Готові списки джерел за темами / REFLECTANCE MATCHING

Добірка наукової літератури з теми "REFLECTANCE MATCHING"

Автор: Grafiati

Опубліковано: 11 вересня 2023

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Статті в журналах з теми "REFLECTANCE MATCHING"

Adachi, Yusuke, Ryota Kikuchi, Kenta Obata, and Hiroki Yoshioka. "Relative Azimuthal-Angle Matching (RAM): A Screening Method for GEO-LEO Reflectance Comparison in Middle Latitude Forests." Remote Sensing 11, no. 9 (May 8, 2019): 1095. http://dx.doi.org/10.3390/rs11091095.

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This study introduced a data screening method for comparing the reflectances in middle latitude forest regions collected by a Geostationary Earth Observing (GEO) satellite and a Low Earth Orbit (LEO) satellite. This method attempts to reduce the differences between the relative azimuth angles of the GEO and LEO observations. The method, called relative azimuthal-angle matching (RAM), takes advantage of the high temporal resolution of the GEO satellites, which enables collection of a wide range of relative azimuth angles within a day. The performance of the RAM method was evaluated using data in the visible and near-infrared bands collected by the Himawari-8/Advanced Himawari Imager (AHI) and the Terra/Moderate Resolution Imaging Spectroradiometer (MODIS). The consistency of the reflectance pairs of MODIS and AHI selected by the RAM method was compared with the consistency of the reflectance pairs acquired simultaneously by the two sensors. The data were matched pixel-by-pixel after applying atmospheric corrections and cloud screening. The results show that RAM improved the reflectance ratio by approximately 10% for the red and NIR bands on average relative to the simultaneous observations. Significant improvements in the two bands were observed (20%), especially among data collected in the fall and winter. Performance of RAM depends largely on season. Especially in summer, the reflectance pair chosen by RAM showed less consistency than solar zenith-angle matching (SZM). The results also indicated the relatively large influence of the spectral response functions on the green and red bands of the two sensors.

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Hamilton, Paul, Brian Sullivan, and Diann Gaalema. "Short-term changes in dorsal reflectance for background matching in Ornate Tree Lizards (Urosaurus ornatus)." Amphibia-Reptilia 29, no. 4 (2008): 473–77. http://dx.doi.org/10.1163/156853808786230488.

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AbstractSome lizards are thought to exhibit short-term changes in color to match their background, but this ability has not been verified empirically. We tested the hypothesis that lizards will change dorsal reflectance over a series of days to match their backgrounds. We housed male and female Ornate Tree Lizards (Urosaurus ornatus) for five days in aquaria painted to match environmental extremes in substrate reflectance. Standardized photographs were taken each day yielding dorsal percent reflectance values. After the first day, reflectance of lizards changed significantly to more closely match their backgrounds; this effect became more pronounced through the fifth and final day of the experiment.

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Romney, A. K., and T. Indow. "Estimating physical reflectance spectra from human color-matching experiments." Proceedings of the National Academy of Sciences 99, no. 22 (October 18, 2002): 14607–10. http://dx.doi.org/10.1073/pnas.222558899.

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Lundgaard, Stefan, Soon Hock Ng, Yoshiaki Nishijima, Michael Mazilu, and Saulius Juodkazis. "Black Metals: Optical Absorbers." Micromachines 11, no. 3 (February 28, 2020): 256. http://dx.doi.org/10.3390/mi11030256.

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We demonstrate a concept and fabrication of lithography-free layered metal-SiO2 thin-film structures which have reduced reflectivity (black appearance), to as low as 0.9%, with 4.9% broadband reflectance (8.9% for soda lime) in the 500–1400 nm range. The multi-layered (four layers) thin-film metamaterial is designed so that optical impedance matching produces minimal reflectance and transmittance within the visible and infra-red (IR) spectral region for a range of incident angles. The structure has enhanced absorbance and is easily tuned for reduced minimal transmission and reflection. This approach should allow for novel anti-reflection surfaces by impedance matching to be realized.

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Mishra, V. D., J. K. Sharma, and R. Khanna. "Review of topographic analysis methods for the western Himalaya using AWiFS and MODIS satellite imagery." Annals of Glaciology 51, no. 54 (2010): 153–60. http://dx.doi.org/10.3189/172756410791386526.

