A Clifford Algebra analysis method of THz-TDS images

A novel Clifford Algebra analysis method of terahertz time domain spectroscopy (THz-TDS) images is presented, which is based on the physical basis of the THz-TDS transmission system. Pixels in THz-TDS images, as well as the complex refractive indexes of materials in THz band, can be expressed as vectors in a high-dimensional space, or hyper-complex numbers in the Clifford algebra. Based on that the magnitude and phase of the transfer function of the THz-TDS system are primarily governed by the materialpsilas intrinsic complex refractive index and its thickness, two functions are given to construct hyper-complex numbers in Clifford algebra, and then several properties of data distributions in the THz-TDS signal vector space are discussed with Clifford algebra analysis. Finally, experiments are given to show the potential of the proposed method.