On the validity of two-flux and four-flux models for light scattering in translucent layers: angular distribution of internally reflected light at the interfaces.

Optical characterization and appearance prediction of translucent materials are required in many fields of engineering such as computer graphics, dental restorations or 3D printing technologies. In the case of strongly scattering materials, flux transfer models like the Kubelka-Munk model (2-flux) or the Maheu's 4-flux model have been successfully used to this aim for decades. However, they lead to inaccurate prediction of the color variations of translucent objects of different thicknesses. Indeed, as they rely on the assumption of lambertian fluxes at any depth within the material, they fail to model the internal reflectance at the interfaces, penalizing the accuracy of the optical parameter extraction. The aim of this paper is to investigate the impact of translucency on light angular distribution and corresponding internal reflectances by the mean of the radiative transfer equation, which describes more rigorously the impact of scattering on light propagation. It turns out that the light angular distribution at the bordering interfaces is often far from being lambertian, and that the internal reflectance may vary significantly according to the layer's thickness, refractive index, scattering and absorption coefficients and scattering anisotropy. This work enables to better understand the impact of scattering within a translucent layer and also invites to revisit the well-known Saunderson correction used in 2- or 4-flux models.

Redox-active ions unlock substitutional doping in halide perovskites.

Electrical doping of metal halide perovskites (MPHs) is a key step towards the use of this efficient and cost-effective semiconductor class in modern electronics. In this work, we demonstrate n-type doping of methylammonium lead iodide (CH3NH3PbI3) by the post-fabrication introduction of Sm2+. The ionic radius of the latter is similar to that of Pb2+ and can replace it without altering the perovskite crystal lattice. It is demonstrated that once incorporated, Sm2+ can act as a dopant by undergoing oxidation to Sm3+. This results in the release of a negative charge that n-dopes the material, resulting in an increase of conductivity of almost 3 orders of magnitude. Unlike substitution doping with heterovalent ions, furtive dopants do not require counterions to maintain charge neutrality with respect to the ions they replace and are thus more likely to be incorporated into the crystalline structure. The incorporation of the dopant throughout the material is evidenced by XPS and ToF-SIMS, while the XRD pattern shows no phase separation at low and medium doping concentrations. A shift of the Fermi level towards a conduction energy of 0.52 eV confirms the doping to be n-type with a charge carrier density, calculated using the Mott-Schottky method, estimated to be nearly 1017 cm-3 for the most conductive samples. Variable-temperature conductivity experiments show that the dopant is only partially ionized at room temperature due to dopant freeze-out.

Performance of two-flux and four-flux models for predicting the spectral reflectance and transmittance factors of flowable dental resin composites.

OBJECTIVE: To evaluate the prediction accuracy of the Kubelka-Munk Reflectance Theory and other more innovative two-flux and four-flux models for predicting the reflectance and transmittance factors of two flowable dental resin composites of various thicknesses within clinically acceptable color difference. METHODS: Cylindrical samples of Aura Easy Flow resin composite (Ae1, Ae2, Ae3, Ae4 shades) and Estelite Universal Flow SuperLow resin composite (A1, A2, A3, A3.5, A4, A5 shades) were prepared with thicknesses ranging from 0.3 mm to 1.8 mm. Their reflectance and transmittance factors were measured with a spectrophotometer based on an integrating sphere, and were also predicted by 3 different two-flux models and 2 different four-flux models. The accuracy of reflectance and transmittance factor predictions was assessed using the CIEDE2000 color distance metric and 50:50% acceptability and perceptibility threshold criteria. RESULTS: Eymard's four-flux model is found to be the most accurate for predicting the spectral reflectance and transmittance factors, with 85% (resp. 100%) of all color deviations below the acceptability threshold, and below the perceptibility threshold for 40% (resp. 57%) of the samples with thickness ranging from 0.3 to 1.8 mm in reflectance (resp. transmittance) mode. The Kubelka-Munk Reflectance Theory is found to be the least accurate model for predicting the spectral reflectance and transmittance factors of dental resin of thickness ranging from 0.3 to 1.8 mm. SIGNIFICANCE: Eymard's four-flux model enables to predict the color of slices of dental materials within acceptable color differences. Eymard's four-flux model's optical parameters thus describe light-matter interactions in dental materials more accurately than state of the art Kubelka-Munk Reflectance Theory.

Evaluating edge loss in the reflectance measurement of translucent materials.

In many commercial instruments for measuring reflectance, the area illuminated on the measured object is identical to the area from which light is collected. This configuration is suitable for strongly scattering materials such as paper, but issues arise with translucent materials, because a portion of the incident light spreads around the illuminated area by subsurface transport and escapes the detection system. This phenomenon, referred to as edge loss, yields erroneous, underestimated reflectance measurements. In the case of colored and opalescent materials, the impact of edge loss on the measured reflectance varies with the wavelength, which is a significant issue for spectrophotometer and colorimeter users. In the present study, we investigate the edge-loss phenomenon with an emphasis on human skin measurement. In particular, we use a mathematical model to estimate the PSF of translucent materials, relying on the diffusion approximation of the radiative transfer theory, to predict edge-loss measurement error. We use this model to discuss the suitability of several commercial spectrophotometers to accurately measure the translucent materials of various optical properties and show that not all devices can adapt to all translucent materials.

Three-dimensional maps of human skin properties on full face with shadows using 3-D hyperspectral imaging.

Hyperspectral imaging has shown great potential for optical skin analysis by providing noninvasive, pixel-by-pixel surface measurements from which, applying an optical model, information such as melanin concentration and total blood volume fraction can be mapped. Such applications have been successfully performed on small flat skin areas, but existing methods are not suited to large areas such as an organ or a face, due to the difficulty of ensuring homogeneous illumination on complex three-dimensional (3-D) objects, which leads to errors in the maps. We investigate two methods to account for these irradiance variations on a face. The first one relies on a radiometric correction of the irradiance, using 3-D information on the face's shape acquired by combining the hyperspectral camera with a 3-D scanner; the second relies on an optimization metric used in the map computation, which is invariant to irradiance. We discuss the advantages and drawbacks of the two methods, after having presented in detail the whole acquisition setup, which has been designed to provide high-resolution images with a short acquisition time, as required for live surface measurements of complex 3-D objects such as the face.