Time frequency analysis in terahertz pulsed imaging

Recent advances in laser and electro-optical technologies have made the previously under-utilized terahertz frequency band of the electromagnetic spectrum accessible for practical imaging. Applications are emerging, notably in the biomedical domain. In this chapter the technique of terahertz pulsed imaging is introduced in some detail. The need for special computer vision methods, which arises from the use of pulses of radiation and the acquisition of a time series at each pixel, is described. The nature of the data is a challenge since we are interested not only in the frequency composition of the pulses, but also how these differ for different parts of the pulse. Conventional and short-time Fourier transforms and wavelets were used in preliminary experiments on the analysis of terahertz pulsed imaging data. Measurements of refractive index and absorption coefficient were compared, wavelet compression assessed and image classification by multidimensional clustering techniques demonstrated. It is shown that the timefrequency methods perform as well as conventional analysis for determining material properties. Wavelet compression gave results that were robust through compressions that used only 20% of the wavelet coefficients. It is concluded that the time-frequency methods hold great promise for optimizing the extraction of the spectroscopic information contained in each terahertz pulse, for the analysis of more complex signals comprising multiple pulses or from recently introduced acquisition techniques

Method and apparatus for analyzing material properties using reflected ultrasound

A method and apparatus which assesses the mechanical properties of a material by launching an ultrasound signal at the material while varying the angle of incidence and analyzing the amplitude of the ultrasound wave reflected by the material. The method and apparatus correlates extrema (maxima or minima inflection points) in the reflected angle with the angle of incidence of the transmitted signal to identify critical angles of incidence. The velocity of the pressure wave in the material has been found to be a function of a first critical angle corresponding to a first maxima as the angle of incidence is increased in the range 0.degree.-90.degree.. The velocity of the shear wave in the material has been found to be a function of a second critical angle corresponding to a second maxima following the first maxima. Young's modulus of elasticity, Poisson's modulus, and density can be approximated using the velocity of the pressure wave and shear wave for isotropic materials. A third critical angle corresponding to a minima after the first critical angle (reflected amplitude approaching o) has been found particularly useful in conjunction with the first and second critical angles in assessing bone density and in determining whether the second critical point is at a maximum or an inflection point. The extension of the method in which the plane of scattering is rotated around the normal to bone while keeping the point of observation fixed has been found particularly useful in assessing the mechanical properties of anisotropic materials such as cortical bone.Board of Regents, University of Texas Syste

Canonical Cortical Field Theories

We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural field model with a simple functional form that still able to predict or reproduce empirical findings. Each neural unit was modelled using a neural mass and the accompanying field theory was derived in the continuum limit. The field theory comprised coupled (real) Klein-Gordon fields, where predictions of the model fall within the range of experimental findings. These predictions included the frequency spectrum of electric activity measured from the cortex, which was derived using an equipartition of energy over eigenfunctions of the neural fields. Moreover, the neural field model was invariant, within a set of parameters, to the dynamical system used to model each neuronal mass. Specifically, topologically equivalent dynamical systems resulted in the same neural field model when connected in a lattice; indicating that the fields derived could be read as a canonical cortical field theory. We specifically investigated non-dispersive fields that provide a structure for the coding (or representation) of afferent information. Further elaboration of the ensuing neural field theory, including the effect of dispersive forces, could be of importance in the understanding of the cortical processing of information.Comment: 19 pages, 1 figur