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Determination of scattering and absorption coefficients from experimental data: Application to sunscreen lotions
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Solid State Physics.ORCID iD: 0000-0002-8279-5163
Lundellska Skolan, Uppsala.
2013 (English)In: Optics & Photonics in Sweden 2013, 2013Conference paper, Poster (Other academic)
Abstract [en]

Materials with pronounced light scattering are of large interest in a variety of scientific and technical disciplines. Their optical properties can to a good approximation be described by two-flux (Kubelka-Munk) theory [1]. This theory considers one light beam propagating in the forward direction and one beam propagating in the backward direction in the material. The optical properties of the material are described by phenomenological scattering (S) and absorption (K) coefficients. Additional parameters are the internal reflection coefficients for diffuse light at the interfaces and the reflection coefficient for incident collimated light at the front interface. The large amount of parameters makes it difficult to invert experimental measurements of transmittance (T) and reflectance (R) in order to obtain the parameters S and K characterizing the material [2,3]. We propose a method to partially overcome this problem in special cases by invoking physically realistic approximations for the reflection coefficients. 

We consider viscous emulsions or polymeric materials positioned between two transparent substrates separated by a spacer. Many organic and polymeric materials have refractive indices sufficiently close to those of glass and quartz substrates so that reflections between the material and the glass can be neglected. The reflection coefficient of the substrate for collimated light is known from its refractive index. Measurements of R and T in a region of weak scattering and absorption allow us to put quite stringent limits on the internal reflection coefficients for diffuse light. In this way good approximative values for S and K can be obtained.

We apply this method to spectrophotometric measurements on two commercial sunscreen lotions. A drop of lotion was applied on a quartz substrate and a second quartz plate was put on top. The quartz plates were separated by aluminium foil of thickness 11 mm, except in the area covered by the lotion. Measurements of total R and T were taken by a Perkin-Elmer lambda-900 spectrophotometer equipped with an integrating sphere, in the wavelength range 250-800 nm. The samples were completely diffuse scattering and measurements in a low scattering region indicated a preferential forward scattering. The absorption coefficient was found to be low in the visible region and increased very much in the ultraviolet (UV). The scattering coefficient increased towards shorter wavelengths in the visible but exhibited differing behaviours in the UV. A sunscreen containing TiO2 particles exhibited a very low UV scattering together with higher scattering in the visible range, see fig. 1.


Fig. 1. Scattering (S) and absorption (K) coefficients for a sunscreen containing a mix of chemical pigments and TiO

[1] P. Kubelka, J. Opt. Soc. Am. 38 (1948) 448.

[2] R. Levinson, P. Berdahl and H. Akbari, Solar Energy Mater. Solar Cells, 89  (2005) 319.

[3] D. Barrios, R. Vergaz, J.M. Sanchez-Pena, C.G. Granqvist and G.A. Niklasson, Solar Energy Mater. Solar Cells, 111 (2013) 115.

Place, publisher, year, edition, pages
National Category
Other Engineering and Technologies
Research subject
Engineering Science with specialization in Solid State Physics
URN: urn:nbn:se:uu:diva-210794OAI: diva2:664365
Optik & Fotonik i Sverige 2013 (Optics & Photonics in Sweden), 22-23 October, 2013; Uppsala, Sweden
Available from: 2013-11-14 Created: 2013-11-14 Last updated: 2014-07-15Bibliographically approved

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