A Microwave Tomography Framework for Monitoring of Pharmaceutical Processes

Licentiate thesis, 2011

Industrial pharmaceutical processes may be very difficult to monitor and control. Today, an important research fields is non-invasive measurement techniques that provide information about the material distribution inside the process. In this thesis, a microwave tomography (MWT) framework for monitoring of pharmaceutical processes is presented. MWT provides relatively high spatial resolution compared to many other non-invasive techniques. We wish to reconstruct the permittivity distribution for an unknown medium inside the process vessel. Thus, an inverse scattering problem is solved. The reconstruction algorithm is a gradient-based algorithm, where a goal function is minimized subject to appropriate constraints. The goal function involves the misfit between the computed and the measured scattering parameters. The sensitivity of the goal function, with respect to changes in the material parameters, is formulated in terms of the field solution of the original field problem and an adjoint field problem. Thus, the computational cost is independent of the number of material parameters used to describe the permittivity. Moreover, the sensitivity is derived from the continuum form of Maxwell's equations. This allows for more flexibility with respect to the choice of the field solver. The material parameters are expressed in terms of a sum of basis functions with unknown coefficients. The basis functions are space dependent and they can be either (i) global or (ii) local on a parameterization mesh. The coefficients may be frequency dependent according to an appropriate dispersion model, e.g., Debye model. This representation allows for fewer degrees of freedom in the reconstruction problem. Furthermore, it gives the possibility of incorporating a priori information about the object and it is independent of the computational mesh. This allows for refinement of the computational mesh to attain higher accuracy in the field solution without influencing the degrees of freedom in the reconstruction problem. This microwave tomography framework has been tested for two different cases: (i) a parameterization based on global basis functions where the medium is non-dispersive and axisymmetric with respect to space; and (ii) a parameterization mesh with local basis functions for a dispersive medium with a discontinuous permittivity profile.