Article

ACT: A leaf BRDF model taking into account the azimuthal anisotropy of monocotyledonous leaf surface

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Abstract

Keywords: Sorghum Wheat Leaf Surface roughness BRDF BRF Reflectance Conoscope Azimuthal anisotropy Optical properties Goniometer Physical model Refractive index Leaf reflectance of monocotyledons generally displays a strong azimuthal anisotropy due to the longitudinal orientation of the veins. The Cook and Torrance (CT) bidirectional reflectance distribution function model was adapted to account for this distinctive feature. The resulting ACT (Anisotropic Cook and Torrance) model is based on the decomposition of the roughness parameter into two perpendicular components. It is evaluated on sorghum (Sorghum halepense) and wheat (Triticum durum) leaf BRF (Bidirectional Reflectance Factor) measurements acquired using a conoscope system. Results show that the ACT model fits the measurements better than azimuthally isotropic surface models: the root mean square error computed over all the BRF measurements for both leaves decreases from ≈0.06 for the Lambertian model to ≈0.04 for the CT model and down to ≈0.03 for the ACT model. The adjusted value of the refraction index is plausible (n ≈ 1.32) for both leaves while the retrieved roughness values perpendicular to the veins (sorghum = 0.56; wheat = 0.46) is about two times larger than that parallel to the veins (sorghum = 0.27; wheat = 0.18). Nonetheless, the observed residual discrepancies between the ACT model simulations and the measurements may be explained mainly by the Lambertian assumption of the volume scattering.

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... In this section, we indicate that our measured BRF results for the vegetation covers are consistent with those of previous studies [36,[53][54][55] and can be used to represent the reflection property of a leaf and vegetation covers. In Fig. 3, we show the spectral BRF curves of single leaf and two vegetation covers, which were measured at different viewing zenith angles in the principal plane at an incident zenith angle of 40°. ...
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This article reviews the progress of atomic force microscopy (AFM) in ultra-high vacuum, starting with its invention and covering most of the recent developments. Today, dynamic force microscopy allows to image surfaces of conductors \emph{and} insulators in vacuum with atomic resolution. The mostly used technique for atomic resolution AFM in vacuum is frequency modulation AFM (FM-AFM). This technique, as well as other dynamic AFM methods, are explained in detail in this article. In the last few years many groups have expanded the empirical knowledge and deepened the theoretical understanding of FM-AFM. Consequently, the spatial resolution and ease of use have been increased dramatically. Vacuum AFM opens up new classes of experiments, ranging from imaging of insulators with true atomic resolution to the measurement of forces between individual atoms. Comment: In press (Reviews of Modern Physics, scheduled for July 2003), 86 pages, 44 figures
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The sharp retroreflective peak that is commonly exhibited in the bidirectional reflectivity distribution function of diffuse surfaces was investigated for several materials relevant to ladar applications. The accurate prediction of target cross-sections requires target surface BRDF measurements in the vicinity of this peak. Measurements were made using the beamsplitter-based scatterometer at the U.S. Army's Advanced Measurements Optical Range (AMOR) at Redstone Arsenal, Alabama. Co-polarized and cross-polarized BRDF values at 532 nm and 1064 nm were obtained as the bistatic angle was varied for several degrees about, and including, the monostatic point with a resolution of better than 2 mrad. Measurements covered a wide range of incidence angles. Materials measured included polyurethane coated nylons (PCNs), Spectralon, a silica phenolic, and various paints. For the co-polarized case, a retroreflective peak was found to be nearly ubiquitous for high albedo materials, with relative heights as great as 1.7 times the region surrounding the peak and half-widths between 0.11° and 1.3°. The shape of the observed peaks very closely matched coherent backscattering theory, though the phenomena observed could not be positively attributed to coherent backscattering or shadow hiding alone. Several data features were noted that may be of relevance to modelers of these phenomena, including the fact that the widths of the peaks were approximately the same for 532 nm as for 1064 nm and an observation that at large incidence angles, the width of the peak usually broadened in the in-plane bistatic direction.
