1 keeping the μs  ′   the same as the top layer. A unique crossover point (Cp) was found in the DR intensity profile against distance. We examined the slope before and after the Cp. These two slopes indicate the difference between the optical properties of the top and bottom layers. Our technique got further verification, as we successfully determined the Cp with different Indian black ink concentrations, placed at the junction between the agar and silicone-based phantom layers. Results: The DR measurements were applied to 2L phantoms. Two different slopes were found in 2L phantoms compared to the one-layer (optical properties equal to the top layer of 2L). We extracted the slopes before and after the Cp in the 2L phantoms. The calculated absorption coefficients before the Cp were 0.014  ±  0.0004, 0.022  ±  0.0003, 0.028  ±  0.0003, and 0.036  ±  0.0014  mm  −  1, and the absorption coefficients after the Cp were 0.019  ±  0.0013, 0.013  ±  0.0004, 0.014  ±  0.0006, and 0.031  ±  0.0001  mm  −  1, respectively. The calculated absorption coefficients before the Cp were in good agreement with the optical properties of the bottom layer. The calculated absorption coefficients after the Cp were not the same as the top layer. Our DR system successfully determines the crossover points 12.14  ±  0.11 and 11.73  ±  0.15  mm for 70% and 100% ink concentrations placed at the junction of the agar and silicone layers. Conclusions: In a 2L tissue structure, the Cp depends on the absorption coefficients of top and bottom layers and the thickness of the top layer. With the help of the Cp and the absorption coefficients, one can determine the thickness of the top layer or vice versa. The slope value before the Cp in the DR profile allowed us to determine the absorption properties of the bottom layer instead of having the average behavior of the 2L phantom in the far detection range (11.0 to 17.0 mm).