A novel strategy regarding geometric product for liquids discrimination based on THz reflection spectroscopy

A novel expression of geometric product that associated with the geometric relationship from geometric algebra constructed by the vectorized refractive index and absorption coefficient in THz region is proposed, which could provide a new insight into the THz properties of materials. From the novel expression, the candidate characteristic parameters are extracted for liquids discrimination and present the abundant second order correlation information of optical parameters with the consideration of dimension rising. Three groups of liquids, containing C-reactive protein calibrators and alpha fetoprotein calibrators, were selected as examples to validate the feasibility of the proposed strategy. Comparing with the traditional THz parameters, including refractive index, absorption coefficient, and complex permittivity, the novel approach exhibits notable superiority for differentiation with the evaluation of statistical differences and effect sizes. The proposed geometric product expression could have a large potential on promoting the substance identification in some applications of THz technology.