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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.

Avec l’invention de la peinture à l’huile au XVe siècle, la couleur prend une autre dimension : elle se construit dans l’épaisseur de la matière picturale. En effet, le nombre de couches déposées module la clarté et la saturation de la couleur, tandis qu’un fond blanc diffusant donne l’impression d’une lumière provenant de l’arrière du tableau tel un rétro-éclairage. Étudier la matière picturale comme un composant optique permet de simuler l’apparence d’un tableau, aide qui peut être précieuse lors d’une opération de restauration sur les couches picturales. Cette approche est aussi à la source de procédés innovants d’impression 3D couleur s’inspirant de la technique des peintres de la Renaissance.

International audience; Metal nanostructures supported on a dielectric substrate possess unique plasmonic properties that are highly dependent on their morphologies. We show that such nanostructures can be modified upon exposure to an ultralow-energy ion-beam bombardment (< 100 eV) near the sputtering threshold of the metal. This plasma treatment can be easily implemented in a vacuum deposition chamber and allows the achievement of morphologies, and therefore optical properties, that are difficult to achieve otherwise by physical vapor deposition. We present the effects obtained (i) on self-organized Ag nanoparticles with unidirectional orientation and bimodal distribution, and (ii) on Ag layers in the form of percolated, quasi-continuous or island thin films. Our results show that the plasmonic dichroism of self-organized assemblies can be tuned thanks to the preferential sputtering of the smaller particles associated with gradual erosion of the larger ones. Ion-induced modifications of percolated or quasi-continuous films lead to the formation of isolated tiny particles with areal densities smaller than 500 μm − 2. In both cases, the duration of the ion bombardment makes it possible to finely control the desired structural and plasmonic modifications.

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. We show that the errors made in their measurements come not only from experimental uncertainties but also from incomplete knowledge of the physical properties of light, leading to incorrect assumptions in their models. The main errors are (i) the fact that light is totally reflected at grazing incidence, (ii) the glass plates they used were not perfectly clear, and (iii) light is partially polarized after transmission across the surface. By highlighting the impact of these three errors, we can better understand the state of knowledge in optics at that time and question our current practices in radiometric measurements and calculations.

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since the bidirectional reflectance distribution function applies to scattering media, it is inherently prone to speckle. Conditions to average out speckle by integration over solid angle both on the illumination side and on the detection side are analyzed.

Comment mesurer une quantité de lumière ? Cette question fondamentale pour toute expérience optique n’allait pas de soi jusqu’au XVIIIe siècle. Il fallait inventer un instrument et un protocole de mesure utilisant le seul photodétecteur alors disponible : l’œil humain. Plusieurs savants et quelques grands peintres contribuèrent sur plus de deux siècles à l’élaboration du premier photomètre.

International audience; 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.

13 pags., 2 figs., 1 tab., The bidirectional reflectance distribution function (BRDF) and the bidirectional scattering - surface reflectance distribution function (BSSRDF), which relate radiance at the surface to irradiance and radiant flux, respectively, are regarded as the most fundamental scattering quantities used to determine the reflectance of objects. However, for materials where the optical radiation is transmitted under the surface, this radiance depends not only on irradiance and radiant flux, but also on the size of the irradiated area of the surface. This article provides insight into such dependence under the special condition in which the radiance is evaluated within the irradiated area and, consequently, is produced by both the insurface reflection and the subsurface scattering, in contrast to the situation in which the radiance is evaluated at non-irradiated areas and only subsurface scattering contributes. By explicitly considering both contributions, two other scattering quantities are defined: one that accounts exclusively for the insurface reflection and the other that accounts for subsurface scattering. In this regard, these quantities might be considered more fundamental than the BRDF and the BSSRDF, although they are coincident with these two functions apart from the above-mentioned special condition and for materials with negligible subsurface scattering. In this work, the relevance of the proposed scattering quantities is supported by experimental data, practical considerations are given for measuring them, and their relation to the bidirectional transmittance distribution function (BTDF) is discussed., This investigation was carried out within the scope of EMPIR project 18SIB03, “New quantities for the measurement of appearance” (BxDiff). EMPIR is jointly funded by the EMPIR participating countries within EURAMET and the European Union. Some of the authors (CSIC) are would like to acknowledge project PGC2018-096470-B-I00 BISCAT (MCIU/AEI/FEDER,UE). We are grateful to Covestro Deutschland AG for providing with translucent samples.