Article
The reflection properties of pressed polytetrafluoroethylene powder have been under investigation by the Radio- metric Physics Division at the National Bureau of Standards for the past five years. This material has a great po- tential use, both as a standard of diffuse reflectance and as a coating for integrating spheres for applications in re- flectance spectrophotometry and other signal-averaging devices. It possesses certain physical and optical proper- ties that make it ideal for use in these applications. Techniques are given for preparing reflection standards and coating integrating spheres with the pressed powder. The effects of powder density and thickness on its reflec- tance are reported, and observations of possible problems with fluorescence that are due to the presence of contam- inants in the powder are discussed. The absolute reflectance (6"/hemispherical reflectance factor relative to a per- fect diffuser) is reported for the spectral range of 200-2500 nm. The directional/hemispherical reflectance factor relative to 6°/hemispherical reflectance is given for several wavelengths in the ultraviolet and visible spectrum and for angles of incidence between 5 and 75'. The bidirectional reflectance factor is reported for 300, 600, and 1500 nm at angles of incidence of -10, -30, -50, and -70' and at viewing angles at 10" intervals from -80 to +80°.
Article
Nitrogen is the most important crop limiting factor, thus plant nitrogen status during plant cycle is a key parameter for crop monitoring. Many new techniques, based on leaf optical properties have been proposed for a non-destructive diagnosis to replace Nitrogen Nutrition Index which is a costly and destructive method. We intend here to study leaf nitrogen concentration accessibility from reflectance (400-1000 nm) spectra of whole plants from a field hyperspectral imaging set-up including difficulties related to variable solar lighting and potential specular reflexion. Firstly, we calibrated a chemo-metrical model between leaf nitrogen concentration and reflectance spectra of flat leaves (R(2)=0.903, SEP = 0.327%DM), which validated the sensor and our reflectance correction process. As a second step, we calibrated a chemometrical model between nitrogen concentration and reflectance spectra of individual leaves from isolated plants grown in pots in greenhouse (R(2) = 0.889, SEP = 0.481%DM) or under field conditions (R(2) = 0.881, SEP = 0.366%DM). Pooling the two datasets provided us a relevant model to predict leaf nitrogen content for the two culture conditions (R(2) = 0.875, SEP = 0.496% DM) suggesting that this technique is promising to assess nitrogen plant parameters with a non destructive method. This tool could be used to follow-up plant nitrogen dynamics criteria or to generate nitrogen spatial cartographies.
Article
Particle size, scatter, and multi-collinearity are long-standing problems encountered in diffuse reflectance spectrometry. Multiplicative combinations of these effects are the major factor inhibiting the interpretation of near-infrared diffuse reflectance spectra. Sample particle size accounts for the majority of the variance, while variance due to chemical composition is small. Procedures are presented whereby physical and chemical variance can be separated. Mathematical transformations—standard normal variate (SNV) and de-trending (DT)—applicable to individual NIR diffuse reflectance spectra are presented. The standard normal variate approach effectively removes the multiplicative interferences of scatter and particle size. De-trending accounts for the variation in baseline shift and curvilinearity, generally found in the reflectance spectra of powdered or densely packed samples, with the use of a second-degree polynomial regression. NIR diffuse NIR diffuse reflectance spectra transposed by these methods are free from multi-collinearity and are not confused by the complexity of shape encountered with the use of derivative spectroscopy.
Article
A theory is developed by which diffuse reflection from dielectric surfaces may be studied by measuring the polarization of the light diffusely reflected from such surfaces. Observations of the ratio of the intensities of light vibrating parallel to and perpendicular to the plane of incidence indicate that for ground and etched glass surfaces, illuminated by a collimated beam, regular reflection from small mirror-like planes, oriented at random, is responsible for much of the diffuse reflection.
Article
The theory and applications of scattering of electromagnetic waves from rough surfaces are addressed. The topics considered include: the general Kirchoff solution for scattering from rough surfaces; periodically rough surfaces; random rough surfaces: surfaces generated by random processes and other models; the statistical distribution of the scattered field; depolarization of electromagnetic waves scattered from a rough surface; reflection of electromagnetic waves by a perfectly smooth earth; the reflection of waves from irregular ground; methods of measurement of the reflection coefficients of the earth; experimental investigation of the specular reflection coefficient of the earth; experimental investigation of diffuse scattering from the earth's surface; practical applications of specular reflection and of diffuse scattering; scattering by atmospheric sheets; reflection of radio waves by the moon and the planets.
