Generalization of the variance-covariance method for microdosimetric measurements. I. Basic equations and estimation formulae for constant and time-varying fields.

The variance method of microdosimetric measurements and its extension, the variance-covariance method, permit the determination of an essential parameter of radiation quality, the dose mean event size, y(d). The methods have--among other advantages--the feature that they permit measurements for smaller simulated sites than the conventional single-event technique. It is, therefore, desirable to employ them also for the determination of further moments of the distribution of y. The formulae for the first three moments are here derived both for the case of constant dose rate and of fluctuating dose rates. A second article will use the same mathematical approach to deduce formulae that remain valid even if there are slow changes of the ratio of dose rates in the two detectors for the variance-covariance method. A third article will explore--in terms of microdosimetric data--the applicability of the formulae.