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

The Kubelka-Munk reflectance is compared with the exact reflectance of an isotropically scattering material, under normal experimental conditions, by obtaining estimates of the accuracy of both methods in predicting the colour of mixtures of dyes on textiles. The exact analysis produces results that, on average, are 14% more accurate than those obtained with the Kubelka-Munk analysis.     

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     

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.     

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.     

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.     

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     

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.     

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.     

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.     

The n-type Ge photodetectors with gold nanoparticles deposited to enhance the responsivity

Gold nanoparticles (AuNPs) have been deposited on n-type Ge photodetectors to improve the responsivity. Two different coverage ratios, including 10.5 and 30.3% of AuNPs have been prepared, and the fabricated photodetectors are compared with the control sample. The 1,310-nm responsivities at -2 V of the control, 10.5% AuNPs, and 30.3% AuNPs samples are 465, 556, and 623 mA/W, respectively. The AuNPs could increase the responsivities due to the plasmon resonance. The reflectance spectra of these samples have been measured to verify that plasmon resonance contributes to the forward scattering of incident light. The reflectance decreases with AuNP deposition, and a denser coverage results in a smaller reflectance. The smaller reflectance indicates more light could penetrate into the Ge active layer, and it results in a larger responsivity.     

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.     

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.     

Light trapping structures in wing scales of butterfly Trogonoptera brookiana

The fine optical structures in wing scales of Trogonoptera brookiana, a tropical butterfly exhibiting efficient light trapping effect, were carefully examined and the reflectivity was measured using reflectance spectrometry. The optimized 3D configuration of the coupling structure was determined using SEM and TEM data, and the light trapping mechanism of butterfly scales was studied. It is found that the front and back sides of butterfly wings possess different light trapping structures, but both can significantly increase the optical path and thus result in almost total absorption of all incident light. An optical model was created to check the properties of this light trapping structure. The simulated reflectance spectra are in concordance with the experimental ones. The results reliably confirm that these structures induce efficient light trapping effect. This functional "biomimetic structure" would have a potential value in wide engineering and optical applications.     

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.     

Electrical Control of the Reflectance of Porous Silicon Layers

In this paper we demonstrate the filling of porous silicon (PS) layers with liquid crystals (LC's) in order to control the reflectance electrically. The preparation of PS and the choice of the right group of LC's will be presented. Especially an oxidation of PS is necessary so that the methods and parameters of oxidation will also be discussed. As a first result the increasing and decreasing of the thickness oscillations in the reflectance as a function of the applied voltage can be observed.     

Application of Thermoluminescence and Reflectance Methods to Study of Lattice Defects in Alumina Ceramics

Alumina ceramics irradiated with gamma rays emit light of varying intensity as they are warmed. The resulting glow curve may be resolved into discrete peaks, each of which corresponds to a separate electron trapping level. The energy depth of each trap may be estimated from the glow-peak temperature and the temperature at which the light intensity reaches half its maximum value. Resolved glow curves are presented for a series of alumina ceramics including specimens having less than 100 p.p.m. of impurities as well as others contaminated with low concentrations of Si, Ti, Fe, Mg, and Ca oxides. Curves are also given for high-purity aluminas which were heated in oxygen and in hydrogen after firing. Where possible, glow peaks are identified with the causative impurity ion or annealing treatment, and estimated trap depths are tabulated. Because of its inverse relation to optical absorption, reflectance is also sensitive to changes in the number and type of lattice defects. Annealing in oxygen and introduction of Ca²⁺ ions produce a significant lowering of the reflectance of irradiated alumina ceramics, whereas exposure to hydrogen has the opposite effect.     

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.     

Monitoring Delamination Progression in Thermal Barrier Coatings by Mid-Infrared Reflectance Imaging

Mid-infrared (MIR) reflectance imaging is shown to be a reliable diagnostic tool for monitoring delamination progression in thermal barrier coatings (TBCs). MIR reflectance imaging utilizes the maximum transparency of TBCs in the 3–6 μm wavelength region to probe below-surface delamination crack propagation that is typically hidden from visible wavelength inspection. The image contrast that identifies delamination progression arises from the increased reflectance produced by a large component of total internal reflection at the TBC/buried-crack interface. Imaging was performed at a wavelength of 4 μm to take advantage of the relatively high transmittance of plasma-sprayed 8 wt% yttria-stabilized zirconia (8YSZ) TBCs along with a desirable relative insensitivity to potentially interfering absorptions by atmospheric constituents at that wavelength. A key advantage of MIR reflectance imaging over competing techniques is that it is sensitive to delamination progression even at very early stages before delamination cracks start linking together; therefore, TBC health assessment can be achieved throughout the life of the TBC well before TBC failure is imminent. Examples are presented to demonstrate monitoring delamination progression by MIR reflectance imaging in 8YSZ TBC-coated specimens subjected to furnace cycling to 1163°C. The experimental results were in good agreement with reflectance values predicted by a four-flux Kulbelka–Munk approximation applied to the extreme cases of a completely adherent and a completely detached TBC. Practical considerations, including potential interfering effects from surface contamination, sintering, and erosion are discussed.     

Lithography-Free Fabrication of Large Area Subwavelength Antireflection Structures Using Thermally Dewetted Pt/Pd Alloy Etch Mask

We have demonstrated lithography-free, simple, and large area fabrication method for subwavelength antireflection structures (SAS) to achieve low reflectance of silicon (Si) surface. Thin film of Pt/Pd alloy on a Si substrate is melted and agglomerated into hemispheric nanodots by thermal dewetting process, and the array of the nanodots is used as etch mask for reactive ion etching (RIE) to form SAS on the Si surface. Two critical parameters, the temperature of thermal dewetting processes and the duration of RIE, have been experimentally studied to achieve very low reflectance from SAS. All the SAS have well-tapered shapes that the refractive index may be changed continuously and monotonously in the direction of incident light. In the wavelength range from 350 to 1800 nm, the measured reflectance of the fabricated SAS averages out to 5%. Especially in the wavelength range from 550 to 650 nm, which falls within visible light, the measured reflectance is under 0.01%.