Article
Many pre-processing methods aim at improving calibration model robustness in relation to the effect of an influence factor G. Orthogonal projection methods, such as OSC (Orthogonal Signal Correction) or EPO (External Parameter Orthogonalisation), are particularly well suited to process existing calibration databases. This work proposes a pre-processing strategy for the numerous cases where G variability is missing in the existing calibration database, and where effects of G and Y, the variable of interest, are not independent. The application in this study concerns the correction of the light scattering effect in NIR turbid spectra of grape musts. Ethanol content was thus correctly predicted (RMSEP = 0.5°) on very turbid samples (below 3000 NTU), much better than using all other geometric or multidimensional existing pre-processings tested.
Article
Radiative transfer (RT) models for canopies entail multiple implicit and explicit assumptions. In this case study six different commonly used assumptions were evaluated on a detailed virtual orchard model. This model was constructed in a physically based ray-tracing environment using detailed sub-models for the description of tree geometry, leaf and soil bidirectional reflectance and diffuse illumination. After calibration and validation with both the RAMI Online Model Checker (ROMC) and field data obtained in a Citrus orchard in Wellington, South Africa, the model was used as a reference to analyze the different assumptions. A first set of three assumptions focused on leaf optical properties, evaluating the effect of the spectral mixing of randomly distributed leaves and trees, leaf asymmetry and leaf bidirectional reflectance and transmittance. The fourth assumption investigated the structure effects of variations in leaf shape and leaf curl. Finally, the last two assumptions were tested at the orchard level and dealt with the row orientation of trees and the angular distribution of diffuse irradiance. Errors induced by each assumption were evaluated in side-by-side comparisons with the reference. Only for the first assumption no measurable error could be detected. All other assumptions caused variable relative errors of up to 70%. The size of the errors was found to be spectrally variable and depends on canopy structure, leaf optical properties and illumination conditions. Corrections with minimal additional complexity in implementation in 3D RT models were suggested.
Article
This paper aims to link the spectral and directional variations of the leaf Bidirectional Reflectance Distribution Function (BRDF) by differentiating specular and diffuse components. To do this, BRDF of laurel (Prunus laurocesarus), European beech (Fagus silvatica) and hazel (Corylus avellana) leaves were measured at 400 wavelengths evenly spaced over the visible (VIS) and near-infrared (NIR) domains (480–880 nm) and at 400 source-leaf-sensor configurations. Measurement analysis suggested a spectral invariance of the specular component, the directional shape of which was mainly driven by leaf surface roughness. A three-parameter physically based model was fitted on the BRDF at each wavelength, confirming the spectral invariance of the specular component in the VIS, followed by a slight deterioration in the NIR. Due to this component, the amount of reflected light which did not penetrate into the leaf, could be considered as significant at wavelengths of chlorophyll absorption. Finally, by introducing the PROSPECT model, we proposed a five-parameter model to simulate leaf spectral and bidirectional reflectance in the VIS–NIR.
Article
In this paper we present a new spectrogoniophotometer (SGP) dedicated to the assessment of plant leaf bidirectional optical properties. It consists of a mechanical apparatus coupled with an imaging spectrometer using a bidimensional CCD photodetector. Unpolarized light fluxes are sampled at high spectral and directional resolution to provide biconical reflectance and transmittance factors, every nanometer from 500 nm to 880 nm and at 800 source-sensor configurations (four illumination directions by 200 viewing directions covering the whole sphere). From these calibrated measurements we derive the leaf Bidirectional Reflectance and Transmittance Distribution Functions (BRDF and BTDF). The angular-integrated quantities defined as the Directional Hemispherical Reflectance and Transmittance Function (DHRF and DHTF) are also calculated. The first three sections emphasize the instrumental and calibration issues, as well as the radiometric definitions. In the last section we present some experimental results acquired on various monocot and dicot leaves with special attention to surface reflection. The shape, position and magnitude of the specular lobe, which is a characteristic of many leaves in the forward direction, is investigated for beech (Fagus sylvatica L.) and laurel (Prunus laurocerasus L.) using a leaf BRDF model. The width of the specular peak is very variable according to the species and the illumination angle, as well as its contribution to the directional–hemispherical reflectance. Finally, implications in plant physiology or remote sensing are broached.
