Semiconductor γ-ray spectrometer devices, which possess attractive properties over alternative devices (e.g., scintillators), have received due attention recently. Evidently, efficient and accurate modeling of these devices, in particular, of the induced charges and internal fields, is crucially important for further development and engineering implementation. Previous attempts to analyze the spectrometers were either oversimplified, i.e., Image Charges (IC) in an idealized infinite parallel plate capacitor, or time consuming, utilizing a Point Charge Moment Method (PCMM) scheme. While the first attempt results in poor accuracy, the second leads to an enhanced accuracy but with the cost of large computation time. Thus, it is desirable to develop a modeling technique that is capable of generating both accurate and efficient solutions. An attempt in this direction is outlined in our work, which introduces the Fourier Series Expansion (FSE) scheme. The model utilizes the eigenfunctions of an idealized infinite two-dimensional array of anodes, namely, Fourier harmonics. These base functions exhibit an accurate and fast converging solution. Thus, it can be effectively applied for practical (finite) devices as long as edge effects can be neglected. This constraint is generally satisfied in practical devices, since the device contains a large number of anodes and the detectable photogenerated carriers are located sufficiently far from the device edges. Numerical comparison of the FSE scheme with the PCMM and IC techniques reveals the effectiveness and usefulness of the proposed scheme. While the FSE and PCMM techniques agree within 2%, the agreement with the IC method is within 7%, as expected.

A novel electrical impedance tomography method is introduced for reconstruction of layered biological tissues with continuous plane-stratification. The algorithm implements the recently proposed reconstruction scheme for piecewise constant conductivity profiles, based on an improved Prony method in conjunction with Legendre polynomial expansion (LPE). It is shown that the proposed algorithm is capable of successfully reconstructing continuous conductivity profiles with moderate (WKB) slop. Features of the presented reconstruction scheme include, an inherent linearity, achieved by the linear LPE transform, a locality feature, assigning analytically to each spectral component a local electrical impedance associated with a unique location, and effective performance even in the presence of noisy measurements.

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