A Comparison of the Kubelka-Munk Reflectance with the Exact Reflectance for Isotropic Scattering

For a medium that scatters isotropically, the exact reflectance, for a variety of distributions of incident light, is compared with the Kubelka-Munk reflectance. It is shown that, although the Kubelka-Munk reflectance is not identical to the exact reflectance forany incident light, it does have a good correlation with the reflectance produced by a single beam incident at 63d? to the surface normal.     

Radiative transfer theory solid color-matching calculations

Radiative transfer theory concepts for color-matching calculations of solid color coatings are reviewed. Two flux approximations to the exact radiative transfer theory for isotropic scatters are developed. The Kubelka-Munk theory is discussed in the framework of two flux theories. A comparison is made between reflectances calculated from the Kubelka-Munk, two flux approximate radiative transfer, and the exact radiative transfer theory for 45/0 and diffuse/near-normal measuring geometries. A color-matching method is presented for radiative transfer color-matching calculations. This method, which can be implemented on a personal computer, is shown to give good color matches for the exact radiative transfer theory. The proposed color-matching algorithm, which can be applied to all three models, gives results equivalent to established Kubelka-Munk calculations. A comparison of the Kubelka-Munk, two flux approximate radiative transfer, and exact radiative transfer color calculations shows them to give equivalent results for diffuse/near-normal reflectance data. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 72–87, 1997     

Structural and Concentration Effects on the Diffuse Reflectance Ftir Spectra of Cellulose,Lignin and Pulp

Experiments were conducted to determine the effect of sample type and concentration on the diffuse reflectance infrared fourier transform (DRIFT) spectra of unbleached softwood kraft and thermomechanical pulps, microcrystalline cellulose (Avicel) and kraft lignin (Indulin AT). The absorption of characteristic bands, in Kubelka-Munk units, was followed as a function of sample concentration in potassium bromide, and, in the case of the two pulps, was also determined on handsheets. Anomalous dispersion occurred at concentrations of 1% or below. This phenomenon resulted in a decrease of absorption of specific bands with increasing concentration and was particularly significant for kraft pulp, less important for thermomechanical pulp and microcrystalline cellulose, and practically absent in pure kraft lignin. These effects of specular reflectance could not be completely eliminated by diluting the sample in a non-absorbing matrix, as previously claimed, but could only be minimized at low concentrations.     

Prediction of absorbance from reflectance for an absorbing-scattering fabric

Beer's law of light absorption and the Kubelka-Munk analysis are applied to absorbing-scattering fabric. A relation between the Kubelka-Munk function F(R) and the absorbance of dyed fibers is proposed. The relation is used to predict the absorbance of a colorant from the reflectance of a substrate dyed with it. Samples of polyester fibers dyed with different colorants are used. The predicted absorbances of these samples agree fairly well with those measured directly on the spectrophotometer. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 32–39, 1997.     

A neutron activation method for soil removal measurements: A comparison of the reflectance method and the neutron activation method

A nondestructive neutron activation analysis technique has been developed to determine the amt of particulate kaolinite clay soil removed from cotton fibers during a wash cycle. Neutron bombardment of aluminum, present as a constituent of the kaolinite lattice structure, produces short-lived aluminum-28. The amt of particulate soil present on a piece of cotton cloth before and after the wash cycle is determined by γ scintillation counting of the aluminum-28, thus providing an absolute method for the determination of the percentage of soil removed. A comparison of this method with the reflectance method has been made, and equations relating reflectance to clay concn for washed and unwashed soiled cloths have been developed for a given surfactant. It was found that the relationship of the concn of the soil on the test cloths and the measured reflectance depends upon whether the cloth has been washed or unwashed. The validity of the applicability of the Kubelka-Munk equation relating reflectance to soil content on cotton fabric has been experimentally confirmed for soiled cloths have high reflectivity. Presented in part at the AOCS Meeting, Minneapolis, 1963, and at the 15th Annual Chemistry Conference, Kansas City Sec., ACS.     

