Noise in position measurement by centroid calculation

The position of a particle trajectory in a gaseous (or semiconductor) detector can be measured by calculating the centroid of the induced charge on the cathode plane. The charge amplifiers attached to each cathode strip introduce noise which is added to the signal. This noise broadens the position resolution line. Our article gives an analytical tool to estimate the resolution broadening due to the noise per strip and the number of strips involved in the centroid calculation. It is shown that the position resolution increases faster than the square root of the number of strips involved. We also consider the consequence of added interstrip capacitors, intended to diminish the differential nonlinearity. It is shown that the position error increases slower than linearly with the interstrip capacities, due to the cancellation of correlated noise. The estimation we give, can be applied to calculations of position broadening other than the centroid finding.