Badania wpływu niedokładności równoległych torów pomiarowych na dokładność rekonstrukcji przewodności w tomografii elektrycznej

W pracy przedstawiono analizę wpływu oddziaływań addytywnych oraz multiplikatywnych w torze pomiaru napięć międzyelektrodowych na dokładność rekonstrukcji rozkładu przestrzennego przewodności w tomografii elektrycznej (TE). Przedstawiono ogólną zasadę konstruowania obrazu TE, metodę pomiarową realizującą równoległy pomiar napięć międzyelektrodowych oraz algorytm rekonstrukcji obrazu przewodności.

The influence analysis of additive and multiplicative interactions in measuring system of inter-electrode voltages on accuracy of reconstruction of conductivity spatial distribution in electrical tomography has been presented in this paper. The measurement method based on parallel controlling of interelectrode voltages was considered. It was referred to analogical research based on serial measurement method [3]. The errors of measuring apparatus were presented as sum of three basic components: random additive, systematic additive and systematic multiplicative. For quantitative comparison of particular errors influence on reconstruction errors the conversion factor was introduced. It was defined as square root of ratio of reconstruction variance errors. The results of investigations of conversion degree of instrumental errors in relation to errors of conductivity image obtained from relations (6) and (7) as well as using Mote Carlo method have been compared (Fig.1). The instrumental errors have bigger negative influence on reconstruction accuracy of elements conductivity in the internal area of considered object (lower numbers in figures). They are cause of results' retrogradation in this area. The influence of systematic additives and random errors is significantly bigger than systematic multiplicative. The derived relations can be applied for the requirement formulation in relation to accuracy requirements of measuring systems on the beginning of tomography system design process.