Observer variability in metameric color matches using color reproduction media

Standard color-matching functions are designed to represent the mean color-matching response of the population of human observers with normal color vision. When using these functions, two questions arise. Are they an accurate representation of the population? And what is the uncertainty in color-match predictions? To address these questions in the dual context of human visual performance and cross-media reproduction, a color-matching experiment was undertaken in which twenty observers made matches between seven different colors presented in reflective and transmissive color reproduction media and a CRT display viewed through an optical apparatus that produced a simple split-field stimulus. In addition, a single observer repeated the experiment 20 times to estimate intra-observer variability. The results were used to evaluate the accuracy of three sets of color-matching functions, to quantify the magnitude of observer variability, and to compare intra- and inter-observer variability in color-matching. These results are compared with various techniques designed to predict the range of color mismatches. The magnitude of observer variability in this experiment also provides a quantitative estimate of the limit of cross-media color reproduction accuracy that need not be exceeded. On average, the differences between matches made by two different observers was approximately 2.5 CIELAB units. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 174–188, 1997     

一种迷彩涂料配色方法的研究

以Kubelka-Munk理论为基础,阐述了一种全光谱配色的方法,利用该方法进行了迷彩涂料的计算机配色,探讨了影响配色结果的因素。     

GENERAL LINEARIZED MATRIX THEORY OF ELECTROCHEMICAL MASS TRANSFER WITH APPLICATIONS TO ELECTRODE PROCESSES AND ION EXCHANGE

A general linearized matrix theory for electrochemical mass transfer is presented. The accuracy of the theory when applied to cases where electric current exists is tested by comparing results with exact calculations of the effect of ionic migration on limiting currents at a rotating disk electrode with laminar flow and at a flat plate electrode adjacent to a stagnant fluid film. Application of the theory is further illustrated by using it to calculate the effect of ionic migration on limiting currents in a turbulent, law-of-the-wall boundary layer. Finally, the theory is used to evaluate commonly used “film-model” methods for generalizing binary mass-transfer correlations to multicomponent nonideal mixtures. For this last purpose, a film-model generalization method was developed for nonideal electrolyte mixtures. The method is equivalent to that used by Krishnamurthy and Taylor (1985) for mass-transfer in nonideal nonelectrolyte mixtures. Results using the film-model method are compared to matrix calculations of multicomponent ion-exchange mass transfer across a laminar boundary layer and in fixed and fluidized beds.     

Formulation of blends of precolored nylon fiber

Two-constant Kubelka-Munk formalism was used to describe the color of blends of precolored nylon fibers. Pseudo-Kubelka-Munk absorption constants K and pseudo-Kubelka-Munk scattering constants S were calculated using masstone samples and blends of colored fiber with white. A masstone means 100% colored fiber in which no white or black is mixed. Various mixtures with white were tried and no systematic dependence of the calculated optical parameters on composition was discernable. With some colors, notably yellow and orange, mixtures with black were required for the calibration. Accurate color matches were obtained using the two-constant formalism especially when the proposed match contained the same primary fibers as did the standard. For matches in which the primary fibers used in the sample differed from those in the standard, the closeness of the visual match depended on how closely the primary colors in the sample resembled those in the standard. Since the eye can discern individual colors in a fiber blend, it was possible to have a visual mismatch despite colorimetric equivalence. With a large enough group of primary colors, it was generally possible to find one or more alternative formulations which matched the standard. Sample-preparation and measurement errors were found to be critical for determining color-matching accuracy. All of the color-matching error could be accounted for in terms of the sample-preparation and measurement errors alone. This suggests that the sampling error was, in fact, a limiting factor in determining color-matching accuracy.     

彩色纤维配色方法研究初探

利用库贝尔卡-芒克理论及其推论研究混色纤维的K/S值与单纤维K/S之间的关系,并利用简易算法计算双组分混色纤维混配比例,同时进行了双组分混色纤维配色研究。     

Moderne Verfahren zur Berechnung des Strahlungsaustausches in brennstoffbeheizten Röhrenöfen

Modern procedures for calculation of radiational heat transfer in fueled tubular furnaces . The zone method due to Hottel, the Monte-Carlo method and the flux method are of great importance for the calculation of radiational heat transfer in combustion chambers, along with simple zero- to two-dimensional models. Only the first three methods can be used for three-dimensional problems. The zone method and the Monte-Carlo method are mathematically exact, while the flux method gives only approximate values. The radiational heat transfer to the pipes of a cracking furnace is calculated by a simple zero-dimensional zone method to show, for example, that simple models often also give reasonable results.     

