Diffuse reflectance spectroscopy of γ-irradiated UHMWPE: A novel fractional order based filters approach for accessing the radiation modification

Abstract

Spectral data pre-processing is a very effective method to improve the accuracy of constructing hyper spectral models, and differential spectroscopy is a valuable analysis method for the pre-processing of hyper spectral signals. It is usually used to increase the intensity of spectral signals and makes the researcher able to figure out hidden inflection points along with the minimum and maximum bands. In this particular study, fractional derivatives have been employed for the analysis of UV-VIS spectra of PE (ultra-high, MW) samples. The fractional order derivatives of UV-VIS (reflectance) spectra of un-irradiated and irradiated samples are simulated, and radiation modifications in UHMWPE are assessing. The classic definition of Riemann-Liouville (RL) integral is used for the calculation fractional order derivatives. For this the rule given by Lagrange operator (differential) is used i.e., taking the nth derivative over the (n−α)th order integral gives the derivative of αth order. It is of particular importance to mention here that n is the neighboring integer satisfying the condition n>α. Staring from following definition of RL integral (fractional) with 0<α<1 and initial value a=0.Ja+αf(x)=1Γ(α)∫ax(x−τ)α−1f(τ)dτ It is observed that the fractional order differential transformation gives better estimates regarding spectral pre-processing and accessing the radiation modification of UHMWPE while minimizing the loss of original data.