Abstract
The optical properties of 1 μm polystyrene in the wavelength range of 500–750 nm were estimated by using a white light spectrophotometric transmittance spectroscopy and a single integrating sphere system. To retrieve the optical characteristics, two analytical methods, namely, diffusion approximation and Kubelka–Munk were used, and then their results were compared with Mie theory calculations. The correspondence of the Kubelka–Munk scattering coefficient with Mie was obvious, and relative errors varied between 6.73% and 2.66% whereas errors varied between 6.87% and 3.62% for diffusion theory. Both analytical methods demonstrated the absorption property of polystyrene over the abovementioned wavelength range. Although absorption coefficient turned out to be much lower than scattering, constructing a realistic optical phantom requires taking into account absorption property of polystyrene. Complex refractive index of polystyrene based on these two methods was determined. Inverse Mie algorithm with scattering coefficient was also used to retrieve the real part of refractive index and absorption coefficient for calculating the imaginary part of refractive index. The relative errors of the real part did not exceed 2.6%, and the imaginary part was in consistence with the prior works. Finally, the presented results confirm the validity of diffusion theory with a single integrating sphere system.
Highlights
Optical characterization techniques require both an experimental setup to measure the radiometric characteristics and a light propagation method to extract the macroscopic optical properties
Kubelka–Munk theory is an analytical solution of a radiative transfer equation (RTE) based on some presumptions. e simplicity of the Kubelka–Munk method has been the main reason for its widespread uses [6, 7]. is theory introduced special coefficients: K is a Kubelka–Munk absorption coefficient and S is a Kubelka–Munk scattering coefficient, which are related to macroscopic optical coefficients as follows [1, 6]: K
K–M scattering was in agreement with Mie calculation and the relative errors varied between 6.73% to 2.66%, but scattering coefficient estimated by diffusion approximation turned out to be higher, and low absorption property could be noticed that was obvious from albedo values, Figure 5(b)
Summary
Optical characterization techniques require both an experimental setup to measure the radiometric characteristics and a light propagation method to extract the macroscopic optical properties These techniques are categorized as direct and indirect methods [1, 2]. Kubelka–Munk may be considered as the simplest analytical method that has been used for optical characterization, but the drawback of this method is limited to the case of highly scattering medium, and the sample’s thickness should exceed the transport length. This model does not take into account the jump in the refractive index between the sample and surrounding medium [6, 7]. This approach has been modified to overcome the refractive index mismatch between the sample and holder, and the thickness does not exceed the transport length [7]. e present method has been investigated with a single integrating sphere system
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