Article
PROSPECT is a radiative transfer model based of Allen's generalized “plate model” that represents the optical properties of plant leaves from 400 nm to 2500 nm. Scattering is described by a spectral refractive index (n) and a parameter characterizing the leaf mesophyll structure (N). Absorption is modeled using pigment concentration (Ca+b), water content (Cw), and the corresponding specific spectral absorption coefficients (Ka+b and Kw). The parameters n, Ka+b, and Kw have been fitted using experimental data corresponding to a wide range of plant types and status. PROSPECT has been tested successfully on independent data sets. Its inversion allows one to reconstruct, with reasonable accuracy, leaf reflectance, and transmittance features in the 400–2500 nm range by adjusting the three input variables N, Ca+b, and Cw.
Article
Light absorption by plant organs affects the development of a canopy directly through photobiological processes as well as indirectly through its action on organ temperature. Recent radiative models enable light absorption to be estimated for each individual organ within a canopy. These models require parameters describing incident radiation, canopy structure, and optical properties of phytoelements. Among these parameters, the bidirectional optical properties of phytoelements are a stumbling block: they are difficult to measure and take into account efficiently. Thus, most radiative models resort to what is referred to the Lambertian approximation. However, few studies have verified its suitability. In this paper, we assess this approximation in terms of individual leaf absorption for dense crop canopies in the solar spectrum. Simulations were performed with Monte Carlo ray tracing for three canopies, three sun positions, and two spectral domains (photosynthetically active radiation (PAR) and near infrared (NIR)). Results validate the suitability of the Lambertian approximation to simulate the light absorption by plants given the conditions under study.
Article
A laboratory goniometer consisting of a helium - neon laser (632.8 nm), vertical leaf holder, and silicon photovoltaic detector was used to measure the bidirectional scattering (both transmittance and reflectance) of red oak (Quercus rubra L.) and red maple (Acer rubrum L.). Three illumination angles were used, 0° (i.e., nadir), 30°, and 60°, and the scattering was recorded approximately every 10° in the principal plane. The scattering profiles obtained show the non-Lambertian characteristics of the scattering, particularly for the off-nadir illumination directions. The transmitted light was more isotropic than the reflected light. The reflectance of the adaxial side,of the leaf was greater than the adaxial side, although the transmittances of the two sides were about the same. Measurements taken during leaf senescence show that reflectance and transmittance increase as the leaf changes color from green to red to yellow. An equation is proposed as a simple representation of the scattering profiles.
Conference Paper
The Bidirectional Reflectance Distribution Function (BRDF) describes the appearance of a material by its interaction with light at a surface point. A variety of analytical models have been proposed to represent BRDFs. However, analysis of these models has been scarce due to the lack of high-resolution measured data. In this work we evaluate several well-known analytical models in terms of their ability to fit measured BRDFs. We use an existing high-resolution data set of a hundred isotropic materials and compute the best approximation for each analytical model. Furthermore, we have built a new setup for efficient acquisition of anisotropic BRDFs, which allows us to acquire anisotropic materials at high resolution. We have measured four samples of anisotropic materials (brushed aluminum, velvet, and two satins). Based on the numerical errors, function plots, and rendered images we provide insights into the performance of the various models. We conclude that for most isotropic materials physically-based analytic reflectance models can represent their appearance quite well. We illustrate the important difference between the two common ways of defining the specular lobe: around the mirror direction and with respect to the half-vector. Our evaluation shows that the latter gives a more accurate shape for the reflection lobe. Our analysis of anisotropic materials indicates current parametric reflectance models cannot represent their appearances faithfully in many cases. We show that using a sampled microfacet distribution computed from measurements improves the fit and qualitatively reproduces the measurements. 1.
Conference Paper
A new device for measuring the spatial reflectance distributions of surfaces is introduced, along with a new mathematical model of anisotropic reflectance. The reflectance model presented is both simple and accurate, permitting efficient reflectance data reduction and reproduction. The validity of the model is substantiated with comparisons to complete measurements of surface reflectance functions gathered with the novel reflectometry device. This new device uses imaging technology to capture the entire hemisphere of reflected directions simultaneously, which greatly accelerates the reflectance data gathering process, making it possible to measure dozens of surfaces in the time that it used to take to do one. Example measurements and simulations are shown, and a table of fitted parameters for several surfaces is presented.