Colouring of opaque ceramic glaze with zircon pigments: Formulation with simplified Kubelka-Munk model

In this study a simplified Kubelka-Munk model is proposed for colour matching purposes. Opaque glazes were prepared to determine the absorption optical constants from the reflectance curves measured with a spectrophotometer. After the physical and chemical characterization of the glaze components (frit and pigments), to analyze the spectrophotometric results a simplification of the Kubelka-Munk model was suggested. To experimentally verify the model, two target green colour were reproduced in laboratory by adding in an opaque glaze a yellow praseodymium-doped zircon ((Zr,Pr)SiO₄) and blue vanadium-doped zircon ((Zr,V)SiO₄) pigments. The results were in good agreement with the experimental reflectance curves and the prediction of colour green glazes was possible with a reduced number of experiments.     

Analysis of Solid Wood Surfaces by Diffuse Reflectance Infrared Fourier Transform (Drift) Spectroscopy

Comparison of infrared spectra of wood taken by several methods indicated that the DRIFT spectrum of a dispersion of wood powder in KBr, expressed in Kubelka-Munk units, agreed best with the spectrum taken by transmission FTIR of solid wood sections; the DRIFT spectrum of solid wood, expressed in Kubelka-Munk units, was a close second, while the solid-wood DRIFT spectrum expressed in absorbance units differed most. The DRIFT spectrum of solid wood depended to a minor extent on the grain orientation and choice of late- vs early-wood. The spectrum depended strongly, however, on surface roughness with rougher surfaces producing more transmission-like spectra. Depth of penetration at 2242 cm-¹ (90% loss in intensity of CN peak of polyacrylonitrile placed under wood sections) varied between 37 and 138 μm with an inverse linear relationship to wood density. DRIFT spectral analysis of chemically treated wood surfaces indicated an increase in carbonyl functional groups after chlorine or nitrogen dioxide treatment, followed by water extraction, and disappearance of aromatic nuclei after chlorine treatment. The DRIFT spectrum of heat-treated wood suggested formation of furan aromatic structures, while that of wood treated with oxygen radiofrequency plasma showed no discernible changes. The last result was most likely due to wood ablation predominantly by physical sputtering rather then chemical oxidation, coupled with the shallowness of plasma-induced effects compared with the depth of infrared light penetration.     

Spectral Reflectance of Sintered Oxides

Spectral reflectance in the 0.23 to 2.65μ region was measured on sintered oxides of Al₂O₃, CeO₂, TiO₂, Y₂O₃, and ZnO. The oxides were sintered at various temperatures up to 1550°C. Large changes in reflectance occurred as a result of different extents of sintering of the specimens. The data were interpreted in terms of changes in the distance between the particles, the water content, and the surface roughness. Loss of trace-water and decrease in surface roughness result in an increase in reflectance, whereas shrinkage of the specimen causes a decrease in reflectance.     

Silica-silicon composites for near-infrared reflection: A comprehensive computational and experimental study

Compact layers containing embedded semiconductor particles consolidated using pulsed electric current sintering exhibit intense, broadband near-infrared reflectance. The composites consolidated from nano- or micro-silica powder have a different porous microstructure which causes scattering at the air-matrix interface and larger reflectance primarily in the visible region. The 3 mm thick composite compacts reflect up to 72% of the incident radiation in the near-infrared region with a semiconductor microinclusion volume fraction of 1% which closely matches predictions from multiscale Monte Carlo modeling and Kubelka-Munk theory. Further, the calculated spectra predict a reddish tan compact with improved reflectance can be obtained by decreasing the average particle size or broadening the standard deviation. The high reflectance is achieved with minimal dissipative losses and facile manufacturing, and the composites described herein are well-suited to control the radiative transfer of heat in devices at high temperature and under harsh conditions.     

