Theoretical basis for position correction method for improving the energy resolution of cryogenic imaging detectors

In this paper, the theoretical basis for the position correction method has been developed. The theory of branching cascade processes is applied to the signal formation in an imaging detector and the formula for the energy resolution is derived. It is shown that the energy resolution of an imaging detector is determined by the fluctuations caused by spatial variations of the primary particle interaction point. It is also shown why the position correction method can improve the energy resolution of this type of detectors.