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AbstractThe topographic effects of differential terrain illumination in optical satellite imagery of rugged mountainous regions have serious consequences for qualitative and quantitative analysis for various snow applications. Therefore, effective removal or minimization of topographic effects is necessary in satellite image data of mountainous regions. Different methods for topographic corrections, including C-correction, Minnaert corrections (including slope) and slope-matching method, are analysed in the context of snow reflectance. Combination of dark-object subtraction models DOS1 and DOS3 is used for image-based atmospheric corrections while considering the effect of Rayleigh scattering on the transmissivity in different spectral bands of AWiFS and MODIS image data. The performance of different models is evaluated using (1) visual analysis, (2) change in snow reflectance on sunny and shady slopes after the corrections, (3) validation with in situ observations and (4) graphical analysis. The results show that the slope-matching technique could eliminate most of the shadowing effects in Himalayan rugged terrain and correctly estimate snow reflectance from AWiFS and MODIS imagery. The validation of results with in situ observations for both types of imagery suggests that all other methods significantly underestimate reflectance values after the corrections.

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Churmakov, D. Y., I. V. Meglinski, and D. A. Greenhalgh. "Influence of refractive index matching on the photon diffuse reflectance." Physics in Medicine and Biology 47, no. 23 (November 20, 2002): 4271–85. http://dx.doi.org/10.1088/0031-9155/47/23/312.

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Li, Shande, Xiaoxun Wu, Jinxiu Duan, Shuai Yuan, Cun Wang, Yane Ma, and Zhifu Zhang. "A Composite Matching Layer with Anti-Reflection Characteristics for Broadband Acoustic Scattering Reduction." Shock and Vibration 2021 (December 15, 2021): 1–10. http://dx.doi.org/10.1155/2021/1480264.

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A composite matching layer composed of periodically arranged scatters with anti-reflection (AR) characteristics is proposed for broadband scattering reduction. The anti-reflection structure is composed of periodically arranged metal foam scatters, and it is the first attempt to be applied in the field of suppressing acoustic reflection. A complete theoretical model is developed to reveal the mechanism of scattering reduction and acoustic absorption based on effective medium theory and the transfer matrix method. The correctness and effectiveness of the theoretical model are verified by the finite element method (FEM), showing acoustic reflectance of less than 13.5% at broadband frequencies. The variation trends of reflectance are deeply investigated. The superior acoustic scattering reduction performance suggests that the matching layer possesses potential for acoustic imaging equipment and acoustic stealth.

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LEE, MAL-REY, and TAE-EUN KIM. "ESTIMATION OF HYBRID REFLECTANCE PROPERTIES AND SHAPE RECONSTRUCTION USING THE LMS METHOD." International Journal on Artificial Intelligence Tools 08, no. 01 (March 1999): 1–17. http://dx.doi.org/10.1142/s0218213099000026.

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This paper presents a new method to estimate reflectance properties of non–Lambertian surface by the least-mean-square (LMS) algorithm. In this paper, hybrid reflectance of an object is represented by the Torrance–Sparrow model. We determine reflectance parameters which minimize the sum squared difference of the intensity distribution between the image of a sample sphere and the calculated image. The estimated reflectance parameters provide the range data with intensity distributions. Therefore, we generate three reference images of a range sphere, which has the same diameter as that of the sample, from the same viewpoint with different light directions. Direct matching of the object images to the references can precisely reconstruct the shape of the object. This paper uses a plate diffuse illumination to alleviate the effects of specular spike and highlights. The simulation results show that the proposed method can estimate reflectance properties of the hybrid surface, and also recover the object shape.

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LEE, MAL-REY. "3D SHAPE RECONSTRUCTION OF HYBRID REFLECTANCE USING THE LMS ALGORITHM." International Journal of Pattern Recognition and Artificial Intelligence 15, no. 04 (June 2001): 723–34. http://dx.doi.org/10.1142/s0218001401001040.