Measurement and Analysis of Object Reflectance Spectra

Recent algorithms developed in the field of color vision make assumptions based on the spectral reflectance curves of Munsell chips and natural materials. Some of them rely on data collected many years ago. which is partially incomplete in the visible spectrum. or contains many occurrences of the same material in it. In this article. we present a set of new measurements of different materials. In particular. we measured the spectral reflectance of Munsell chips, paints. and various natural materials in the 390–730-nm range. In addition, we have analyzed. through principal-component analysis, the possibility of representing the data collected with a set of basis functions. We show the implications of varying the number of principal components used (from 7 down to 3) on the errors introduced using this method.     

Colors of dope and yamn of spun-dyed cellulose acetate

A method of color control of bulk-dyed cellulose acetate is described, based on the transmittance spectrum of the dope. Control can be effected only if the spectrum is recorded from thick samples which amplify the absorption from small amounts of impurities that later cause unacceptable color differences on the yarn. The calculation of the reflectance spectrum, and hence the color, of the yarn from the transmittance spectrum of the dope by Kubelka-Munk theory is not satisfactory due to faint turbidity of the ‘bright’ dope. The reflectance spectrum of the yarn can be calculated from a series expansion of the experimental Lambert law absorption coefficient with very satisfactory results. A fully computer-managed color-control method is employed successfully in industrial practice.     

Light scattering by optically heterogeneous polymer systems: stress whitening in polypropylene materials

Summary A theoretical background is presented which allows the assessment of the physical nature of turbidity in heterogeneous polymeric materials. The theory (based on the diffusion approximation of the transfer theory and Kubelka-Munk theory) predicts a decreasing spectral dependence of turbidity with increasing wavelength for a matrix with embedded particles of slightly different refractive indices, but a flat dependence of this quantity for a matrix material with microvoids. It is demonstrated that the diffuse reflectance displays the same type of wavelength dependence for the thick layer approximation. Indeed, diffuse light reflectance experiments on bulk specimens using an integrating sphere accessory reveal the first type of behaviour for nondeformed neat and rubber-modified polypropylenes. On the other hand, the second type of behaviour was observed with stress-whitened neat and rubber-modified polypropylenes after solid-state drawing.     

Effect of the continuous medium on the color of discontinuous substrates. IV. The effect of the refractive index of the continuous medium

It is known from experience that light scattering–absorbing substrates are darker when the continuous medium is water instead of air. This is due to the decrease in scattering efficiency of the scattering particles caused by the smaller value of the ratio n₁/n₂ of the refractive indices of the scattering particles (n₁ = 1.5 to 1.7) to that of water (n₂ = 1.33) as compared to that ratio when the continuous medium is air (n₂ = 1). Experimental evidence for this phenomenon is presented for polyester fabric viewed in air, water, and a concentrated sucrose solution. The wavelength range from 0.4 to 0.7 microns, and absolute “dry” reflectances from 0.02 to 0.7 were covered. The phenomenon cannot be adequately described with the Kubelka-Munk theory of the color of scattering–absorbing substrates.¹ Evidence is presented that at high reflectance values (0.4–0.7), the theory describes the color adequately and the results are consistent with a prediction based on a modified Mie equation for the scattering efficiency of “large” particles.^2,3 At low reflectance values (<0.05), the Kubelka-Munk theory breaks down completely. This is consistent with the observation that this theory is not capable of predicting precisely high dye concentrations on textiles but is quite adequate for low concentrations.     

Reflectance factor measurement systematic errors due to near infrared fluorescence

Orange and red ceramic tiles that are widely used as measurement standards for reflectance factor unexpectedly exhibit near infrared fluorescence. Two measurement methods, illuminating the sample with broadband light and spectrally resolving the reflectance or illuminating the sample with monochromatic light and using a broadband detector, are commonly used to measure reflectance factor. The effect this fluorescence component has on the measured reflectance factor utilizing different measurement methods is analyzed. Published 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

煤岩反射率在宝钢的应用

介绍了煤岩反射率在宝钢的应用,重点论述了用其进行煤质剖析,惰性物含量自动测定及对炼焦煤的粘结性评价等。     

Structural,morphological, optical,and thermal properties of electrospun PbS/PVP-PEO nanofibers