Abnormal Hue-Angle change of the gemstone tanzanite between CIE illuminants d65 and a in CIELAB color space

The blue-to-purple color appearance change observed in some rare specimens of the gemstone tanzanite between daylight and incandescent light is contrary to the hue-angle change calculated between CIE illuminants D65 and A in CIELAB color space. This abnormal calculated hue-angle change for tanzanite can be corrected by using the spectral sensitivity functions of the three kinds of cone photoreceptors to directly calculate color. This study suggests that the cone spectral sensitivity functions are more fundamental in color calculations than the CIE color-matching functions.     

ON THE RELATIONSHIP BETWEEN THE EXACT AND LINEARISED SOLUTIONS OF THE MAXWELL-STEFAN EQUATIONS FOR THE MULTICOMPONENT FILM MODEL

The exact solution of the Maxwell-Stefan equations for multicomponent mass transfer based on a film model is compared with the solution of the linearised equations. It is first shown that the formulation of the mass transfer coefficients for the two solutions can be written in identical form as the product of a square matrix of composition dependent low flux mass transfer coefficients and a square matrix of correction factors which accounts for the presence of finite rates of transfer. In the exact solution the low flux mass transfer coefficients are evaluated at a film boundary composition while in the linearised theory they are evaluated at the mean film composition. The comparison clearly shows the influence of the rates of transfer in modifying these mass transfer coefficients. It is the constituent molar fluxes which are important in the exact solution whereas it is the convective contribution to these fluxes alone which appear in the linearised theory.

Despite these fundamental differences the molar transfer rates predicted by the two methods are usually in excellent agreement relative to the average absolute rate of transfer. It is argued that this will be the case in distillation examples where composition differences are small (the matrices of mass transfer coefficients are therefore almost equal) and the matrices of correction factors are closely approximated by the diagonal unit matrix. Further, in processes involving unidirectional mass transfer, such as condensation, the large differences between the respective matrices of mass transfer coefficients and correction factors frequently compensate for each other: As a result the errors introduced by linearising the equations are usually low, even in mixtures of high concentration and with high rates of mass transfer.     

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.     

适于混合气体基于k分布的灰气体加权和模型

工业燃烧环境的复杂性,使得传统的灰气体加权和（WSGG）模型很难满足气体辐射特性计算的精度要求。基于HITEMP2010数据库,利用等级相关原理将k分布法引入WSGG模型,并假设各参与性气体之间是统计非关联的,采用叠加法建立了适用于任意浓度、温度分布的混合气体WSGG模型。对四种不同燃烧条件下的非等温、非均匀混合气体的辐射换热进行了计算,将新模型计算的辐射热流和辐射源项与逐线法（LBL）及其他模型计算结果进行比较来验证新模型的有效性。结果显示新模型参数能很好地预测任意工况下混合气体的辐射特性。     

Radiative transfer simulation of dust-like aerosols: Uncertainties from particle shape and refractive index

The composition, particle shape, number concentration, size distribution, and spatial and temporal distributions of dust aerosols cause significant uncertainties in relevant radiative transfer simulations. The spherical particle approximation has been generally recognized to introduce errors in radiative transfer calculations involving dust aerosols. Although previous studies have attempted to quantify the effect of non-spherical particles, no consensus has been reached as to the significance of the dust aerosols non-spherical effect on flux calculations. For this study, we utilize a newly developed ultra-violet-to-far-infrared spectral database of the single-scattering properties of tri-axial ellipsoidal, mineral dust-like aerosols to study the non-spherical effect on radiative forcing. The radiance and flux differences between the spherical and ellipsoidal models are obtained for various refractive indices and particle size distributions. The errors originating from using the spherical model and the uncertainties in the refractive indices are quantified at both the top and bottom of the atmosphere. The dust non-spherical effect on the net flux and heating rate profile is obtained over the entire range of the solar spectrum. The particle shape effect is found to be related to the dust optical depth and the surface albedo and can be an important uncertainty source in radiative transfer simulation. The particle shape effect is largest over water surfaces and can cause up to a 30% difference in dust forcing at the top of the atmosphere.     

Application of multi‐flux theory based on Mie scattering to the problem of modeling the optical characteristics of colored pigmented paint films

Multi‐flux theory for multiple scattering calculations in pigmented/protective coating is described. Performance evaluation of the theory is made by comparing theoretically computed reflectance with experimentally measured ones for selected wavelengths for three different paint samples. Diffuse reflectance spectra for hypothetical particulate systems in visible spectral range are generated through computer calculations. Effect of variation in average pigment size and pigment size distribution on reflectance spectra is studied. Overall thrust of morphological characteristics of pigments on the color exhibited by paint dispersion is studied by calculating CIE color and color‐difference parameters of particulate systems. Results show that a very complex relationship exists between the morphological characteristics of pigments and color exhibited by the system. The outcome of the study is important for applications in paint, coating, and plastic industries. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 234–245, 2001     

ANALYSIS OF SIMULTANEOUS RADIATIVE AND CONDUCTIVE HEAT TRANSFER IN FLUIDIZED BEDS

In the bubbling regime of operation for fluidized beds, the major mechanism for heat transfer is transient conduction to periodic packets of densely packed particles at the heat transfer surface. The well known Mickley and Fairbanks model, with various subsequently proposed modifications, adequately describes this transient conduction mechanism. However, no adequate theory exists for heat transfer in high-temperature fluidized beds where radiative contribution becomes significant.