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In this paper, we present a new approach for determining the reflectance properties of surface and recovering 3D shapes from intensity images. We determine reflectance parameters which minimize the sum squared difference of the intensity distribution between the image of a sample sphere and the calculated image. The estimated reflectance parameters provide the range data with intensity distributions. Therefore, we generate three reference images of a range sphere, which has the same diameter as that of the sample, from the same viewpoint but with different light directions. Direct matching of the object images to the references can precisely reconstruct the shape of the object. This paper uses a plate diffuse illumination to alleviate the effects of specular spike and highlights. The simulation results show that the proposed method can estimate reflectance properties of the hybrid surface, and also recover the object shape.

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Luo, Lin, Hui-Liang Shen, Si-Jie Shao, and John Xin. "Empirical model for matching spectrophotometric reflectance of yarn windings and multispectral imaging reflectance of single strands of yarns." Journal of the Optical Society of America A 32, no. 8 (July 10, 2015): 1459. http://dx.doi.org/10.1364/josaa.32.001459.

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Дисертації з теми "REFLECTANCE MATCHING"

Zhou, Wei. "Scene illuminant estimation with binocular stereo matching." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file 2.74Mb, 160 p, 2005. http://wwwlib.umi.com/dissertations/fullcit/3181859.

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Mazauric, Serge. "Modèles spectraux à transferts de flux appliqués à la prédiction de couleurs sur des surfaces imprimées en demi-ton." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSES064/document.

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La protection des documents fiduciaires et identitaires contre la fraude exige le développement d’outils de contrôle fondés sur des effets visuels sans cesse renouvelés, difficiles à contrefaire (même pour un expert ... de la contrefaçon !). Ce projet de recherche s’inscrit dans cette problématique et vise à apporter des solutions originales via l’impression de supports diffusants d’une part, et le développement de modèles de rendu visuel d’autre part. Les effets visuels recherchés sont des ajustements de couleurs entre les deux faces d’un imprimé lorsque celui-ci est observé par transparence devant une source lumineuse. Pour obtenir facilement des ajustements de couleurs quelles que soient les couleurs visées, il est capital d’avoir un modèle à disposition, permettant de calculer les quantités d’encre à déposer. Un modèle doit être capable de prédire les facteurs spectraux de réflexion et de transmission du support imprimé en décrivant les phénomènes de diffusion optique présents en pratique dans les couches d’encre et le support. Nous nous intéressons plus particulièrement aux imprimés translucides contenant des couleurs en demi-ton des deux côtés de la surface avec pour objectif de prédire le rendu visuel pour diverses configurations d’observation. Pour cela, nous proposons une nouvelle approche basée sur l’utilisation de matrices de transfert de flux pour prédire les facteurs spectraux de réflexion et de transmission des imprimés lorsqu’ils sont éclairés simultanément des deux côtés. En représentant le comportement optique des différents composants d’un imprimé par des matrices de transfert, la description des transferts de flux entre ces composantes s’en trouve simplifiée. Ce cadre mathématique mène à la construction de modèles de prédiction de couleurs imprimées en demi-ton sur des supports diffusants. Nous montrons par ailleurs que certains modèles existants, comme le modèle de Kubelka-Munk ou encore le modèle de Clapper-Yule, peuvent également être formulés en termes de matrices de transfert. Les résultats obtenus avec les modèles proposés dans ce travail mettent en évidence des qualités de prédiction équivalentes, voire supérieures, à celles qu’on retrouve dans l’état de l’art, tout en proposant une simplification de la formulation mathématique et de la description physique des échanges de flux. Cette simplification fait de ces modèles des outils de calcul qui s’utilisent très facilement, notamment pour la détermination des quantités d’encre à déposer sur les deux faces de l’imprimé afin d’obtenir des ajustements de couleurs
The protection of banknotes or identity documents against counterfeiting demands the development of control tools based on visual effects that are continuously renewed. These visual effects become thus difficult to counterfeit even by an expert forger ! This research tries to deal with that issue. Its objective is to bring new solutions using on the one side, the printing of diffusing materials, and on the other side the development of visual rendering models that can be observed. The visual effects that are sought-after are the color matching on both sides of a printed document when observed against thelight. To easily obtain a color matching, whatever the colors that are aimed for, it is essential to have a model that helps in calculating the quantity of ink to be left on the document. A model must be used to predict the spectral reflectance and the transmittance factors of the printed document by describing the phenomena of optical diffusion really present in the ink layers and in the document. We shall focus our interest especially on translucent printed documents that have halftone colors on both sides. Our goal here is to predict the visual rendering in different configurations of observation. To that end, we are offering a new approach based on the use of flux transfer matrices to predict the spectral reflectance and transmittance factors of prints when they are simultaneously lit up on both sides. By representing with transfer matrices the optical behavior of the different components present in a printed document, we see that the description of flux transfer between these elements is thus simplified. This mathematical framework leads to the construction of prediction models of halftone printed colors on diffusing materials. We also show that some existing models, such as the Kubelka-Munk or the Clapper-Yule models, can also be formulated in transfer matrices terms. The results that we get with the models used in this work make apparent identical prediction quality and in some cases even better ones to the ones found in the state of the art, while offering a simplification of the mathematical formulation and the physical description of the flux transfer. This simplification thus transforms these models into calculation tools that can easily be used especially for the choice of quantities of ink that must be left on both sides of the document in order to obtain color matching