Article
This study focuses on the directionality of wheat leaf reflectance as a function of leaf surface characteristics. Wheat leaf BRF measurements were completed under 45° zenith illumination angle in three visible broad spectral bands with a conoscope that provides very high angular resolution data over a large portion of the whole hemisphere, including around the illumination direction. The measurements show a clear anisotropy with a specular lobe in the forward scattering direction and a small but significant hotspot feature in the backward scattering direction. The BRF directional features further depend on the illumination orientation because of the leaf roughness created by longitudinal veins: the specular lobe was more pronounced when the illumination was perpendicular to the veins, while specular reflection was more spread over azimuths for longitudinal illumination. Moreover, a sharp hotspot feature was observed for transversal illumination where the apparent roughness is the largest. The scattering was tentatively decomposed into specular, hotspot and isotropic components. Results showed that the hotspot contribution to the directional hemispherical reflectance factor (DHRF) was marginal conversely to that of the specular component that ranges between 0.036 and 0.050 (absolute DHRF value). The specular component was almost the same in the three visible bands considered. The isotropic component originating from volume scattering was contributing the most to the DHRF and was depending on wavelength, ranging between 0.055 and 0.097 in absolute DHRF value. A simple model was proposed to estimate the volume scattering from the isotropic and the surface components. Consequences of these findings were drawn on the ability to estimate leaf biochemical composition independently from leaf surface scattering, as well as on the interpretation of remote sensing at the canopy level.
Article
A unified approach to the specification of reflectance, in terms of both incident- and reflected-beam geometry, is presented. Nomenclature to facilitate this approach is proposed. Under specified conditions - including uniform irradiance, a uniform, isotropic, plane surface, and allowance for edge effects due to sub-surface scattering - the geometrical reflecting properties of a reflecting surface are readily characterized or specified in terms of the bidirectional reflectance-distribution function (BRDF). The BRDF is a derivative, a distribution function, relating the irradiance incident from one given direction to its contribution to the reflected radiance in another direction. Nomenclature (concepts, terms, symbols, and units) for categorizing and specifying reflectance quantities for a variety of different beam configurations (both incident and reflected beams) is described, and all are defined and interrelated in terms of the BRDF.
Article
The luminance and luminous intensity characteristics of the leaves of several forest species of eucalypts have been investigated and compared with freshly smoked magnesium oxide. Results indicate that different species of the same genus can have distinctive indicatrices. Inspection of the indicatrices for the leaves showed that, for practical purposes, three types of reflection are recognizable, i.e., diffuse, spread, reflex. It seems important therefore that the research worker should be aware of the type of reflection being measured, since this may influence his conclusions. The cusp in the direction of reflex reflection was found to increase rapidly about the normal (0 degrees ) to the leaf's surface and to attain a maximum at the normal. As the angle of incident light is increased from 0 degrees to 45 degrees or more, the spread reflection component becomes increasingly conspicuous. With normal incidence, the maximum luminous intensity was attained in the direction of reflex reflection, but rapidly decreased toward zero beyond about +/-60 degrees to the normal.
Article
Bidirectional reflection and transmission distribution functions are measured for healthy green soybean and corn leaves in vivo, for nineteen narrow wavelength bands from 375 nm to 1000 nm. Off-normal incidence reflection distribution functions show considerable specular contributions at wavelengths of strong absorption, while transmission distribution functions show a near-lambertian shape for all wavelengths employed. An empirical m-layer leaf model affords a reasonable qualitative understanding of these scattering distributions.
Article
In applications, for instance in optics and astrophysics, there is a need for high-accuracy integration formulae for functions on the sphere. To construct better formulae than previously used, almost equidistantly spaced nodes on the sphere and weights belonging to these nodes are required. This problem is closely related to an optimal dispersion problem on the sphere and to the theories of spherical designs and multivariate Gauss quadrature formulae. We propose a two-stage algorithm to compute optimal point locations on the unit sphere and an appropriate algorithm to calculate the corresponding weights of the cubature formulae. Points as well as weights are computed to high accuracy. These algorithms can be extended to other integration problems. Numerical examples show that the constructed formulae yield impressively small integration errors of up to 10-12.
