Quantitative electron phase imaging with high sensitivity and an unlimited field of view.

As it passes through a sample, an electron beam scatters, producing an exit wavefront rich in information. A range of material properties, from electric and magnetic field strengths to specimen thickness, strain maps and mean inner potentials, can be extrapolated from its phase and mapped at the nanoscale. Unfortunately, the phase signal is not straightforward to obtain. It is most commonly measured using off-axis electron holography, but this is experimentally challenging, places constraints on the sample and has a limited field of view. Here we report an alternative method that avoids these limitations and is easily implemented on an unmodified transmission electron microscope (TEM) operating in the familiar selected area diffraction mode. We use ptychography, an imaging technique popular amongst the X-ray microscopy community; recent advances in reconstruction algorithms now reveal its potential as a tool for highly sensitive, quantitative electron phase imaging.

Optimization and stability of the contrast transfer function in aberration-corrected electron microscopy.

The Contrast Transfer Function (CTF) describes the manner in which the electron microscope modifies the object exit wave function as a result of objective lens aberrations. For optimum resolution in C3-corrected microscopes it is well established that a small negative value of C3, offset by positive values of C5 and defocus C1 results in the most optimal instrument resolution, and optimization of the CTF has been the subject of several studies. Here we describe a simple design procedure for the CTF that results in a most even transfer of information below the resolution limit. We address not only the resolution of the instrument, but also the stability of the CTF in the presence of small disturbances in C1 and C3. We show that resolution can be traded for stability in a rational and transparent fashion. These topics are discussed quantitatively for both weak-phase and strong-phase (or amplitude) objects. The results apply equally to instruments at high electron energy (TEM) and at very low electron energy (LEEM), as the basic optical properties of the imaging lenses are essentially identical.

Intrinsic instability of aberration-corrected electron microscopes.

Aberration-corrected microscopes with subatomic resolution will impact broad areas of science and technology. However, the experimentally observed lifetime of the corrected state is just a few minutes. Here we show that the corrected state is intrinsically unstable; the higher its quality, the more unstable it is. Analyzing the contrast transfer function near optimum correction, we define an "instability budget" which allows a rational trade-off between resolution and stability. Unless control systems are developed to overcome these challenges, intrinsic instability poses a fundamental limit to the resolution practically achievable in the electron microscope.

A Contrast Transfer Function approach for image calculations in standard and aberration-corrected LEEM and PEEM.

We introduce an extended Contrast Transfer Function (CTF) approach for the calculation of image formation in low energy electron microscopy (LEEM) and photo electron emission microscopy (PEEM). This approach considers aberrations up to fifth order, appropriate for image formation in state-of-the-art aberration-corrected LEEM and PEEM. We derive Scherzer defocus values for both weak and strong phase objects, as well as for pure amplitude objects, in non-aberration-corrected and aberration-corrected LEEM. Using the extended CTF formalism, we calculate contrast and resolution of one-dimensional and two-dimensional pure phase, pure amplitude, and mixed phase and amplitude objects. PEEM imaging is treated by adapting this approach to the case of incoherent imaging. Based on these calculations, we show that the ultimate resolution in aberration-corrected LEEM is about 0.5 nm, and in aberration-corrected PEEM about 3.5 nm. The aperture sizes required to achieve these ultimate resolutions are precisely determined with the CTF method. The formalism discussed here is also relevant to imaging with high resolution transmission electron microscopy.

Aberrations of the cathode objective lens up to fifth order.

In this paper we discuss a topic that was close to Prof. Gertrude Rempfer s interests for many years. On this occasion of her 100th birthday, we remember and honor Gertrude for her many outstanding contributions, and for the inspiring example that she set. We derive theoretical expressions for the aberration coefficients of the uniform electrostatic field up to 5th order and compare these with raytracing calculations for the cathode lens used in Low Energy Electron Microscopy and Photo Electron Emission Microscopy experiments. These higher order aberration coefficients are of interest for aberration corrected experiments in which chromatic (C(c)) and spherical (C3) aberrations of the microscope are set to zero. The theoretical predictions are in good agreement with the results of raytracing. Calculations of image resolution using the Contrast Transfer Function method show that sub-nanometer resolution is achievable in an aberration corrected LEEM system.