In volume fluorescence microscopy, refractive index matching is essential to minimize aberrations. There are, however, common imaging scenarios where a refractive index mismatch (RIM) between immersion and a sample medium cannot be avoided. This RIM leads to an axial deformation in the acquired image data. Over the years, different axial scaling factors have been proposed to correct for this deformation. While some reports have suggested a depth-dependent axial deformation, so far none of the scaling theories has accounted for a depth-dependent, non-linear scaling. Here, we derive an analytical theory based on determining the leading constructive interference band in the objective lens pupil under RIM. We then use this to calculate a depth-dependent re-scaling factor as a function of the numerical aperture (NA), the refractive indices n₁ and n₂, and the wavelength λ. We compare our theoretical results with wave-optics calculations and experimental results obtained using a measurement scheme for different values of NA and RIM. As a benchmark, we recorded multiple datasets in different RIM conditions, and corrected these using our depth-dependent axial scaling theory. Finally, we present an online web applet that visualizes the depth-dependent axial re-scaling for specific optical setups. In addition, we provide software that will help microscopists to correctly re-scale the axial dimension in their imaging data when working under RIM.

We designed and built a compact bi-axial electron beam separator. This separator is an indispensable electron optical element in the development of MEMS-mirror-based miniaturized concepts for quantum electron microscopy (QEM) and aberration-corrected low-voltage scanning electron microscopy (AC-SEM). The separator provides the essential cycling of the electron beam between the two parallel optical axes that are part of these systems. This requires crossed electric and magnetic fields perpendicular to the beam path, as can be found in Wien-filter type beam separators. In our miniaturized QEM or AC-SEM concepts, the parallel axes are separated by only 1 mm. Conventional Wien-filter-based beam separator concepts rely on in-plane electric and magnetic multipole electrode configurations that are larger than the restricted available volume in these miniaturized QEM/AC-SEM systems. Our compact beam separator design introduces three stacked dipole electrode layers, which enables simultaneous beam separation at two parallel axes that are in close proximity. The outer layer electrodes maintain an electric field for which the direction on the one axis is opposed to that on the other axis. The middle layer generates a perpendicularly oriented magnetic field that spans both axes. The total field configuration enables the deflection of the beam on one axis and simultaneously provides a straight passage on the other axis. The deflection strength and distortion fields of the beam separator are experimentally obtained with a 2 keV electron beam energy. The results validate the use of the beam separator for electron energies up to 5 keV and deflection angles up to 100 mrad.