H. Rose

Electron microscopy image enhanced

One of the biggest obstacles in improving the resolution of the electron microscope has always been the blurring of the image caused by lens aberrations. Here we report a solution to this problem for a medium-voltage electron microscope which gives a stunning enhancement of image quality.

Hamiltonian magnetic optics

Abstract Starting from Hamiltons principle, the imaging properties of charged particle beams in arbitrary static magnetic fields are outlined. The magnetic scalar potential is expressed as a series of multipoles about an arbitrary space curve which need not necessarily coincide with a trajectory of the beam. Appropriate power series expansions are given for the components of the magnetic vector potential where the expansion coefficients are related to the complex curvature of the axis and the strengths of the multipole components of the magnetic scalar potential. The general laws which govern the propagation of the charged particles are discussed by means of Hamiltons characteristic functions. It is shown that the Poisson and the Lagrange brackets are equivalent representations of the symplectic condition. The Poincare invariant is used for elucidating some characteristic imaging properties of magnetic fields. A perturbation eikonal is introduced which allows a systematic and simultaneous calculation of the geometrical and chromatic aberrations to any order. The method has the advantage that it reveals at the very beginning all interrelations between the aberration coefficients. The iteration procedure starts from the paraxial rays which are supposed to be known. The algorithm is especially suited for numerical calculation of the higher-order aberrations.

Time-dependent perturbation formalism for calculating the aberrations of systems with large ray gradients

Abstract A time-dependent perturbation formalism is outlined which enables the calculation of aberrations for systems with large gradients of the particle trajectories in a consistent way. The position of a particle is referred to that of an axial reference particle making the axial coordinate a small quantity. The initial conditions of the trajectory are incorporated by transforming the Lorentz equations in a set of coupled inhomogeneous integral equations for the three positional coordinates of the particle. The integral equations are solved by an iteration procedure which starts from the paraxial approximation. The number of required iteration steps is equal to the rank of the aberration minus one. As an example, the primary and secondary axial aberrations of mirrors are investigated in detail.

Optimum rotationally symmetric detector configurations for phase-contrast imaging in scanning transmission electron microscopy

A configured STEM detector yields simultaneously several signals which can be arbitrarily combined. We have calculated the optimum annular subdivision of the detector which maximizes the signal-to-noise ratio in the image of weak scatterers. The optimum detector doubles the signal-to-noise ratio as compared to the conventional STEM detector, increases the resolving power of the instrument and enhances the contrast of strong scatterers located on a supporting foil.

Optimum bright-field imaging of strong scatterers in CTEM and STEM

Abstract The quality of bright-field images in the presence of strong scatterers has been investigated for both the conventional (CTEM) and the scanning transmission electron microscope (STEM). The imaging parameters are determined which yield optimum contrast and maximum signal-to-noise ratio (S/N) in the special cases of low and high irradiation doses. The calculations demonstrate that the phase of the complex scattering amplitude influences only the optimum illumination cone angle in CTEM and the optimum detector angles in STEM respectively. In the latter instrument object details are optimally visualized if the diameter of the scanning spot is adjusted to approximately half the size of the details. Contour plots of both contrast and S/N are presented to survey their dependence on the defocus and the illumination cone angle in CTEM and the detector angles in STEM respectively.

Defocus determination in the STEM by phase contrast methods

Abstract The imaging parameters of the scanning transmission electron microscope (STEM), in particular the defocus, can be obtained from a focal series of phase contrast images of an amorphous carbon film. By using a tilted specimen the phase contrast transfer characteristic (PCTC) and the mean-square contrast have been determined for a specific instrument. The PCTC contains all the information about the defocus dependence of the phase contrast. The results agree well with those obtained from a focal series of a non-tilted object and with the theoretical predictions.

A compact aberration-free imaging filter with inside energy selection

Abstract An aberration-free imaging energy filter is proposed, which consists of three deflection magnets and two additional magnetic quadrupole elements. The deflection system can be considered as a special compact four-element Ω filter where the first and the fourth sector magnet coincide. Since the entire deflection system is nondispersive, energy selection is performed at the midplane within the filter. Owing to the imposed symmetry conditions, all second-order (geometrical) aberrations vanish outside of the deflection system.

Fast charge-simulation procedure for planar and simple three-dimensional electrostatic fields

Abstract A charge-simulation method for two-dimensional and simple three-dimensional electrostatic systems is outlined. The charge-simulation method allows a rapid calculation of the potential by superimposing the potentials of line and sheet charges, slit apertures and arrays of line charges, since the potential of each of these charge elements can be expressed in analytical form. Accordingly, the electric field is also given as a sum of analytical expressions. The trajectories of electrons moving within these fields can be calculated most accurately by using an appropriate Runge-Kutta method. The power of the proposed methode is demonstrated for two special arrangements.

Fast charge-simulation procedure for determining the electron-optical properties of electrostatic systems

Abstract A charge-simulation method is outlined which allows a rapid calculation of the potential distribution of two- and some three-dimensional electrostatic systems. The potential of the true charge distribution is approximated by that of line and sheet charges, slit apertures and arrays of line charges. The trajectories of electrons moving in the resulting fields are calculated by using the Runge-Kutta method. Contrary to the well known finite element and finite difference methods, the charge-simulation method allows a fast and precise calculation of the electron trajectories. The power of the proposed method is demonstrated for two special arrangements.

Optimization of imaging energy filters for high-resolution analytical electron microscopy

Abstract A survey is given of recent progress made in the design of high-performance imaging energy filters for transmission electron microscopes. For accelerating voltages smaller than about 80 kV both the Zeiss-Castaing filter and the retarding Wien filter are well suited for high-resolution analytical electron microscopy. At higher voltages purely magnetic imaging filters are mandatory. Fully and partially corrected filters of the Ω and α type are discussed which allow energy selection with small energy windows without affecting the image formed by the transmitted electrons.