Peter Hawkes

Science of microscopy

Imaging With Electrons.- Atomic Resolution Transmission Electron Microscopy.- Scanning Transmission Electron Microscopy.- Scanning Electron Microscopy.- Analytical Electron Microscopy.- High-Speed Electron Microscopy.- In Situ Transmission Electron Microscopy.- Cryoelectron Tomography (CET).- LEEM and SPLEEM.- Photoemission Electron Microscopy (PEEM).- Aberration Correction.- Imaging With Photons.- Two-Photon Excitation Fluorescence Microscopy.- Nanoscale Resolution in Far-Field Fluorescence Microscopy.- Principles and Applications of Zone Plate X-Ray Microscopes.- Near-Field Scanning Probes.- Scanning Probe Microscopy in Materials Science.- Scanning Tunneling Microscopy in Surface Science.- Atomic Force Microscopy in the Life Sciences.- Low-Temperature Scanning Tunneling Microscopy.- Holographic And Lensless Modes.- Electron Holography.- Diffractive (Lensless) Imaging.- The Notion of Resolution.

The Electron Microscope as a Structure Projector

The intuitive understanding of the process of three-dimensional reconstruction is based on a number of assumptions, which are easily made unconsciously; the most crucial is the belief that what is detected is some kind of projection through the structure. This “projection” need not necessarily be a (weighted) sum or integral through the structure of some physical property of the latter; in principle, a mono-tonically varying function would be acceptable, although solving the corresponding inverse problem might not be easy. In practice, however, the usual interpretation of “projection” is overwhelmingly adopted, and it was for this definition that Radon (1917) first proposed a solution. In the case of light, shone through a translucent structure of varying opacity, a three-dimensional transparency as it were, the validity of this projection assumption seems too obvious to need discussion. We know enough about the behavior of x-rays in matter to establish the conditions in which it is valid in radiography. In this chapter, we enquire whether it is valid in electron microscopy, where intuition might well lead us to suspect that it is not. Electron—specimen interactions are very different from those encountered in x-ray tomography, the specimens are themselves very different in nature, creating phase rather than amplitude contrast, and an optical system is needed to transform the information about the specimen that the electrons have acquired into a visible image. If the electrons encounter more than one structural feature in their passage through the specimen, the overall effect is far from easy to guess, whereas in the case of light shone through a transparent structure, it is precisely the variety of such overlaps or superpositions that we use to effect the reconstruction. If intuition were our only guide, we might easily doubt whether three-dimensional reconstruction from electron micrographs is possible: there is no useful projection approximation for the balls on a pin-table! Why then has it been so successful? To understand this, we must examine in detail the nature of the interactions between the electrons and the specimen and the characteristics of the image-forming process in the electron microscope. Does the information about the specimen imprinted on the electron beam as it emerges from the latter represent a projection through the structure? How faithfully is this information conveyed to the recorded image? These are the questions that we shall be exploring in the following sections.

The correction of electron lens aberrations.

The progress of electron lens aberration correction from about 1990 onwards is chronicled. Reasonably complete lists of publications on this and related topics are appended. A present for Max Haider and Ondrej Krivanek in the year of their 65th birthdays. By a happy coincidence, this review was completed in the year that both Max Haider and Ondrej Krivanek reached the age of 65. It is a pleasure to dedicate it to the two leading actors in the saga of aberration corrector design and construction. They would both wish to associate their colleagues with such a tribute but it is the names of Haider and Krivanek (not forgetting Joachim Zach) that will remain in the annals of electron optics, next to that of Harald Rose. I am proud to know that both regard me as a friend as well as a colleague.

Superconductivity and electron microscopy.

In this review article, two aspects of the role of superconductivity in electron microscopy are examined: (i) the development of superconducting devices (mainly lenses) and their incorporation in electron microscopes; (ii) the development of electron microscope techniques for studying fundamental and technological problems associated with superconductivity.

On the optical properties of magnetic lenses with fields of the form B(z) z-n, n = 2, 3, 4

Summary The trajectories of electrons in magnetic lenses with field distributions in the form of an inverse power law can be expressed in terms of Bessel functions of fractional order. It is shown that the focal lengths and spherical and chromatic aberration coefficients can be evaluated explicitly. The results confirm and elucidate numerical results published by A. V. Crewe [1].