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PATEL, RISHI. "MATERIAL CLASS MAPPING BY REFLECTANCE MATCHING OF HYPER/MULTISPECTRAL IMAGERY." Thesis, 2017. http://dspace.dtu.ac.in:8080/jspui/handle/repository/16037.

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The main objective of this study is material mapping in hyperspectral image with the help of spectral reflectance matching. Presence of reflectance curve is the heart and soul of any operation performed, considering hyperspectral imagery. Certain material shows unique or characteristic reflectance plot known as signature plot or footprint within the range of spectrum. This feature of Hyperspectral image is exploited in case of material mapping. Visible materials like road, plantation, rooftops etc or even invisible materials like, soil constituents (carbonates, Na, K salts, water presence) or even the presence of ores of minerals (e.g. cuprite, alunite) beneath the surface of the earth can be predicted with sufficient accuracy. Hyperspectral data pose challenges to image interpretation, because of the need for calibration, redundancy in information, and high data volume due to large dimensionality of the feature space. In this project, hyperspectral image classification, band reduction and new technique for hyperspectral image classification is proposed and implemented. Both visual and quantitative results are calculated with the help of matlab. This project also designs a basic toolbox in MATLAB for processing and classification of hyperspectral image. Processing of hyperspectral image is divided into five modules, each performing specific operation. First, Acquisition of hypermultispectral image and display of its basic properties. Second, Formulation of classes with the help of user selecting points over displayed hyper-multispectral image. For the images in which signature reflectance library is already available user help for the selection of spectral signature is not required. Third, Reduction of Dimension of hyperspectral image up to user specified number of bands and calculation of the amount of information lost. Fourth, Material class mapping by reflectance Matching of hyper\multispectral image using traditional SAS, SDS, SCS deterministic approach. New method proposed for material classification over traditional SAS, SDS, SCS approach, (regression transform is used over reflectance curve to obtained separate regression distance class matrix) displaying the result using windowing technique and enhancing the output using Floyd dithering technique. Fifth, this part calculates the number of pixels, amount of area classified under each class, processing time, accuracy comparison between traditional and proposed techniques. Proposed method shows considerable improvement both visually and quantitatively over previous method. For the data set downloaded who’s ground truth is not available, pictorial result is shown and quantitative analysis is done for the images with ground truth present.

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Liu, Chen-chih, and 劉振志. "A Research of Color-Mixing And Color-Matching To Measure Polyester By Reflectance Method." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/39487061703545841319.

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黃泰碩. "An inverse radiation analysis for estimation of color matching coefficients from reflectance and transmittance measured by spectrometer." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/33031346358140083286.

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Тези доповідей конференцій з теми "REFLECTANCE MATCHING"

Kang, Zhizhong, and Sisi Zlatanova. "New point matching algorithm for panoramic reflectance images." In International Symposium on Multispectral Image Processing and Pattern Recognition, edited by S. J. Maybank, Mingyue Ding, F. Wahl, and Yaoting Zhu. SPIE, 2007. http://dx.doi.org/10.1117/12.751570.

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Sewall, Laura, and Daniel Kersten. "Limits to lightness constancy." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.tuh2.

