Mathematical analysis of RF imaging techniques and signal processing using wavelets

Non-linear optics plays an important role in the imaging. In this paper using non-linearity, we have derived three different techniques for imaging. In the first technique, an algorithm is developed for the scattering of electromagnetic waves from the medium, which gives higher-order harmonics of the EM wave. Here, the linear and non-linear interactions of molecules with the applied electromagnetic waves play an important role in target detection. We assume the material is inhomogeneous and represented by its susceptibility tensor. Second technique for detection of non-linearity or higher-order harmonic is using anharmonic oscillator model where the perturbation due to non-linearity in the electron moment is derived and mapped to the second harmonic generation of electromagnetic waves. Third technique is applied using Gaussian monopulse where the non-linear interaction of wave with the matter makes the phase change of the wave. When wavelet transforms with dilations and translation are applied to these non-linear waveforms, we get the details of region of interest in terms of wavelet coefficients. The region of interest may be 1-dimensional, 2-dimensional or 3-dimensional. These methods can be used in biomedical applications and other areas where target is in the near-field range.