Diffract-and-destroy: can X-ray lasers "solve" the radiation damage problem?

From the beginning, radiation damage has always appeared to set the ultimate limit to resolution in biological imaging. Many ingeneous techniques have been developed to circumvent this barrier, the most successful of which take advantage of redundancy, either crystallographic or artificial (as in cryo-electron microscopy). For the imaging of individual biological structures, a recent survey of measurements of dose against resolution [1] suggests that dose varies as the inverse fourth power of resolution for X-ray tomography, so that the damage penalty for small improvements in resolution is severe indeed. One requires statistical significance between adjacent resolution-limiting pixels, but must remain below the damage threshold for that resolution. Spot-fading experiments from protein crystals provide much of the most reliable measurements of dose against resolution, with high order beams fading first. At a somewhat lower level of resolution, remarkable advances have recently been made using visible light beyond the diffraction limit (despite bleaching effects), and probe microscopies, where damage is harder to quantify, continue to advance. There is now accumulating evidence that this nexus between resolution and dose may be broken by exploiting an entirely new parameter—the duration of the imaging pulse [2]. In a series of remarkable experiments, scientists at the Flash Free-electron Laser facility at Hamburg’s DESY lab have published (or submitted) papers showing that, at least for soft X-rays, a single femtosecond pulse of extremely intense radiation produces a scattering pattern from apparently undamaged sample, before completely destroying it. The first of these papers [3] used a single 25 fs pulse of 32 nm wavelength radiation to obtain a diffraction pattern, apparently from undamaged material, before vaporizing the sample at 60 kK. (The pulse contained 10 photons.) More recently, by analogy with sub-wavelength resolution measurements using crystals, it has been shown [4] that damage in the periodically averaged structure is absent at the 0.3 nm level when using a 25 fs pulse of 32 nm X-rays. Since then the wavelength has been reduced to 7 nm and the pulse duration to 8 fs, and these new results (which again show no evidence of damage) will soon appear in the literature. The patterns are inverted to two-dimensional images using new iterative solutions to the phase problem (recent breakthroughs in this fascinating field are reviewed elsewhere [5]). A further reduction to 3 nm wavelength is expected soon. X-ray lasers are under construction at many sites around the world (European XFEL, LCLS at Stanford), and these will move steadily into the hard X-ray, femtosecond range over the next decade.

Computer-aided design in electron optics

Abstract The computer is used to help designers of electron-optical devices to find optimum arrangements by two different strategies. By accelerating the calculation of the properties of a class of possible instruments, a wide choice of possible designs is made available. Alternatively, direct methods can now provide optimum designs starting from a set of physical prerequisites. Each of these procedures is described in some detail.

The evolution of electron image processing and its potential debt to image algebra

The types of digital electron microscope image processing of greatest interest are not the same in the three major types of electron microscope. In the TEM, electron tomography and crystallography, particularly for 3‐D reconstruction of biological specimens, and procedures that enable the physicist to establish the atomic structure, and especially defects in crystalline material, from one or more of a host of different records — bright‐ and dark‐field images, traditional or convergent‐beam diffraction patterns, energy‐loss spectra, holograms — have attracted the greatest attention. In the SEM, image enhancement and image analysis (counting and measurement of geometrical or compositional features of the image) have always been important and the earliest attempts to process SEM images were in these fields. In the STEM, it is the possibility of using all the information in the far‐field diffraction pattern from every element of the object that has provoked the most exciting and original ideas.

The Finite-Element Method (FEM)

The chapter focuses on the finite-element method (FEM). FEM came into practical use with the development of modern computers and has found widespread application in mechanical and electrical engineering. Typical examples are problems in fluid dynamics and aerodynamics, elasticity, heat conduction, and magnetic field computations for electric machines. An interesting application of the FEM to magnetic lenses is the calculation of magnetic circuits made of anisotropic material. In this case the reluctance v(β) is to be replaced by a symmetric tensor. Its components depend directly on the position r as a consequence of the variable crystallographic orientation in the material and indirectly due to saturation effects. Such calculations are extremely complicated; nevertheless, magnetic circuits with anisotropic material can be advantageous.

Should it be ‘picoscopy’?

Here are a few books for John Spence to read (or avoid) in the aftermath of his birthday festivities, preceded by some partially coherent reflections.