Examining the Geometric Mean Method for the Extraction of Spatial Resolution

The spatial resolution of a detector, using a reference detector telecscope, can be measured applying the geometric mean method, with tracks reconstructed from hits of all the detectors, including ($\sigma_\mathrm{in}$) and excluding ($\sigma_\mathrm{ex}$) the hit from the detector under study. The geometric mean of the two measured resolution values ($\sigma=\sqrt{\sigma_\mathrm{ex}\sigma_\mathrm{in}}$), is proposed to provide a more accurate estimate of the intrinsic detector resolution. This method has been tested using a Monte Carlo algorithm and is proven to give accurate results, independently of the distance between the detectors used for the track fitting. The method does not give meaningful results if all the detectors do not carry the same characteristics.