Article
Bui-Tuong Phong published his illumination model in 1973, in the paper titled "Illumination for Computer-Generated Images". Phong's model is a local illumination model, which means only direct reflections are taken into account. Light that bounces off more than one surface before reaching the eye is not accounted for. While this may not be very realistic, it allows the lighting to be computed efficiently. To properly handle indirect lighting, a global illumination method such as radiosity is required, which is much more expensive. In addition to Phong's basic lighting equation, we will look at a variation invented by Jim Blinn. Blinn changed the way specular is calculated, making the computations slightly cheaper. Blinn published his approach in his paper "Models of Light Reflection for Computer Synthesised Pictures" in 1977.
Article
The light scattering properties of leaves are used as input data for models which mathematically describe the transport of photons within plant canopies. Polarization measurements may aid in the investigation of these properties. This paper describes an instrument for rapidly determining the bidirectional light scattering properties of leaves illuminated by linearly polarized light. Results for one species, magnolia, show large differences in the bidirectional light scattering properties depending whether or not the electric vector E is parallel to the foliage surface.
Article
Reflectance indices are frequently used for the nondestructive assessment of leaf chemistry, especially pigment content, in environmental or developmental studies. Since reflectance spectra are influenced by trichome density, and trichome density displays a considerable phenotypic plasticity, we asked whether this structural parameter could be a source of variation in the values of the most commonly used indices. Trichome density was manipulated in detached leaves of three species having either peltate (Olea europaea and Elaeagnus angustifolius) or tubular (Populus alba) trichomes by successive removal of hairs. After each dehairing step, trichome density was determined by light or scanning electron microscopy and reflectance spectra were obtained with a diode-array spectrometer. Although species-specific differences were evident, most of the indices were considerably affected even at low trichome densities. In general, the less-affected indices were those using wavebands within the visible spectral region. The index that could be safely used even at very high hair densities in all species was the red edge index (lambda(RE)) for chlorophyll. The results indicate that changes in reflectance indices should be interpreted cautiously when concurrent changes in trichome density are suspected. In this case, the red edge for chlorophyll content may be the index of choice.
Article
Spectrophotometric transmittance and reflectance curves were recorded for wavelengths from 0.45 (in some cases 0.34) to 2.7 micrometers for faces and backs of leaves and for stacked leaves of several plant species. Measurements were made at different angles of illumination. Leaf spectrophotometric curves were compared with curves for leaf extracts, potato tuber tissue, glass beads in water, and frozen leaves to demonstrate the physical bases for the leaf curves. Leaves were infiltrated with liquids of different refractive indices for further comparison of spectrophotometric curves. Goniophotometric reflectance curves were recorded, giving visible reflectance and degree of polarization as functions of viewing angle for two different angles of illumination.No retroreflection was observed, and no phenomena were observed which could be attributed to interference because of similarity between leaf structural sizes and wavelengths used.
Article
In the context of the backscattering of waves from a random rough surface, a theoretical model is used to investigate the geometrical self-shadowing of a surface described by Gaussian statistics. Expressions are derived for various shadowing probabilities as functions of the parameter characterizing surface roughness and of the angle of incidence of the illuminating beam. The theoretical shadowing functions compare closely with those obtained experimentally from a recent computer simulation of a Gaussian surface.
Article
Lambert's model for body reflection is widely used in computer graphics. It is used extensively by rendering techniques such as radiosity and ray tracing. For several realworld objects, however, Lambert's model can prove to be a very inaccurate approximation to the body reflectance. While the brightness of a Lambertian surface is independent of viewing direction, that of a rough surface increases as the viewing direction approaches the light source direction. In this paper, a comprehensive model is developed that predicts body reflectance from rough surfaces. The surface is modeled as a collection of Lambertian facets. It is shown that such a surface is inherently non-Lambertian due to the foreshortening of the surface facets. Further, the model accounts for complex geometric and radiometric phenomena such as masking, shadowing, and interreflections between facets. Several experiments have been conducted on samples of rough diffuse surfaces, such as, plaster, sand, clay, and cloth. All...
Experimental analysis of BRDF modelsAvailable at: http://www.merl.com/reports
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Oeuvres complètes d'Augustin Fresnel
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