Analysis of the radiative contribution is complicated by the nonlinear interaction of radiation with conduction/convection. This paper describes a differential formulation of the combined radiative/ conductive heat transfer process. The discrete flux method used by Churchill et al. for radiative transport in heterogeneous media is applied here to the problem of transient heat transfer to packets in fluidized beds. Packets are modeled as radiatively participating media with absorption, scattering, and emission of radiation. Simultaneous solution of the governing differential equations for temperature and forward and backward radiation fluxes permits calculation of instantaneous heat flux at the heat-transfer surface. Radiative transfer during bubble contact is added as a time-weighted contribution.

Using experimental data on radiative cross sections (from packed media experiments) and experimental data on packet residence times (from fluidized bed experiments), the combined conductive/radiative heat transfer to packets was obtained for examples of fluidized beds at different fluidizing velocities and wall temperatures. The analytical results indicate that the relative importance of radiation is affected by particle size, average packet residence time, and the radiative attenuation cross sections. For operating conditions representative of fluidized bed combustion, the model estimates a 10 to 20 percent contribution by radiation to the total heat transfer. Comparison to limited experimental data from the literature shows reasonable agreement.     

Measurement of radiative heat transfer coefficient in a high temperature circulating fluidized beds

Experimental measurements of the radiative heat flux were made, and radiative heat transfer coefficients were determined for a circulating fluidized bed of sand particles of mean diameters of 137 and 264 microns. The bed used in this study measured 0.05 m in diameter. The heat transfer test section was 0.9 m long and located in the middle of CFB riser. Operating temperature was varied from 200–600 °C, and the gas velocity in the CFB riser varied from 6 m/s to 11 m/s. The suspension densities covered a range from 3 to 35 kg/m³. Time-averaged radiative heat flux was directly measured with a radiometer. Radiative heat flux and suspension emissivity showed strong dependence on the suspension density. Particle size effect on suspension emissivity was observed. Experimentally determined suspension emissivities, which ranged from 0.3 to 0.85, were in good agreement with the predicted suspension emissivity based on independent scattering theory. The radiative heat transfer coefficients were determined from the measured radiative heat fluxes and were found to be well predicted by the Stefan-Boltzmann law. It was also found that for a dilute system, the prediction of suspension emissivity by Hottel and Sarofim, in conjunction with independent scattering theory of Brewster and Tien, showed good agreement with experimentally determined suspension emissivity.     

Theoretical and practical aspects of selected fiber-blend color-formulation functions

Color matching blends of precolored fiber using three different methods was studied. Best color-matching accuracy was obtained using a two-constant Kubelka-Munk (KM) procedure. First-formula color differences averaged 1.6 CIELAB units and were found to be within the experimental error of 1.6 CIELAB units. Useful approximations were obtained using the methods proposed by Friele and by Stearns. First-formula color matches averaged 2.4 CIELAB units for the Stearns and 2.7 CIELAB units for the Friele methods. The methods are mathematically compared and the merits of each are discussed. Where possible, interpretation of the empirical parameters each method employs is attempted. It is pointed out that absorption and scattering constants calculated for fibers using the KM formalism are not true KM absorption and scattering constants. It is demonstrated that too literal an interpretation of these constants leads to apparent anomalies. It is shown that the fiber KM scattering constants which are normally considered unchanged as dye is applied cannot be considered unchanged if these same fibers are subsequently to be used in blends with other colored fibers.     

ON THE RELATIONSHIP BETWEEN THE EXACT AND LINEARISED SOLUTIONS OF THE MAXWELL-STEFAN EQUATIONS FOR THE MULTICOMPONENT FILM MODEL

The exact solution of the Maxwell-Stefan equations for multicomponent mass transfer based on a film model is compared with the solution of the linearised equations. It is first shown that the formulation of the mass transfer coefficients for the two solutions can be written in identical form as the product of a square matrix of composition dependent low flux mass transfer coefficients and a square matrix of correction factors which accounts for the presence of finite rates of transfer. In the exact solution the low flux mass transfer coefficients are evaluated at a film boundary composition while in the linearised theory they are evaluated at the mean film composition. The comparison clearly shows the influence of the rates of transfer in modifying these mass transfer coefficients. It is the constituent molar fluxes which are important in the exact solution whereas it is the convective contribution to these fluxes alone which appear in the linearised theory.

