Weight functions for biases in atomic frequency standards

Many perturbations that affect atomic frequency standards vary during the period of measurement. To include this time variation, we introduce 3 time-dependent weight functions built from the solution of the unperturbed equations of motion of a 2-level system. The integral of the time-dependent part of a perturbation with a weight function gives the associated first-order change in transition probability. Biases are then found easily. The same weight function may be used for different perturbations, thus unifying the derivation of their associated biases. We give several examples of the use of weight functions.