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.

Bronzing effect: predicting the color shine of printed surfaces by estimating the refractive index of the inks.

This paper investigates the optical phenomenon responsible for the colored shine that sometimes appears at the surface of ink layers in the specular direction, often called "bronzing" or "gloss differential." The prediction of this shine effect relies on the Fresnel formulas of the air/ink interface. The complex refractive index of the ink must therefore be determined, which is made difficult because of the roughness of inked printing supports.

Photometric properties of piles of glass plates: retrospective.

Stacked glass plates have discreetly accompanied the understanding of light since the origins of modern optics. They were studied by Bouguer, Lambert, Brewster, Arago, Stokes, Rayleigh, and many others, whose successive works progressively refined the predictive formulas of the reflectance and transmittance of piles of glass plates as a function of the number of plates and the angle of incidence by considering the decay of light flux by absorption, the multiple reflections between plates, the change in the degrees of polarization, and the possible interferential effects. Through this history of ideas about the optical properties of piles of glass plates, up to the mathematical formalisms from only a few years ago, we show that these successive works, and their subsequent errors and corrections, are inseparable from the evolution of the quality of the glass available each time, in particular its absorptance and its transparency, which strongly influence the quantities and the degree of polarization of the reflected and transmitted beams.

Instructive errors of Bouguer, Lambert, and Arago in the first determinations of angular reflectances on flat surfaces: discussion.

The first photometric measurements performed in the eighteenth century were based on brightness matching between two illuminated surfaces. In 1760, Bouguer and Lambert proposed the first methods to measure the angular reflectance of a flat surface, and Arago proposed a third one in the mid-nineteenth century. These pioneering experiments provided rather good estimates of the values we can predict or measure much more accurately today, considering that the human visual system was the only available light detector at that time.

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.

Design of rough microgeometries for numerical simulation of material appearance.

Microfacet-based material appearance models are commonly considered as a physical plausible representation of matter-light interaction. With such models, the microgeometry of a surface element is defined by a statistical distribution of microfacets. The mathematical formulation ensures physical plausibility, such as energy conservation and reciprocity.

Angular reflectance model for ridged specular surfaces, with comprehensive calculation of inter-reflections and polarization.

The color of a surface structured at the mesoscopic scale differs from the one of a flat surface of the same material because of the light inter-reflections taking place in the concavities of the surface, as well as shadowing effects. The color variation arises not only in scattering materials, but also in the absence of scattering, e.g.

Modeling, measuring, and using BRDFs: significant French contributions.

The scattering of light by a surface is described by the bidirectional reflectance distribution function (BRDF). Unfortunately, this function cannot be straightforwardly acquired or modeled. French researchers have proposed interesting contributions to the field, with several models and accurate experimental systems.

Halo and subsurface scattering in the transparent coating on top of a diffusing material.

Strongly scattering supports coated with thick transparent medium display a bright halo with a characteristic ring shape when illuminated in one point by a thin pencil of light. The halo, whose size is related to the coating thickness, is due to the Fresnel internal reflections of the light scattered by the diffusing support at the coating-air interface. The angular distribution of the reflected light strongly varies over the halo according to the distance from the point initially illuminated, a fact that cannot be observed when a large area of the surface is illuminated as in usual reflectance and bidirectional reflectance distribution function measurements.

Rendering Rough Opaque Materials with Interfaced Lambertian Microfacets.

Specular microfacet distributions have been successfully employed by many authors for representing glossiness of materials. They are generally combined with a Lambertian term to account for the colored aspect. These representations make use of the Fresnel reflectance factor at the interface, but the transmission factor at the interface should also be managed.

Spectral and Color Changes of Ag/TiO Photochromic Films Deposited on Diffusing Paper and Transparent Flexible Plastic Substrates.

Giving paper and polymer photochromic properties under laser irradiation is challenging due to the low resistance of these materials to heat, their flexibility, and their possibly irregular structure. However, we could successfully deposit TiO/Ag/TiO layers stacking on flexible white glossy paper and transparent polyethylene terephalate (PET) substrates using a reactive magnetron sputtering technique, and tailor coloration changes after laser irradiation, alternating visible and ultraviolet (UV) wavelengths. The sample colors are characterized by a panel of chromas depending on the irradiation conditions.