Despite these fundamental differences the molar transfer rates predicted by the two methods are usually in excellent agreement relative to the average absolute rate of transfer. It is argued that this will be the case in distillation examples where composition differences are small (the matrices of mass transfer coefficients are therefore almost equal) and the matrices of correction factors are closely approximated by the diagonal unit matrix. Further, in processes involving unidirectional mass transfer, such as condensation, the large differences between the respective matrices of mass transfer coefficients and correction factors frequently compensate for each other: As a result the errors introduced by linearising the equations are usually low, even in mixtures of high concentration and with high rates of mass transfer.     

ANALYSIS OF SIMULTANEOUS RADIATIVE AND CONDUCTIVE HEAT TRANSFER IN FLUIDIZED BEDS

In the bubbling regime of operation for fluidized beds, the major mechanism for heat transfer is transient conduction to periodic packets of densely packed particles at the heat transfer surface. The well known Mickley and Fairbanks model, with various subsequently proposed modifications, adequately describes this transient conduction mechanism. However, no adequate theory exists for heat transfer in high-temperature fluidized beds where radiative contribution becomes significant.

Analysis of the radiative contribution is complicated by the nonlinear interaction of radiation with conduction/convection. This paper describes a differential formulation of the combined radiative/ conductive heat transfer process. The discrete flux method used by Churchill et al. for radiative transport in heterogeneous media is applied here to the problem of transient heat transfer to packets in fluidized beds. Packets are modeled as radiatively participating media with absorption, scattering, and emission of radiation. Simultaneous solution of the governing differential equations for temperature and forward and backward radiation fluxes permits calculation of instantaneous heat flux at the heat-transfer surface. Radiative transfer during bubble contact is added as a time-weighted contribution.

Using experimental data on radiative cross sections (from packed media experiments) and experimental data on packet residence times (from fluidized bed experiments), the combined conductive/radiative heat transfer to packets was obtained for examples of fluidized beds at different fluidizing velocities and wall temperatures. The analytical results indicate that the relative importance of radiation is affected by particle size, average packet residence time, and the radiative attenuation cross sections. For operating conditions representative of fluidized bed combustion, the model estimates a 10 to 20 percent contribution by radiation to the total heat transfer. Comparison to limited experimental data from the literature shows reasonable agreement.     

A COMPARISON OF APPROXIMATE AND EXACT SOLUTIONS FOR HOMOGENEOUS IRREVERSIBLE CHEMICAL REACTION IN THE LAMINAR BOUNDARY LAYER

A comparison of approximate and exact solutions for homogeneous irreversible chemical reaction in the laminar boundary layer flow has been made. By using the Method of Weighted Residuals, approximate analytical expressions for the velocity and concentration profiles were developed for the case of a laminar boundary layer flow over a flat plate at zero incidence angle, where isothermal, homogeneous, nth order chemical reaction takes place. Both the Subdomain and Galerkin methods were employed to examine the influence of the choice of the weighting function on the predictions, and to provide a means for improving the solutions systematically. The problem was also solved numerically for the case of first order reaction by using a similarity solution for the hydrodynamic flow and a power series expansion method for the mass transfer. The analytical results were compared with the exact solutions in order to evaluate the accuracy of the approximate analytical solutions. The Method of Weighted Residuals provided approximate solutions that are qualitatively correct and, within limits, quantitatively accurate. The resulting approximate expressions can be used to give quick estimates for reactions investigated herein and to predict the results for higher order reactions when there are no exact solutions.     

Modeling of the scattering and radiative properties of nonspherical dust-like aerosols

The optical and radiative properties of dust particles in solar and thermal infrared regions are investigated. Dust particles are assumed to be spheres and spheroids for a comparison aimed at understanding the nonsphericity effect of these particles on the radiation at the top of a dusty atmosphere. The classical Lorenz–Mie theory is employed to compute the optical properties of spherical dust particles. To compute the single-scattering properties of spheroidal dust particles, a combination of the T-matrix method and an approximate method is used in the present study. In the approximate method, applicable to large particles, the geometric optics method is applied to the computation of the scattering phase matrix. A combination of the solution from the geometric optics method and the contribution of the so-called edge effect is used to compute the extinction efficiency of a spheroidal particle whose absorption efficiency is computed by adding the so-called above- and below-edge effect (a term from the well-known complex angular momentum theory) to the geometric optics result. Numerical results show that the results from the T-matrix method and the present approximate approach converge at a size parameter of 50 for computing the integrated scattering properties (i.e., the extinction efficiency, single-scattering albedo, and asymmetry factor). Additionally, the phase functions computed from the two methods are quite similar for size parameters larger than 40 although some considerable differences may still be noticed for other phase matrix elements. Furthermore, the effect of surface roughness on the single-scattering properties of spheroidal particles is discussed. The present radiative transfer simulations illustrate the nonsphericity effect of dust particles is significant at short wavelengths, however, not at the thermal infrared wavelengths.