This study describes the preparation and characterization of PVP-PEO nanofibers filled with PbS nanoparticles. The effect of polymer concentrations, surface morphology, and diameter distribution studies of the nanofibers was evaluated by Scanning Electron Microscopy (SEM). The SEM images revealed that smooth and homogeneous nanofibers could be achieved at 12% PVP-PEO (50:50 wt%) concentration. The XRD and TEM analysis confirmed the formation of PbS nanoparticles in the PVP-PEO blend matrix, which also revealed the high crystalline behaviour of the PbS nanoparticles. The XRD data showed that the intensity and average crystallite size increase with PbS concentration. The FTIR and TGA studies revealed the interaction between PbS nanoparticles and the PVP-PEO blend matrix. UV–Vis diffuse reflectance studies have shown that the reflectance onset shifted toward a blue shift than bulk PbS. The optical bandgap determined using the Kubelka-Munk function lies 1.08–1.56 eV range by varying PbS concentration.     

Evaluating the Performance of Detergent Powder Formulations Containing Nano Alumina Using Diffuse Reflectance Infrared Spectroscopy and Pattern Recognition Techniques

An analytical method has been introduced based on diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) coupled with pattern recognition techniques to determine the efficiency of various detergent powder formulations containing nano alumina. In order to reach this aim, different multivariate classification methods such as principal component analysis, hierarchical cluster analysis and linear discriminate analysis (LDA) were utilized for diffuse reflectance spectra to evaluate the classification approach. The best model was predicted by LDA, with a correct classification rate (%CC) of 93.55 %. Furthermore, sensitivity and specificity for the test set were 0.90 and 0.95, respectively. These results confirm the capability of DRIFTS coupled with chemometric techniques for estimating the performance of detergent powder formulations containing nano alumina.     

In vitro optical characterization of dental resin composite aged in darkness

The overall objective of this study is to confirm the method of determining the accuracy of Kubelka-Munk reflectance theory (KMRT) for composite materials after undergoing aging unrelated to surface exposure. The specific aims of this study include comparisons of optical characterizations for two dental resin composite materials before and after aging in darkness. Aging of five shades of two nanohybrid dental resin composite materials was accomplished under relatively normal room conditions in a dark enclosure for over 3 years. The accuracy of KMRT was assessed and optical absorption and scattering and color and translucency characterizations were performed. The magnitudes of the error of nonlinear regression of reflectance after aging to KMRT are well within the limits of expected measurement error as applied to regression analysis. The characterizations of inherent optical scattering, inherent color, and translucency indicate that aging in darkness will have some effect for at least some shades of the materials studied. KMRT is a reliable method to predict the reflectance of dental resin aged in darkness and permits subsequent clinically relevant optical characterizations of materials aged in this manner. Although changes in optical scattering were detected due to this aging, such changes appear to have a negligible clinical effect on color and translucency.     

Spectrophotometric color matching based on two-constant kubelka-munk theory

An algorithm is proposed to minimize the spectral difference between the reflectance of a standard and that of a match formed from a mixture of scattering colorants. This method applies linear least-squares techniques and Kubelka-Munk two-constant theory to the calculation of colorant concentrations required to match the K/S curve of a standard. Several advantages may be gained over traditional tristimulus matching: the spectral reflectance of the standard and predicted formulation exhibit lower spectral difference, the use of spectrally similar colorants is enhanced, and formulations can be determined for standards measured over wavelength regions other than the visible spectrum.     

Light-fastness Assessments—An Extension of Recipe Prediction

Fabrics dyed with single dyes have been faded in daylight, the exposure being measured in langleys. The spectral reflectance data before and after exposure have been used, in the Kubelka-Munk function, to calculate the reflectances of the unfaded and faded dyeings. The colour difference ΔE is a measure of the fade. By exposing the BSI blue wool standards alongside the dyes, the colour difference can be converted to blue-scale assessments. The predicted assessments agree with visual assessments within one-half a blue standard.