Yule-Nielsen based recto-verso color halftone transmittance prediction model

The transmittance spectrum of halftone prints on paper is predicted thanks to a model inspired by the Yule-Nielsen modified spectral Neugebauer model used for reflectance predictions. This model is well adapted for strongly scattering printing supports and applicable to recto-verso prints. Model parameters are obtained by a few transmittance measurements of calibration patches printed on one side of the paper. The model was verified with recto-verso specimens printed by inkjet with classical and custom inks, at different halftone frequencies and on various types of paper. Predictions are as accurate as those obtained with a previously developed reflectance and transmittance prediction model relying on the multiple reflections of light between the paper and the print-air interfaces. Optimal n values are smaller in transmission mode compared with the reflection model. This indicates a smaller amount of lateral light propagation in the transmission mode.     

彩色双面半色调印刷品光谱反射率与透射率预测模型

为了准确地预测多色双面半色调印刷品的呈色特性,建立一个统一的半色调印刷品光谱反射透射预测模型,对纸张的固有反射率和透射率以及油墨的光谱透射率进行精确的测量和计算.为提高半色调印刷品反射透射预测模型的精度和双面印刷品在线质量检测仪器的开发,提供理论依据.     

荧光纸基的双面彩色半色调印刷品Clapper-Yule正面反射率模型

目的研究荧光纸基对双面彩色半色调印刷品反射率的影响。方法假设油墨与纸张的折射率相似,考虑到荧光部分可以吸收光线中不可见的紫外光,经过能量转换散发出可见光从而影响总反射率,将这部分影响等效于正、反面油墨的透射率,以及纸张内部向正、反面反射率的改变;考虑光学网点扩大因子,利用Clapper-Yule分程理论进行分析;通过数值模拟,对新、旧模型进行比较,验证新模型的合理性和准确性。结果建立了荧光纸基的双面彩色半色调印刷品Clapper-Yule正面反射率模型。结论色彩预测Clapper-Yule反射率模型必须考虑荧光纸基的影响。     

基于Kubelka-Munk理论的半色调印刷品光谱反射预测模型

首先介绍了经典的Kubelka-Munk理论及其Saunderson校正,并在此基础上推广到半色调印刷品中,考虑到光在印刷品中的横向散射,引入了散射概率函数描述光子从一个界面元进入而从另一个界面元射出的概率,建立了一个统一的半色调印刷品光谱反射预测模型.     

Extending the Clapper-Yule model to rough printing supports

The Clapper-Yule model is the only classical spectral reflection model for halftone prints that takes explicitly into account both the multiple internal reflections between the print-air interface and the paper substrate and the lateral propagation of light within the paper bulk. However, the Clapper-Yule model assumes a planar interface and does not take into account the roughness of the print surface. In order to extend the Clapper-Yule model to rough printing supports (e.g., matte coated papers or calendered papers), we model the print surface as a set of randomly oriented microfacets. The influence of the shadowing effect is evaluated and incorporated into the model. By integrating over all incident angles and facet orientations, we are able to express the internal reflectance of the rough interface as a function of the rms facet slope. By considering also the rough interface transmittances both for the incident light and for the emerging light, we obtain a generalization of the Clapper-Yule model for rough interfaces. The comparison between the classical Clapper-Yule model and the model extended to rough surfaces shows that the influence of the surface roughness on the predicted reflectance factor is small. For high-quality papers such as coated and calendered papers, as well as for low-quality papers such as newsprint or copy papers, the influence of surface roughness is negligible, and the classical Clapper-Yule model can be used to predict the halftone-print reflectance factors. The influence of roughness becomes significant only for very rough and thick nondiffusing coatings.     