Experimental study on merits of virtual cleaning of paintings with aged varnish.

To assess the accuracy of virtual cleaning of Old Master paintings (i.e. digital removal of discolored varnishes), a physical model was developed and experimentally tested using reflectance imaging spectroscopy on three paintings undergoing conservation treatment.

Two-flux transfer matrix model for predicting the reflectance and transmittance of duplex halftone prints.

We introduce a model allowing convenient calculation of the spectral reflectance and transmittance of duplex prints. It is based on flux transfer matrices and enables retrieving classical Kubelka-Munk formulas, as well as extended formulas for nonsymmetric layers. By making different assumptions on the flux transfers, we obtain two predictive models for the duplex halftone prints: the "duplex Clapper-Yule model," which is an extension of the classical Clapper-Yule model, and the "duplex primary reflectance-transmittance model.

Between additive and subtractive color mixings: intermediate mixing models.

The color rendering of superposed coloring components is often an issue either to predict or to simulate the appearance of colored surfaces. In graphical software, for example, transparence options are available to display different layouts on top of each other. With two colored layers, tuning the transparency of the top layer enables transitioning continuously from the color of this top layer to the color of the bottom layer.

Generalization of the geometric description of a light beam in radiometry and photometry.

Radiometric and photometric quantities rely on a geometric description of the beam subtended by a source and a receptor. In this paper, a generalization of this description is proposed as the product of the apparent size of the source times the receptor angular extent, whatever the natures of these elements: point, line, surface, or volume. The obtained flux density per geometric extent expressions are then applied to the determination of the irradiances induced in the near field and far field by a rectilinear source represented as a point source, a line source, and a surface source.

Photometric model of diffuse surfaces described as a distribution of interfaced Lambertian facets.

The Lambertian model for diffuse reflection is widely used for the sake of its simplicity. Nevertheless, this model is known to be inaccurate in describing a lot of real-world objects, including those that present a matte surface. To overcome this difficulty, we propose a photometric model where the surfaces are described as a distribution of facets where each facet consists of a flat interface on a Lambertian background.

Spectral prediction model for piles of nonscattering sheets.

The present paper investigates the reflection and transmission properties of piles of nonscattering sheets. Using a spectral prediction model, we perform a detailed analysis of the spectral and color variations induced by variations of the number of superposed sheets, the absorbance of the sheet material, the refractive index of the medium between the sheets, and the reflectance of the background. The spectral prediction model accounts for the multiple reflections and transmissions of light between the interfaces bounding the layers.

Ray scattering model for spherical transparent particles.

We propose a model for the reflectance of a particle medium made of identical, large, spherical, and absorbing particles in a clear binder. A 3D geometrical description of light scattering is developed by relying on the laws of geometrical optics. The amount of light backscattered by a single particle is determined as a function of its absorbance and refractive index.

Geometrical considerations in analyzing isotropic or anisotropic surface reflections.

The bidirectional reflectance distribution function (BRDF) represents the evolution of the reflectance with the directions of incidence and observation. Today BRDF measurements are increasingly applied and have become important to the study of the appearance of surfaces. The representation and the analysis of BRDF data are discussed, and the distortions caused by the traditional representation of the BRDF in a Fourier plane are pointed out and illustrated for two theoretical cases: an isotropic surface and a brushed surface.

Extension of the Williams-Clapper model to stacked nondiffusing colored coatings with different refractive indices.

We propose a model for predicting the reflectance and transmittance of multiple stacked nonscattering coloring layers that have different refractive indices. The model relies on the modeling of the reflectance and transmittance of a bounded coloring layer, i.e.

Separation between the different fluxes scattered by art glazes: explanation of the special color saturation.

In a previous paper, the special visual appearance of art glazes was explained using the auxiliary function method (AFM) for solving the radiative transfer equation. Glazes are made of low concentrated colored scattering centers embedded in a transparent medium and the artist modulates the color by varying the number of glaze layers. A simple model of glazes and the new solving method have both been validated by comparison between flux measurements and modeling.

Special visual effect of art glazes explained by the radiative transfer equation.

We present the first modeling of the light scattered by a paint layer in a bidirectional configuration. The studied medium is composed of small concentrated pigments embedded in an oil binder. The color is modulated by changing the number of paint layers, called glazes.