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. Many authors have addressed microfacet bidirectional scattering distribution function (BSDF) representations, with various normal distribution functions (NDFs) and their relationship with shadowing and masking, or the effects due to multiple light scattering on the microgeometry. However, an extensive study on how an actual microgeometry drives material appearance still is missing. This question is a key issue for inverse design and manufacturing. This paper contributes to filling this gap by proposing a complete pipeline composed of a microgeometry generation process and numerical lighting simulation. From any input NDF, our method generates a controlled and structured microgeometry, integrated within numerical light scattering simulation. Reflected light is gathered using a virtual goniophotometer. From a given set of parameters, we use our pipeline to study the impact of microgeometry structures on material light scattering in the case of rough surfaces. The obtained results are discussed and compared with already existing approaches when they exist in the pipeline.

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International audience; 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. For instance, the National Metrological Institute (LNE-CNAM) has implemented the best angular resolution goniospectrophotometer (0.015°). Modeling the BRDF has also been deeply studied in France, especially with the microfacet theory in recent years, a better understanding of the shadowing–masking function, new general distribution functions, visible normals, interfaced Lambertian microfacets, and analysis concerning light multiple reflections. This paper presents the state of the art regarding some significant French contributions in these fields.

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., in metals and clear dielectrics, just as a consequence of multiple specular reflections between neighboring flat facets of the surface. In this paper, we investigate such color variation in the case of an infinitely long V-shaped groove, having in mind the visual appearance of a surface composed of many structures of that sort, all parallel and identical. We develop a full model of multiple specular reflections, accounting for the ray position and orientation and the polarization effects occurring at each reflection. We compare that situation with two approximate models, more usual and easier to compute, where light is assumed to remain unpolarized all along, or where the $p$p- and $s$s-polarized components are treated separately. Spectral reflectances were predicted for various materials and angles of cavities, under diffuse illumination. In most cases, the three models predict very similar bi-hemispherical reflectances, but the hemispherical-directional reflectances can vary noticeably in certain observation directions. This study might help achieve a more physically realistic rendering of dielectric or metallic ridged surfaces in computer graphics.

International audience; The effect of Ge alloying on the growth morphology and intrinsic stress evolution during deposition of Cu thin films is investigated using in situ and real time diagnostics, complemented by ex situ microstructural characterizations. Cu1-xGex alloys with x up to 0.15 were sputter-deposited at room temperature on Si substrates, while measuring simultaneously the substrate curvature evolution and surface differential reflectance spectroscopy during the early stages of growth. All films exhibit a typical compressive-tensile-compressive stress behavior, which underpins the distinct stages of a Volmer-Weber growth mode; however, it is revealed that the Ge content plays a decisive role on the nucleation and coalescence stages. This results in a grain size refinement and development of higher compressive stresses for Ge solute additions up to x = 0.07. At higher Ge contents, the strong chemical affinity between Cu and Ge atoms leads to a germanide compound (Cu5Ge) formation and even higher compressive stress. The stress evolutions are discussed considering the surfactant character of Ge atoms affecting Cu adatom mobility and growth morphology. This study highlights the possibility to tailor the early stages of growth and film microstructure (grain size, texture, surface roughness) by introducing solute concentrations of Ge in Cu films. We also determined for the elemental Cu film the percolation and film continuity thicknesses and discussed theses values with respect to those reported for other metallic films.

Photochromic reaction dynamics in silver nanoparticles embedded in mesoporous titanium dioxide thin films is investigated by combining real-time grazing incidence small-angle x-ray scattering (GISAXS) and optical transmission measurements during UV–visible laser exposure cycles. While GISAXS probes changes in the particle size distribution, transmittance measurements are sensitive to spectral changes induced by photo-activated processes. Our results reveal a repeatable photochromic behavior with a good correlation in terms of kinetics between the morphological and optical fluctuations. Visible laser irradiation at 532 nm induces a preferential photo-dissolution of small silver particles, which in turn causes an increase in transmittance near the excitation wavelength. Furthermore, the photo-dissolution process can be significantly accelerated and amplified by associating visible laser with x-ray irradiation. Under UV laser irradiation at 360 nm, the bleaching process can be reverted by photocatalytic reduction with the mesopores in the TiO2 film acting as molds, which have the ability to confine the nanoparticle growth. However, in the irradiation conditions used in the present study, it appears that the photocatalytic growth of silver nanoparticles is slower than the photo-dissolution process, whereas its efficiency gradually degrades throughout the exposures to UV light.

