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This paper presents a study of possible models to describe the relation between the scintillation light point-of-origin and the measured photo detector pixel signals in monolithic scintillation crystals. From these models the X, Y and depth of interaction (DOI) coordinates can be estimated simultaneously by nonlinear least-square fitting. The method depends only on the information embedded in the signals of individual events, and therefore does not need any prior position training or calibration. Three possible distributions of the light sources were evaluated: an exact solid-angle-based distribution, an approximate solid-angle distribution and an extended approximate solid-angle-based distribution which includes internal reflection at side and bottom surfaces. The performance of the general model using these three distributions was studied using Monte Carlo simulated data of a 20 x 20 x 10 mm lutetium oxyorthosilicate (Lu₂SiO₅ or LSO) block read out by 2 Hamamatsu S8550 avalanche photo diode arrays. The approximate solid-angle-based model had the best compromise between resolution and simplicity. This model was also evaluated using experimental data by positioning a narrow 1.2 mm full width at half maximum (FWHM) beam of 511 keV photons at known positions on the 20 x 20 x 10 mm LSO block. An average intrinsic resolution in the X-direction of 1.4 mm FWHM was obtained for positions covering the complete block. The intrinsic DOI resolution was estimated at 2.6 mm FWHM.

The use of temperature-time series measured in streambed sediments as input to coupled water flow and heat transport models has become standard when quantifying vertical groundwater-surface water exchange fluxes. We develop a novel methodology, called LPML, to estimate the parameters for 1-D water flow and heat transport by combining a local polynomial (LP) signal processing technique with a maximum likelihood (ML) estimator. The LP method is used to estimate the frequency response functions (FRFs) and their uncertainties between the streambed top and several locations within the streambed from measured temperature-time series data. Additionally, we obtain the analytical expression of the FRFs assuming a pure sinusoidal input. The estimated and analytical FRFs are used in an ML estimator to deduce vertical groundwater-surface water exchange flux and its uncertainty as well as information regarding model quality. The LPML method is tested and verified with the heat transport models STRIVE and VFLUX. We demonstrate that the LPML method can correctly reproduce a priori known fluxes and thermal conductivities and also show that the LPML method can estimate averaged and time-variable fluxes from periodic and nonperiodic temperature records. The LPML method allows for a fast computation of exchange fluxes as well as model and parameter uncertainties from many temperature sensors. Moreover, it can utilize a broad frequency spectrum beyond the diel signal commonly used for flux calculations.

Measuring the impedance frequency response of systems by means of frequency sweep electrical impedance spectroscopy (EIS) takes time. An alternative based on broadband signals enables the user to acquire simultaneous impedance response data collection. This is directly reflected in a short measuring time compared to the frequency sweep approach. As a result of this increase in the measuring speed, the accuracy of the impedance spectrum is compromised. The aim of this paper is to study how the choice of the broadband signal can contribute to mitigate this accuracy loss. A review of the major advantages and pitfalls of four different periodic broadband excitations suitable to be used in EIS applications is presented. Their influence on the instrumentation and impedance spectrum accuracy is analyzed. Additionally, the signal processing tools to objectively evaluate the quality of the impedance spectrum are described. In view of the experimental results reported, the impedance spectrum signal-to-noise ratio (SNRZ) obtained with multisine or discrete interval binary sequence signals is about 20–30 dB more accurate than maximum length binary sequence or chirp signals.

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