基于辐射传递理论的印刷品光谱反射预测模型

准确预测印刷品的颜色一直是印刷复制中一个十分重要的课题。基于光能的辐射传递理论,通过分析光在油墨层表面及内部传播过程中的散射与吸收等规律,并引入荧光激发函数,对Kubelka-Munk模型预测印刷品时蓝紫波段反射率偏差的问题进行了修正,并建立了新的印刷品光谱反射预测模型。该模型可为计算机光谱配色和高精度仿真印刷系统的开发提供理论基础。     

Probabilistic spectral model of color halftone incorporating substrate fluorescence and interface reflections

A spectral model incorporating three major physical phenomena, lateral light scattering, substrate fluorescence, and interface reflections governing light-print interaction is presented. In the model, light scattering inside a paper substrate is described by probabilities applicable for any degree of light diffusion. The concept of fluorescence enhanced transmittance has been proven very useful for extending the probability approach to prints on fluorescent substrates. The contribution of multiple internal reflections is accounted for by series expansion of fast convergence. Previously developed models like the Neugebauer equation and the Clapper-Yule model can easily be obtained as special cases of the present model.     

Revised Kubelka-Munk theory. II. Unified framework for homogeneous and inhomogeneous optical media

We extend the applicability of the recently revised Kubelka-Munk (K-M) theory to inhomogeneous optical media by treating inhomogeneous ink penetration of the substrate. We propose a method for describing light propagation in either homogeneous or inhomogeneous layers using series representations for the K-M scattering and absorption coefficients as well as for intensities of the upward and downward light streams. The conventional and matrix expressions for spectral reflectance and transmittance values of optically homogeneous media in the K-M theory are shown to be special cases of the present framework. Three types of ink distribution-homogeneous, linear, and exponential-have been studied. Simulations of spectral reflectance predict a depression of reflectance peaks and reduction of absorption bands characteristic of hue shifts and significant reduction of saturation and, in turn, color gamut.     

Rapid simulation of steady-state spatially resolved reflectance and transmittance profiles of multilayered turbid materials

We present a technique for efficiently computing the reflection and transmission of light by arbitrary systems of turbid layers. To approximate the steady-state reflectance and transmittance without the need to solve difficult boundary conditions, we convolve the reflectance and transmittance profiles of individual layers. We extend single-slab boundary conditions to handle index-of-refraction mismatches between turbid slabs and account for interlayer scattering by applying methods similar to Kubelka-Munk theory in frequency space. We demonstrate good agreement between the reflectance and the transmittance predicted by our model and numerical Monte Carlo methods and show that the far-source reflectance and transmittance of multilayered turbid materials are dominated by interlayer scattering.     

调频网印品图像的微观色彩预测模型研究

在考虑网点扩大的情况下,研究了基于Murray-Davies方程的调频网半色调印品色彩预测模型。分析了调频网印品图像的微观结构和特征,建立了理想状态下调频网的反射率模型;考虑到光在纸基中的散射,采用光散射概率理论构建了墨点与墨点间的局部反射与透射关系;最后,建立了基于扩展的Murray-Davies方程的调频网半色调图像的微观色彩预测模型。     

基于油墨不同叠印的二阶调频网物理网点扩大的研究

建立了二阶调频网点构成的半色调图像光谱预测模型。考虑油墨在不同叠印条件下由于油墨铺展引起的物理网点扩大,采用Yule-Nielsen修正的光谱聂格伯尔模型对打印的二阶调频网点图像的光谱进行预测,然后计算色度值,并与测量值进行比较。实验结果表明,考虑油墨在不同叠印条件下的铺展的EYNSN模型预测的平均和最大色差分别为2.64和6.21,与未考虑油墨铺展的预测结果相比,预测精度有所提高。     

Optical properties of an optically rough coating from inversion of diffuse reflectance measurements

A method is developed for determining the optical properties of an optically rough coating on an opaque substrate from reflectance measurements. A modified Kubelka-Munk two- flux model is used to calculate the reflectance of the coating as a function of the refractive index, absorption coefficient, scattering coefficient, and thickness. The calculated reflectance is then fitted to measurements using a spectral projected gradient algorithm, allowing the optical properties to be obtained. The technique is applied to titanium dioxide coatings on a titanium substrate. Realistic values of refractive index and absorption coefficients are generally obtained. Quantities that are useful for solar water-splitting applications are calculated, including the depth profile of absorption and the proportion of the incident photon flux absorbed in the coating under solar illumination.     

