  In conventional particle beam microscopy, knowledge of the beam current is
essential for accurate micrograph formation and sample milling. This generally
necessitates offline calibration of the instrument. In this work, we establish
that beam current can be estimated online, from the same secondary electron
count data that is used to form micrographs. Our methods depend on the recently
introduced time-resolved measurement concept, which combines multiple short
measurements at a single pixel and has previously been shown to partially
mitigate the effect of beam current variation on micrograph accuracy. We
analyze the problem of jointly estimating beam current and secondary electron
yield using the Cramer-Rao bound. Joint estimators operating at a single pixel
and estimators that exploit models for inter-pixel correlation and Markov beam
current variation are proposed and tested on synthetic microscopy data. Our
estimates of secondary electron yield that incorporate explicit beam current
estimation beat state-of-the-art methods, resulting in micrograph accuracy
nearly indistinguishable from what is obtained with perfect beam current
knowledge. Our novel beam current estimation could help improve milling
outcomes, prevent sample damage, and enable online instrument diagnostics.
