From Gauging Accuracy of Quantity Estimates to Gauging Accuracy and Resolution of Measuring Physical Fields

For a numerical physical quantity υ, because of the measurement imprecision, the measurement result υ is, in general, different from the actual value υ of this quantity. Depending on what we know about the measurement uncertainty δυ def = υ - υ, we can use different techniques for dealing with this imprecision: probabilistic, interval, etc. When we measure the values υ(x) of physical fields at different locations x (and/or different moments of time), then, in addition to the same measurement uncertainty, we also encounter another type of localization uncertainty: that the measured value may come not only from the desired location x, but also from the nearby locations. In this paper, we discuss how to handle this additional uncertainty.