Iterative method for the optical characterization of biaxially oriented poly(ethyleneterephthalate) films
Introduction
The investigation described in this paper is part of an ongoing program of research on optical properties of polymer films [1], [2]. Previous publications have reported the use of interference fringes in both infrared and visible regions for measuring properties of industrial polymer films [3], [4], [5]. The Lambert–Beer law have also been employed to evaluate the thickness of photoconductor coatings [6].
Poly(ethyleneterephthalate), PET, is an important material used as substrate for multilayer structures, with a lot of applications [7] in numerous areas, such as photography, radiography, holography, reprography (materials for printers, photocopiers, and so on), optical coatings (coloured, anti-reflecting, electro-optic polymers, photoanodes, and others), or protective coatings (adherent, corrosion resistant, and so on).
The main goal of this work is to present a non-destructive method that allows for an accurate and rapid characterisation of transparent PET films. We stress that an adequate characterisation of the substrate is usually the previous step in any quality control of multilayer films.
Interference effects give rise to a spectrum, due to the constructive and destructive effects of internally reflected waves inside the sample [3]. In this paper we shall show that far from being a nuisance, as in other spectroscopic experiments, these fringes can be used to calculate the optical constants of the film, as well as the geometrical thickness.
Only the spectral interference fringes produced in the optical region are considered in the discussion. All formulas and procedure are, of course, also valid in other spectral regions.
Section snippets
Materials
Our samples were five commercially available PET films, with different thicknesses, provided by Goodfellow, Agfa and DuPont. The films were bioriented due to lengthwise and transverse stresses during the manufacturing process [8], as shown in Fig. 1. As a consequence of the manufacturing procedure, films have an optical anisotropy, with three different refractive indices.
Measurement of geometrical thickness
The thicknesses of the samples were obtained previously by means of an electronic micrometer Mitutoyo, with display unit
Preliminary theoretical considerations
Each sample is assumed to be a parallel homogeneous film. All films studied have a high degree of transparency in the spectral range of 500–800 nm.
Interference effects give rise to oscillations in the transmittance curves. The transmittance, T, of the optical system investigated is a complicated function [9], [10], [11]. For weakly absorbing films, when the condition n2 ≫ k2 in the spectral region considered, the expression for T can be simplified to:
Determination of the optical thickness and the interferometric order
The values of optical thickness and interferometric order were obtained through the wavelengths of maxima of the interference fringes in the transmittance spectrum. We used the equation:where (n · t)j is the optical thickness for each wavelength of maxima, λj, j is an integer (0, 1, 2, …) and m1 is the interferometric order corresponding to the maximum with highest wavelength.
It is well known that, in the visible and near IR spectra, the variation of optical thickness with the
Method
The method employs two spectrophotometric techniques and an iterative process. It starts with the values obtained for geometrical thicknesses through the absorbance of a band at the IR zone and with the optical thicknesses calculated through the interference fringes in the visible zone. Following the ideas exposed by Swanepoel [18], it is then possible to calculate the optical thickness, refractive index, coherence factor, and geometrical thickness. Fig. 4 summarizes in a block diagram, the
Results and discussion
In Fig. 6, Fig. 7 we have represented, a zone of the Visible experimental spectrum and the calculated spectrum by considering the optical thicknesses n1 · t and n3 · t, respectively, for the sample 1. It can be observed a good coincidence in the position of maxima and minima. The height of the simulated bands do not coincide with the experimental data because the coherence factor considered initially is the highest, i.e. 1.00. After calculating the coherence factor, cf1(i), and substituting this
Concluding remarks
We have demonstrated a new method to calculate the film thickness and optical constants, such as refractive indices and coherence factor, of poly(ethyleneterephtalate) films, widely used as substrate in a variety of industrial films. This non-destructive method allows one to calculate the film thickness and the three refractive index simultaneously.
Acknowledgements
The authors wish to express their gratitude to the factory of AGFA-GEVAERT in Aranjuez (Comunidad de Madrid, Spain) for providing part of the equipment used in the measurements.
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