Low-Dosage Maximum-A-Posteriori Focusing and Stigmation

Radiation damage is often an issue during high-resolution imaging, making low-dose focusing and stigmation essential, in particular when no part of the sample can be "sacrificed" for this. An example is serial block-face electron microscopy, where the imaging resolution must be kept optimal during automated acquisition that can last months. Here, we present an algorithm, which we call "Maximum-A-Posteriori Focusing and Stigmation (MAPFoSt)," that was designed to make optimal use of the available signal. We show that MAPFoSt outperforms the built-in focusing algorithm of a commercial scanning electron microscope even at a tenfold reduced total dose. MAPFoSt estimates multiple aberration modes (focus and the two astigmatism coefficients) using just two test images taken at different focus settings. Using an incident electron dose density of 2,500 electrons/pixel and a signal-to-noise ratio of about one, all three coefficients could be estimated to within <7% of the depth of focus, using 19 detected secondary electrons per pixel. A generalization to higher-order aberrations and to other forms of imaging in both two and three dimensions appears possible.