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The limits to lightness constancy can be measured by the accuracy with which human observers estimate the reflectance of an object as a function of various illumination conditions. Our paradigm is analogous to traditional psychophysical methods used for signal identification, with the reflectance representing the signal and the illumination serving as noise. We used computer graphic techniques to simulate monochrome scenes consisting of a plane grid of square pieces of paper with various initial reflectances. The squares were then non-uniformly illuminated. We measured the ability of observers to correctly identify the reflectance of a randomly chosen patch by selecting a matching piece of paper from a standard palette, also simulated. Performance was measured as a function of the number of patches, number of possible reflectance values, illumination contrast, and illumination spatial spectrum. With uniform illumination, observers could accurately identify only six reflectance values for the three conditions varying in number of patches. However, within this range of reflectance patches, reflectance identification was robust over the range of illumination contrasts and spatial frequencies tested. These results suggest interesting constraints to be considered in the formulation of algorithms for lightness constancy.

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Brill, Michael H. "Reflectance ensembles with illuminant-Invariant chromaticity ordering." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.wq6.

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In a color atlas, the uniformity of color spacing between reflectances is disturbed by changes in the spectral power distribution (SPD) of the illumination. Because the atlas may still be useful under different lights, we introduce a new metric of color order that is less sensitive to change of illumination. Three reflectances with labels 1, 2, 3 map to points in chromaticity space (under a particular light) that, if not collinear, are ordered either clockwise or counterclockwise. The ordering parameter P of the reflectances is –1 for clockwise ordering, +1 for counterclockwise ordering, and 0 for collinear points. The perceptual significance of P can be tested via a dichotomous color-blindness test (such as the Farnsworth D-15 test). It has been shown mathematically1 that the P of three reflectances depends on illumination only if, when the reflectances are treated formally as color-matching functions, the chromaticity space that results has a spectrum locus that is not everywhere convex. Illuminants affect P when one or more reflectances is purple—a vindication of the model because purples are known not to be color-constant. A color atlas is called statistically consistent if its first three principal components form a chromaticity space that is convex and well ordered in wavelength. The Munsell atlas is statistically consistent. Convexity of the spectrum locus also insures that no linear combination of the reflectances (or reflectance principal components) has more than two zero crossings. Implications of these theorems for color technology and robotic vision are noted.

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Fang, Li, and Shentu Lian. "Spectral response matching of photodetectors." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.fw4.

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The spectral response matching of photodetectors under diffused illumination is required in almost all applications, especially in vision research. Compared with the others, the full-filter method has been used widely due to its precision and simplicity. Traditionally, the design is made by an iterative method. With the specular transmittance and reflectance, which are functions of thickness, of the filter under collimated illumination as the input, one can obtain an optimal value of filter thickness so that the experimental data can be matched. This procedure may not converge because of the diffused illumination condition. We propose a more efficient method by introducing the equivalent distance to substitute for the random distance that light traveled in the filters. From this assumption, the equivalent coefficient, which is the ratio of the equivalent and actual distance, is found to be where n is the index of refraction of the filter. The equivalent incident angle of a collimating light beam can also be expressed by c: Therefore, the transmittance and reflectance under diffused illumination can easily be calculated. We measured these parameters for various optical glass. The data conform to the theory very well. The spectral matching algorithm of the detector takes two steps. First, we calculate the initial thickness of the filters according to the transmittance and reflectance, neglecting the multiple reflection between the surfaces of the filters. The theoretical results are then compared with measured data to obtain the coefficient of multiple reflection. The final parameters are to be calculated when this coefficient is taken into consideration.

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Dinca, Andreea, Voicu Lupei, and Mihai Dinca. "Symmetry properties of solutions in admittance matching method." In Optical Interference Coatings. Washington, D.C.: Optica Publishing Group, 1997. http://dx.doi.org/10.1364/oic.1998.wf.7.

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The admittance matching method is generally used in the design of optical components which require in the same time high reflectance and high transmission bands. The matching is done at one or at both sides of the basic stack by synthesizing a symmetrical three layer periods with an equivalent layer. In order to obtain a broad transmission band, a quasi-matching is necessary around the matching wavelength [1, 2]. In the following, one analyzes some symmetry regularities exhibited by the solutions obtained for two or three periods in the matching stack.