Diffuse reflectance and transmittance spectra of an interference layer: 1. Model formulation and properties

A model for the calculation of the diffuse reflectance and transmittance of a single interference layer with rough interfaces on a transparent substrate is presented. The model is based on electric field calculations and scalar scattering theory, and it assumes that the interfaces of the layer are totally uncorrelated. Examples are given of calculated spectra in which the parameters of the model are varied systematically to show the influence from different interface roughness and refractive index combinations as well as absorption in the film. A wavelength-dependent effective root-mean-square roughness is introduced. This depends on the nature of the roughness, and the bandwidth limits are given by the experimental conditions. Finally, total integrated scattering spectra are calculated and the importance of taking multiple reflections in the substrate into account is shown.     

Light scattering and ink penetration effects on tone reproduction

Light scattering, or the so-called Yule-Nielsen effect, and ink penetration into the substrate paper play important roles in tone reproduction. We develop a framework in which the influences of both of these effects on the reflectance and tristimulus values of a halftone sample are investigated. The properties of the paper and the ink and their bilateral interaction can be parameterized by the reflectance Rp(o) of the substrate paper, the transmittance Ti of the ink layer, the parameter gamma describing the ink penetration, and p describing the Yule-Nielsen effect. We derive explicit expressions that relate the reflectance of the ink dots (Ri), the paper (Rp) and the halftone image (R) as functions of these parameters. We also describe the optical dot gain as a function of these parameters. We further demonstrate that ink penetration leads to a decrease in optical dot gain and that scattering in the paper results in the printed image's being viewed as more saturated in color.     

光谱Neugebauer模型的抗差最小二乘优化

Yule-Nielsen修正光谱Neugebauer模型是一种用来预测彩色网目调印刷品颜色的重要光谱预测模型。为了提高Neugebauer模型预测精度,在分析光谱Neugebauer模型和抗差估计理论的基础上,提出了将抗差最小二乘法用于计算模型参数网点面积率和基色光谱反射率。常用的抗差估计方案有:Huber估计和IGG估计。实验表明,当存在粗差的情况下,与传统的最小二乘法相比,抗差最小二乘法的光谱Neugebauer模型的预测精度更高且更为稳定。     

Hemispherical and diffuse reflectance and transmittance of a slightly inhomogeneous film bounded by rough, unparallel interfaces

The optical reflectance and transmittance of an ideal thin film are calculated in a well-known way. As far as a non-ideal thin film is concerned - i.e., a slightly inhomogeneous thin film bounded by rough, unparallel interfaces - three categories of spectral coefficients can be defined, i.e.: specular reflectance and direct transmittance (light intensity flux along the optical axis), hemispherical reflectance and transmittance (light intensity flux integrated over the solid half angle π), and diffuse reflectance and transmittance (light intensity flux scattered around the optical axis) coefficients. In this paper a model recently introduced for the specular and direct coefficients is generalized to calculate also the hemispherical and diffuse coefficients of a non-ideal film.     

Revised Kubelka-Munk theory. III. A general theory of light propagation in scattering and absorptive media

A generally applicable theoretical model describing light propagating through turbid media is proposed. The theory is a generalization of the revised Kubelka-Munk theory, extending its applicability to accommodate a wider range of absorption influences. A general expression for a factor taking into account the effect of scattering on the total photon path traversed in a turbid medium is derived. The extended model is applied to systems of ink-dyed paper sheets-mixtures of wood fibers with dyes-which represent examples of systems that have thus far eluded the original Kubelka-Munk model. The results of simulations of the spectral dependence of Kubelka-Munk coefficients of absorption and scattering show that they compare very well with those derived from experimental results.     

Radiative properties of dense nanofluids

The radiative properties of dense nanofluids are investigated. For nanofluids, scattering and absorbing of electromagnetic waves by nanoparticles, as well as light absorption by the matrix/fluid in which the nanoparticles are suspended, should be considered. We compare five models for predicting apparent radiative properties of nanoparticulate media and evaluate their applicability. Using spectral absorption and scattering coefficients predicted by different models, we compute the apparent transmittance of a nanofluid layer, including multiple reflecting interfaces bounding the layer, and compare the model predictions with experimental results from the literature. Finally, we propose a new method to calculate the spectral radiative properties of dense nanofluids that shows quantitatively good agreement with the experimental results.