Merging Mie solutions and the radiative transport equation to measure optical properties of scattering particles in optical phantoms

Abstract

We present a new method to calculate the complex refractive index of spherical scatterers in a novel optical phantom developed by using homemade monodisperse silica nanospheres embedded into a polyester resin matrix and an ethanol–water mixture for applications in diffuse imaging. The spherical geometry of these nanoparticles makes them suitable for direct comparison between the values of the absorption and reduced scattering coefficients ( μ a and μ s ′ , respectively) obtained by the diffusion approximation solution to the transport equation from scattering measurements and those obtained by the Mie solution to Maxwell’s equations. The values of the optical properties can be obtained by measuring, using an ultrafast detector, the time-resolved intensity distribution profiles of diffuse light transmitted through a thick slab of the silica nanosphere phantom, and by fitting them to the time-dependent diffusion approximation solution to the transport equation. These values can also be obtained by Mie solutions for spherical particles when their physical properties and size are known. By using scanning electron microscopy, we measured the size of these nanospheres, and the numerical results of μ a and μ s ′ can then be inferred by calculating the absorption and scattering efficiencies. Then we propose a numerical interval for the imaginary part of the complex refractive index of S i O 2 nanospheres, n s , which is estimated by fixing the fitted values of μ a and μ s ′ , using the known value of the real part of n s , and finding the corresponding value of I m ( n s ) that matches the optical parameters obtained by both methods finding values close to those reported for silica glass. This opens the possibility of producing optical phantoms with scattering and absorption properties that can be predicted and designed from precise knowledge of the physical characteristics of their constituents from a microscopic point of view.