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Burns, Stephen A., Ann C. Elsner, J. M. Gorrand, and Mark R. Kreitz. "Variability in color matching, photoreceptor alignment, and the Stiles-Crawford II effect." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.mx2.

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Color matches depend on the optical density and extinction spectrum of the cone photopigments. In addition it has been proposed that there is a physical effect of cone orientation on color matches (the Stiles-Crawford II effect). We have investigated this in ten observers by measuring (1) the retinal reflectance as a function of position in the pupil plan (the reflectometric version of the Stiles-Crawford I effect) and (2) Rayleigh color matches as a function of retinal illuminance. From the reflectometric data we calculate the position in the pupil and the spatial spread of the reflected light. From the color-matching data we calculate the optical density of the cone photopigments and the half-bleach illuminance. Both the optical density and half-bleach illuminance were significantly correlated with the spatial spread of the reflectance in the plane of the pupil. Observers with a smaller spread had higher densities (r = 0.82) and lower half-bleach illuminances (r = 0.67). Additional measurements of color matches for various pupil entry positions in two observers showed a strong dependence of the low illuminance match on pupil entry but not of the high illuminance (bleached) match. The half-bleach illuminance varied as expected due to the Stiles-Crawford I effect. These results are consistent with an optical density model of the Stiles-Crawford II effect. No additional wavelength dependent properties are required. The data also indicate that the variation in color matches in the normal population includes variation in the physical properties of the cones (e.g., the spread of cone orientations or cone apertures), as well as the optical density of individual cones and the extinction spectrum of the cones photopigments.

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Krewski, Aleksander, Werner L. Schroeder, and Klaus Solbach. "Matching network synthesis for mobile MIMO antennas based on minimization of the total multi-port reflectance." In Propagation Conference (LAPC). IEEE, 2011. http://dx.doi.org/10.1109/lapc.2011.6114021.

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Dewkurun, N., W. C. A. Heng, C. W. Chang, and S. C. Liew. "Retrieving Water Depth, Inherent Optical Properties and Bottom Reflectance by Spectrum Matching in Turbid Coastal Waters." In IGARSS 2008 - 2008 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2008. http://dx.doi.org/10.1109/igarss.2008.4778895.

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Zhu, Xiangyang, Yiling Pan, Bailin Deng, and Bin Wang. "Efficient Multi-View Inverse Rendering Using a Hybrid Differentiable Rendering Method." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. California: International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/205.

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Recovering the shape and appearance of real-world objects from natural 2D images is a long-standing and challenging inverse rendering problem. In this paper, we introduce a novel hybrid differentiable rendering method to efficiently reconstruct the 3D geometry and reflectance of a scene from multi-view images captured by conventional hand-held cameras. Our method follows an analysis-by-synthesis approach and consists of two phases. In the initialization phase, we use traditional SfM and MVS methods to reconstruct a virtual scene roughly matching the real scene. Then in the optimization phase, we adopt a hybrid approach to refine the geometry and reflectance, where the geometry is first optimized using an approximate differentiable rendering method, and the reflectance is optimized afterward using a physically-based differentiable rendering method. Our hybrid approach combines the efficiency of approximate methods with the high-quality results of physically-based methods. Extensive experiments on synthetic and real data demonstrate that our method can produce reconstructions with similar or higher quality than state-of-the-art methods while being more efficient.

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Rife, J. C., and W. R. Hunter. "Multilayer coated diffraction gratings." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.tuo2.

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Анотація:

The recent successes in producing multilayers as reflecting coatings on mirrors for the VUV and soft-x-ray regions has prompted an investigation of their applicability to diffraction gratings. If the grating is to be used at near-normal incidence, matching the coating to the grating is a simple problem. If, however, the grating is to be used at oblique incidence, the matching technique must take into consideration the fact that the grating obeys the simple Bragg law, but the coating follows the corrected Bragg law. Furthermore, even if grating and coating are properly matched for use at grazing incidence there remains the problem of contamination of the spectrum by radiation from "suborders" and longer-wavelength spectral regions, where the outermost layers of the multilayer have a high reflectance. Successful coatings have been produced for both laminar and blazed gratings. Examples will be given of the matching procedure, and calculations and measurements will be presented showing the dramatic increase in efficiency as well as the presence of longer-wavelength radiation.

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