Thermal and optical characterization of multilayered solids using photothermal radiometry


R. Fuente1, E. Apiñaniz1, A. Mendioroz1, R. Celorrio2 and A. Salazar1

1Departamento Fisica Aplicada I, Escuela Tecnica Superior de Ingenieria, Universidad del Pais Vasco, Spain
2Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza, Spain

Keywords: thermal conductivity, optical absorption, depth-profile, inversion
property: thermal conductivity, optical absorption
material: optical glass, cured resin

Modulated photothermal radiometry (PTR) consists of illuminating the sample by an intensity modulated light beam and detecting the oscillating component of the temperature rise by means of an infrared detector connected to a lock-in amplifier. As the temperature rise depends on the optical and thermal properties of the sample, PTR has been used to measure the thermal diffusivity and the optical absorption coefficient of a wide variety of homogeneous materials. In the last years this technique has also been used to retrieve the in-depth thermal conductivity of case hardened steels and the optical and thermal depth profile of cured dental resins [1]. In this work, we have thoroughly studied the application of modulated PTR to retrieve simultaneously the thermal conductivity (K) and the optical absorption coefficient (α) depth-profile of heterogeneous samples with in-depth varying thermal and optical properties, as is the case of functionally graded materials, multilayered samples, photo-polymerized resins, etc. First, we have solved the heat diffusion equation in a sample made of a high number of layers. We have used the thermal quadrupole method, which provides a matrix relation between the surface temperature and the thermal and optical properties of each layer. The following effects have been included in the model: (a) Heat losses by conduction to the surrounding gas, as well as, by convection and radiation, (b) thermal contact resistance between layers, and (c) transparency of the sample to infrared wavelengths. A material with continuously varying properties can be modelled as a multilayered one, provided a high number of layers is used. Then, we have developed an inverse algorithm to retrieve the K and α depth-profile from the frequency dependence of the surface temperature of the sample. As it is a severe ill-posed problem, Tikhonov regularization procedures have been used. Modulated PTR measurements performed on multilayered samples (optical filter stacks, cured resins and glasses with gradient doping level) allow us to validate the quadrupole solution, as well as, the inversion algorithm. This work has been supported by the Ministerio de Ciencia e Innovación (MAT2008-01454).

References
  1. P. Martínez-Torres, A. Mandelis, J.J. Alvarado-Gil, J. Appl. Phys. 108, 054902 (2010).

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