William E. Vargas

Applicability conditions of the Kubelka–Munk theory

The description of optical properties of light-scattering materials has made extensive use of radiative transfer models. One of the most successful and simplest models is that of Kubelka and Munk (KM). With this model, optical properties of particulate films under diffuse illumination can be predicted from effective absorption and scattering coefficients of the material. We consider the applicability conditions of this kind of model. An extended KM model for the case of perpendicular collimated illumination is compared with results from a more general four-flux approach, and the differences between them are characterized in terms of a correction factor that depends on particle scattering and absorption, concentration of the scatterers, and film thickness. It is proved formally that the extended KM model under perpendicular illumination is a good approximation for the cases of optically thick films that contain weakly or nonabsorbing particles.

Optical properties of nano-structured dye-sensitized solar cells

Radiative transfer computations are carried out to describe the intrinsic and effective optical properties of light diffusing and absorbing materials consisting of anatase titania pigments hosted in an electrolyte medium. The intrinsic visible absorption of some of the pigments has been increased by coating them with an absorbing dye monolayer. A multiple scattering approach is applied to compute average path-length parameters and forward-scattering ratios used in four-flux radiative transfer calculations. It is shown that the effective absorption coefficient of the inhomogeneous medium is maximized when the size of the pigments is around 12 nm in diameter, and the effective scattering coefficient is optimized for diameters of the pigments around 250 nm. The intrinsic solar absorptance of the medium is optimized when the diameter of the pigments is around 60 nm.

Optimization of the diffuse reflectance of pigmented coatings taking into account multiple scattering

The optical properties of particulate coatings consisting of homogeneous rutile or anatase pigments randomly distributed through a polymeric binder are considered in the solar spectral range. The sizes of the pigments leading to the highest values of the effective scattering coefficients per unit length are established from a multiple scattering approach. Also, taken into account are boundary reflections of the diffuse radiation at the interfaces of the particulate coatings. Optimizations of the solar reflectance of pigmented coatings are also carried out. Fairly good agreement is found when comparing to solar reflectance values obtained from spectroscopic measurements involving an integrating sphere attachment.

Generalized four-flux radiative transfer model.

General solutions for a four-flux radiative transfer model, derivedfrom the radiative transfer equation and based on Lorenz-Miescattering and absorption parameters, have been obtained. Forwardand backward average path-length parameters have been considered aswell as forward-scattering ratios for diffuse anisotropic radiationgoing into the forward and the backward hemispheres. The reportedsolutions are generalizations of those obtained by Maheu et al. [Appl. Opt. 23, 3353-3362(1984)]. Compared with the generalized solutions, numericalcalculations indicate that the delta-Eddington approximation and thestandard four-flux model of Maheu et al. overestimate thecollimated-diffuse reflectance of particulate coatings, whereas thesemodels give similar results in the case of collimated-diffusetransmittance.

Condensation of water by radiative cooling

Atmospheric humidity can be condensed as dew and used for example in small-scale irrigation. In arid locations, the most favourable conditions for dew collection persist in the late night and around sunrise. We study the possibility to use a dew collector for condensing atmospheric water vapour by exploiting the effect of radiative cooling. In particular, we study pigmented polymer foils with high solar reflectance and high thermal emittance. Suitable pigments are a mixture of TiO2 and BaSO4 particles or a novel SiO2/TiO2 composite. We calculate the condensation rate under different climatic conditions and report on initial field tests.

Light Scattering in Pigmented Coatings:: Experiments and Theory

Abstract Small silica particles uniformly coated by a shell of titania, were produced by wet chemical methods. The pigments were dispersed in polymeric binders and were applied as paints to glass substrates. Total reflectance and transmittance were determined by integrating sphere measurements. Luminous and solar reflectance of paints containing the novel pigments were comparable with paints containing commercial titania. The spectral transmittance and reflectance of the paints were modelled by a four-flux radiative transfer theory. Theory and experiment could be brought into good agreement, if it was assumed that the particles were slightly porous. The studied pigments may find applications in sunscreens or in foils for daylighting and radiative cooling.

Inversion methods from Kubelka–Munk analysis

Diffuse reflectance spectra of light scattering and absorbing coatings are considered in terms of the Kubelka–Munk theory. Partial reflection of the incident diffuse radiation in the front interface of the coating, and internal reflection of backward diffuse radiation at this interface, are taken into account by means of an inversion method from which the effective scattering and absorption coefficients are obtained. The effect of neglecting these reflections of the diffuse radiation is discussed. Significant differences in the effective scattering and absorption coefficients, computed by inversion from diffuse reflectance spectra, are obtained when they are evaluated taking into account the reflection of the diffuse radiation at the front interface of the coating, in comparison with values obtained from the standard approach which neglects these reflections.

Forward average path-length parameter in four-flux radiative transfer models.

The optical properties of films containing spherical particles in a nonabsorbing matrix have been modeled by using a four-flux radiative transfer theory. The forward average path-length parameter takes into account the different path lengths for collimated and diffuse components of the radiation field. This parameter, whose value was known only in special cases, has been used previously as a fitting quantity. We establish a method for evaluating the forward average path-length parameter in a rigorous way. Single-scattering parameters are evaluated from the Lorenz-Mie theory, and multiple-scattering effects are taken into account by means of an extended Hartels theory.

Retrieved optical properties of thin films on absorbing substrates from transmittance measurements by application of a spectral projected gradient method

The refractive index and the extinction coefficient of thin films deposited on absorbing substrates, as well as their thicknesses, are obtained from measurements of direct transmittance. The inversion approach is based on application of a spectral projected gradient method (SPGM). First, simulated transmittance spectra are used to compare the performance of the method with published results considering films with different degrees of absorption and thickness, and then inversions from real measurements taken over the solar spectral range are carried out. It is shown that the use of the SPGM, to minimize the difference between measured and computed transmittance spectra, becomes a powerful tool to solve efficiently the problem of obtaining the optical constants of thin films from spectroscopic measurements.

Generalized method for evaluating scattering parameters used in radiative transfer models

The effective scattering and absorption coefficients used to describe the optical properties of particulate materials in radiative transfer models are determined by the average path-length paramete ...