Ludovic Gustafsson Coppel

Determination of quantum efficiency in fluorescing turbid media

A method is proposed to estimate the optical parameters in a fluorescing turbid medium with strong absorption for which traditional Kubelka-Munk theory is not applicable, using a model for the radiative properties of optically thick fluorescent turbid media of finite thickness proposed in 2009 [J. Opt. Soc. Am. A26, 1896 (2009)]. The method is successfully applied to uncoated papers with different thicknesses. It is found that the quantum efficiency of fluorescent whitening agents (FWAs) is nearly independent of the fiber type, FWA type, FWA concentration, and filler additive concentration used in this study. The results enable an estimation of the model parameters as function of the FWA concentration and substrate composition. This is necessary in order to use the model for optimizing fluorescence in the paper and textile industries.

Point spreading in turbid media with anisotropic single scattering.

Point spreading is investigated using general radiative transfer theory. We find that the single scattering anisotropy plays a significant role for point spreading together with the medium mean free path, single scattering albedo and thickness. When forward scattering dominates, the light will on average undergo more scattering events to give a specific optical response in reflectance measurements. This will significantly increase point spreading if the medium is low absorbing with large mean free path. Any fundamental and generic model of point spreading must capture the dependence on all of these medium characteristics.

Lateral light scattering in fibrous media

Lateral light scattering in fibrous media is investigated by computing the modulation transfer function (MTF) of 22 paper samples using a Monte Carlo model. The simulation tool uses phase functions from infinitely long homogenous cylinders and the directional inhomogeneity of paper is achieved by aligning the cylinders in the plane. The inverse frequency at half maximum of the MTF is compared to both measurements and previous simulations with isotropic and strongly forward single scattering phase functions. It is found that the conical scattering by cylinders enhances the lateral scattering and therefore predicts a larger extent of lateral light scattering than models using rotationally invariant single scattering phase functions. However, it does not fully reach the levels of lateral scattering observed in measurements. It is argued that the hollow lumen of a wood fiber or dependent scattering effects must be considered for a complete description of lateral light scattering in paper.

Lateral light scattering in paper - MTF simulation and measurement

The modulation transfer function (MTF) of 22 paper samples is computed using Monte Carlo simulations with isotropic or strongly forward single scattering. The inverse frequency at half maximum of the MTF (kp) is found inappropriate as a single metric for the MTF since it is insensitive to the shape of the modeled and simulated MTF. The single scattering phase function has a significant impact on the shape of the MTF, leading to more lateral scattering. However, anisotropic single scattering cannot explain the larger lateral scattering observed in paper. It is argued that the directional inhomogeneity of paper requires a light scattering model with both the phase function and scattering distances being dependent on the absolute direction.

Extension of the Stokes equation for layered constructions to fluorescent turbid media

Expressions relating the bispectral reflectance of a stack of n fluorescing layers to each individual layers reflectance and transmittance are derived. This theoretical framework is used together with recently proposed extensions of the Kubelka-Munk model to study the fluorescence from layered turbid media. For one layer over a reflecting background, the model is shown to give the same results as a previous model. The extension to n layers with different optical properties allows simulating the bispectral reflectance from a pad of layered turbid media. The applicability of the model is exemplified with an optimization of fluorophore distribution in layered turbid media.

Angular dependence of fluorescence from turbid media

We perform Monte Carlo light scattering simulations to study the angular distribution of the fluorescence emission from turbid media and compare the results to measured angular distributions from fluorescing white paper samples. The angular distribution of fluorescence emission is significantly depending on the concentration of fluorophores. The simulations show also a dependence on the angle of incidence that is however not as evident in the measurements. A detailed analysis of the factors affecting this angular distribution indicates that it is strongly correlated to the mean depth of the fluorescence process. The findings can find applications in fluorescence spectroscopy and are of particular interest when optimizing the impact of fluorescence on e.g. the appearance of paper as the measured values are angle dependent.

