A fluorescent extension to the Kubelka–Munk model

Shakespeare, Tarja; Shakespeare, J.

doi:10.1002/col.10109

Cited by 65 publications

(31 citation statements)

References 7 publications

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“…It is therefore assumed here that S is independent of the FWA concentration, allowing its determination from the undyed sample. This assumption is made in contradiction with the findings of Shakespeare and Shakespeare (2003), who showed that S was decreasing with increasing K, and hence was dependent on the FWA concentration. On the other hand, B in Eq 2 is only dependent on the ratio…”

Section: Optical Characterisation Of the Samplescontrasting

confidence: 89%

“…Modelling fluorescence with an extended KubelkaMunk model For a medium of infinite thickness, the Kokhanovsky (2009;2010) model gives the same equation as the one obtained by Shakespeare and Shakespeare (2003) and Allen (1964). The Donaldson matrix is computed from the scattering and absorption coefficients, and the quantum efficiency through…”

Section: Optical Characterisation Of the Samplesmentioning

confidence: 80%

“…, introduced by Shakespeare and Shakespeare (2003), is the effective absorption coefficient of the fluorescent dye, assuming additivity of the dye and substrate absorption properties. Eq 2 is originally derived from the assumption that fluorescence is isotropic and that emitted wavelengths are outside the absorption band of the FWA.…”

Section: Optical Characterisation Of the Samplesmentioning

confidence: 99%

See 2 more Smart Citations

Limitations in the efficiency of fluorescent whitening agents in uncoated paper

Coppel¹,

Andersson

Edström

et al. 2011

Nordic Pulp &Amp; Paper Research Journal

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SUMMARY:The fluorescence efficiency of one fluorescent whitening agent (FWA) in uncoated and unfilled paper is characterised at different FWA concentrations. An extended Kubelka-Munk model proposed earlier by several authors is applied to quantify the effect on CIE whiteness of light absorption by the FWA in the visible spectrum. At high FWA concentration, chemical interactions slightly modify the quantum efficiency, which then depends on the FWA concentration. This effect has however a negligible effect on the CIE whiteness for FWA concentrations used in practice. Light absorption by the FWA in the visible spectrum is shown to be the main cause of greening (a shift of the chromaticity towards green) and saturation of the fluorescence effect. With increasing FWA concentration, the positive effect of fluorescence is neutralised by the reduction of the reflected radiance factor in the violet-blue region of the spectrum induced by a significant absorption by the FWA in that region. The effect is well predicted with a simple extension of the Kubelka-Munk model for light scattering in paper.

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Section: Optical Characterisation Of the Samplescontrasting

confidence: 89%

Section: Optical Characterisation Of the Samplesmentioning

confidence: 80%

Section: Optical Characterisation Of the Samplesmentioning

confidence: 99%

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Limitations in the efficiency of fluorescent whitening agents in uncoated paper

Coppel¹,

Andersson

Edström

et al. 2011

Nordic Pulp &Amp; Paper Research Journal

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“…Recent spectral prediction models dealing with the fluorescence phenomenon were focussed mainly on the fluorescence of inks [15][16][17]. They rely on a twoflux approach similar to the Kubelka-Munk theory.…”

Section: Previous Workmentioning

confidence: 99%

Spectral prediction model for color prints on paper with fluorescent additives

Hersch¹

2008

Appl. Opt.

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I propose a model for predicting the total reflectance of color halftones printed on paper incorporating fluorescent brighteners. The total reflectance is modeled as the additive superposition of the relative fluorescent emission and the pure reflectance of the color print. The fluorescent emission prediction model accounts for both the attenuation of light by the halftone within the excitation wavelength range and for the attenuation of the fluorescent emission by the same halftone within the emission wavelength range. The model's calibration relies on reflectance measurements of the optically brightened paper and of the solid colorant patches with two illuminants, one including and one excluding the UV components. The part of the model predicting the pure reflectance relies on an ink-spreading extended Clapper-Yule model. On uniformly distributed surface coverages of cyan, magenta, and yellow halftone patches, the proposed model predicts the relative fluorescent emission with a high accuracy (mean ΔE 94 ¼ 0:42 under a D65 standard illuminant). For optically brightened paper exhibiting a moderate fluorescence, the total reflectance prediction improves the spectral reflectance prediction mainly for highlight color halftones, comprising a proportion of paper white above 12%. Applications include the creation of improved printer characterization tables for color management purposes and the prediction of color gamuts for new combinations of optically brightened papers and inks.

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“…Light scattering in paper is most frequently modelled with the Kubelka-Munk (1931;1948) theory (KM). The KM theory relates two reflectance factor measurements to a scattering coefficient, S, and an absorption coefficient, K. Several extensions of the KM theory have been developed over the years to account for fluorescence (Allen 1964;Fukshansky, Kazarinova 1980;Bonham 1986;Shakespeare 2000;Shakespeare and Shakespeare 2003). However, the use of these extensions is limited to either a defined polychromatic illumination or to a semi-infinite layer.…”

mentioning

confidence: 99%

Fluorescence model for multi-layer papers using conventional spectrophotometers

Coppel

Andersson

Neuman

et al. 2012

Nordic Pulp &Amp; Paper Research Journal

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SUMMARY:We present an extension of a KubelkaMunk based fluorescence model in which we introduce an apparent scattering (S UV ) and absorption (K UV ) coefficient for all wavelengths below 400 nm. We describe a method for modelling the total radiance factor of multi-layer papers and for estimating the optical parameters (S, K and Q) of each layer. Assuming that the fluorescent whitening agent only absorbs below 400 nm, we are able to determine S UV , K UV and the apparent quantum efficiency, Q(UV,) for 400 nm<<700 nm, from spectral radiance measurements in the visual part of the electromagnetic spectrum. We test the proposed method on different layered constructions made of three individual pilot paper layers. The proposed method allows the papermaker to determine the illumination independent fluorescence characteristics of single-and multilayer paper layers using a conventional singlemonochromator spectrophotometer operating in the visible part of the electromagnetic spectrum, and also to predict the radiance factor of fluorescing layered papers.

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A fluorescent extension to the Kubelka–Munk model

Cited by 65 publications

References 7 publications

Limitations in the efficiency of fluorescent whitening agents in uncoated paper

Limitations in the efficiency of fluorescent whitening agents in uncoated paper

Spectral prediction model for color prints on paper with fluorescent additives

Fluorescence model for multi-layer papers using conventional spectrophotometers

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