The characteristic functions of dynamic gauges, based on nuclear or atomic radiation, were developed. These gauges are applied to the examination of material whose properties may vary continuously with time. The approach presented takes into consideration contributions to the uncertainty and blurring from various effects, such as radiation scattering, gauge geometry, and the system’s time constant. The analysis is based on the concept of the line spread function obtained from the derivation of the response to a step change in the inspected property. The response and relative resolving functions were demonstrated for a rectangular change with a gamma-through transmission gauge. The procedure provides a systematic method of obtaining the optimal values for the design parameters of the radio gauge, such as radiation energy, source emission rate, detection efficiency, detector-sample distance, and measurement time. The time constant, for example, reveals a pronounced minimal value for large relative velocity. Due to the radiation scattering in the examined material, there is an advantage to large detector-material distance. The design values may differ considerably more for the dynamic gauge than for a static gauge, i.e., a gauge applied to samples whose properties do not vary during the measurement period.