International audience; 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. One solution is to employ a multi-layered model with a single layer for the rough interface, which requires a numerical simulation for handling the multiple reflections of light between the substrate and the interface. In this paper, we propose rather to use a representation corresponding to a Fresnel interface lying on a Lambertian substrate, for which the multiple reflections of light between the interface and the substrate can be expressed analytically. With this interfaced Lambertian model, we show how Fresnel transmission affects the material appearance for flat and rough surfaces with isotropic and anisotropic distributions, that produce light backscattering effects. We also propose a methodology for using such materials in any physically based Monte Carlo rendering system, as well as an approximate representation, suitable for GPU applications or measured data fitting. Our approach generalizes several previous models, including flat Lambertian materials as well as specular and Lambertian microfacets. Our results illustrate the wide range of materials that can be rendered with this representation. F Figure 1: Rough interfaced Lambertian materials with various parameter values, and comparison with fitted measured materials for a ceramic mug. Our model generalizes and subsumes several previous existing models: Lambert, Cook-Torrance [1], and Oren-Nayar [2].

International audience; The different areas of a concave object illuminate each other by a multiple light reflection process, called interreflections, depending on the geometries of the object and the lighting. For an accurate prediction of the radiance perceived from each point of the object by an observer or a camera, an interreflection model is necessary, taking into account the optical properties and the shape of the object, the orientation(s) of the incident light which can produce shadows, and the infinite number of light bounces between the different points of the object. The present paper focusses on the irradiance of two adjacent planar panels (V-cavity) illuminated by collimated light from any direction of the hemisphere, or by diffuse light. According to the reflectance of the material and the angle of the cavity, the loss of irradiance near the fold due to the shadowing effect is partly compensated by the gain in radiance due to the interreflections.

WTi thin films are known as potential adhesion promoters and diffusion barriers. WTi thin films were deposited by magnetron sputtering from an alloyed target (W:Ti ~ 70:30 at.%). Real-time surface differential reflectance (SDR) spectroscopy and wafer-curvature measurements were performed during deposition to study the growth and the film continuity threshold. SDR measurements during WTi deposition allow the determination of the change in reflectivity of p-polarized light (at Si substrate Brewster's angle) between WTi film and Si substrate in order to monitor layer growth. The comparison between experimental and simulated WTi SDR signals assuming a homogeneous and continuous layer growth shows that film continuity is ensured beyond a thickness of 4.5 ± 0.2 nm. Real-time wafer-curvature measurements allow the determination of the intrinsic stress development in the film. Two regimes are noticed during the growth up to the development of a compressive steady state stress. The early stages of growth are rather complicated and divided into sub-regimes with similar boundaries revealed by both in situ techniques. Deposition of an interfacial continuous layer different from WTi bulk is suggested by both in situ techniques below a thickness of 4.5 nm.

International audience; This paper focuses on microfacet reflectance models, and more precisely on the definition of a new and more general distribution function, which includes both Beckmann's and GGX distributions widely used in the computer graphics community. Therefore, our model makes use of an additional parameter g, which controls the distribution function slope and tail height. It actually corresponds to a bivariate Student's t-distribution in slopes space and it is presented with the associated analytical formulation of the geometric attenuation factor derived from Smith representation.We also provide the analytical derivations for importance sampling isotropic and anisotropic materials. As shown in the results, this new representation offers a finer control of a wide range of materials, while extending the capabilities of fitting parameters with captured data.

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

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. By considering a Lambertian background and a transparent layer on top of it, both of them being possibly absorbing, we develop a bidirectional subsurface scattering reflectance distribution function model, based on analytical equations and matrix numerical computation, which enables a detailed description of the spatial and angular distribution of the scattered light including the multiple reflections between the background and the coating-air interface. Some applications in which this subsurface scattering phenomenon can be an issue are addressed, such as the reflectance measurement, which can be undervalued when the geometry is not adapted to the coating thickness, or the impact of the phenomenon on heterogeneously colored surfaces such as coated or laminated halftone prints.

In situ and real time surface differential reflectance (SDR) spectroscopy is employed to study the growth of metallic Ag and/or dielectric Si 3 N 4 films during deposition by magnetron sputtering. The measurements during Si 3 N 4 sputtering allow determining both the refractive index and the deposition rate. During Ag sputtering, the SDR presents a maximum in the visible range, typical of a surface plasmon resonance (SPR) indicating the 3D growth of silver nanoclusters. After a certain deposition thickness, the SDR change corresponds to a continuous layer growth and allows determining the Ag deposition rate. During Ag/Si 3 N 4 alternate deposition, the SDR spectroscopy enables to follow the SPR modifications (position, amplitude and width) not only during the formation of the Ag nanoclusters but also during their capping by a Si 3 N 4 matrix and during intermediate steps (holding time after the silver sputtering, Si 3 N 4 target ignition and pre-sputtering before the Si 3 N 4 deposition) where significant changes are detected. It suggests possible nanocluster reshaping or physicochemical processes occurring at the nanocluster interface during the different steps.