Аналіз методів визначення мінімуму характеристики відбиття під час поверхневого плазмонного резонансу

Abstract

The paper analyzed the most widely used methods for the determination of the reflection characteristic minimum in the process of the surface plasmon resonance and considers the impact of the refraction index change of the studied environment and its temperature on the accuracy of the measurements, performed by these methods, applying the numerical modeling. It is known that the accuracy of the minimum reflection characteristic determination greatly depends on the mathematical methods of its determination. The most widely used methods of the minimum reflection characteristic determination are the methods of the polynomial approximation, which depend on the form of the reflection characteristic, that influences the accuracy of the minimum determination. The developed alternative method of the center line provides smaller measurement error when the refraction indices change from 1.33 to 1.5 times as compared with the methods of the polynomial approximation for the area of the reflection characteristic with the angular range of 0.125 ang. deg. and almost 8.5 times for the angular range of 0.2 ang. deg, that proves the expediency of the new method application. The smallest absolute error is characteristic for the method of the center line for the area of the reflection characteristic of 0.4, that is connected directly with the number of points, comprising the area of the minimum determination. The method of the center line, used for the study of the temperature changes of the analyte also provides smaller absolute error of minimum determination as compared with the polynomial approximation and has smaller error values scattering in the range of the higher temperatures. As compared with the polynomial methods the center line method has higher accuracy of the determination of the reflection characteristic minimum, because it is less dependent on its asymmetry, which is connected with the flow of the physical processes on the surface of the surface of the plasmons excitation. The results of the numerical analysis, carried out, may be useful for the development of the algorithms of the direct measurements processing by measuring devices on the base of the surface plasmon resonance.