Impact of illumination spectral power distribution on radiance factor of fluorescing materials

The spectral radiance factor and thereby the appearance of fluorescing material is known to depend strongly on the spectral power distribution (SPD) of the illumination in the fluorophores excitation wavelength band. The present work demonstrates the impact of the SPD in the fluorescence emission band on the total radiance factor. The total radiance factor of a fluorescing paper is measured in three different illuminations. The presence of peaks in the SPD of fluorescent light tubes dramatically decreases the luminescent radiance factor. This effect will impact the appearance of fluorescing media under illuminations with large variation in SPD, which includes recent LED illuminations.

Effect of ink spreading and ink amount on the accuracy of the Yule-Nielsen modified spectral Neugebauer model

To control printers so that the mixture of inks results in specific color under defined visual environment requires a spectral reflectance model that estimates reflectance spectra from nominal dot coverage. The topic of this paper is to investigate the dependence of the Yule-Nielsen modified spectral Neugebauer (YNSN) model accuracy on ink amount. It is shown that the performance of the YNSN model strongly depends on the maximum ink amount applied. In a cellular implementation, this limitation mainly occurs for high coverage prints, which impacts on the optimal cell design. Effective coverages derived from both Murray-Davis (MD) and YNSN show large ink spreading. As ink-jet printing is a non-impact printing process, the ink volume deposited per unit area (pixel) is constant, leading to the hypothesis that isolated ink dots have lower thickness that the full-tone ink film. Measured spectral reflectance curves show similar trend, which supports the hypothesis. The reduced accuracy of YNSN can thus be explained with the fact that patches with lower effective coverage have a mean ink thickness very different from that of the full-tone patch. The effect will be stronger for small dot coverage and large dot gain and could partially explain why the Yule-Nielsen n-factor is different for different inks. The performance of the YNSN model could be improved with integration of ink thickness variation.

Lateral light propagation and angular variation of the reflectance of paper

The appearance of translucent materials is strongly affected by bulk (or sub surface) scattering. For paper and carton board, lateral light propagation and angle-resolved reflection have been studied extensively but treated separately. The present work aims at modelling the BSSRDF of turbid media in order to study the angular variation of the reflectance as function of the lateral propagation within the medium. Monte Carlo simulations of the spatial- and angle resolved reflectance of turbid media are performed for different scattering and absorption coefficients, phase functions and surface topographies representative for uncoated paper grades. The angle-resolved radiance factor of turbid media is found to be function of the lateral light propagation within the substrate and both the reflected radiance factor and the fluorescence emission are found to be clearly non- Lambertian, although the latter clearly depends on the light absorption at the excitation wavelength. It is also suggested that the modelling of uncoated paper should not include surface scattering. The findings impact on the appearance of turbid media at different angles and make measurements of the lateral light propagation dependent on the instrument geometry.

Estimating neugebauer primaries for multi-channel spectral printing modeling

Multichannel printer modeling has been an active area of research in the field of spectral printing. The most commonly used models for characterization of such systems are the spectral Neugebauer (SN) and its extensions. This work addresses issues that can arise during calibration and testing of the SN model when modelling a 7-colorant printer. Since most substrates are limited in their capacity to take in large amount of ink, it is not always possible to print all colorant combinations necessary to determine the Neugebauer primaries (NP). A common solution is to estimate the nonprintable Neugebauer primaries from the single colorant primaries using the Kubelka-Munk (KM) optical model. In this work we test whether a better estimate can be obtained using general radiative transfer theory, which better represents the angular variation of the reflectance from highly absorbing media, and takes surface scattering into account. For this purpose we use the DORT2002 model. We conclude DORT2002 does not offer significant improvements over KM in the estimation of the NPs, but a significant improvement is obtained when using a simple surface scattering model. When the estimated primaries are used as inputs to the SN model instead of measured ones, it is found the SN model performs the same or better in terms of color difference and spectral error. If the mixed measured and estimated primaries are used as inputs to the SN model, it performs better than using either measured or estimated.