*J. Appl. Cryst.* (1999) **32**, 378-379

Pp. ix + 250 (CD-ROM included). New York: Plenum Press, 1998. Price: US $72.50. ISBN 0-306-45936-1.

Because of significant improvements in instrument optics, electron sources, and detection systems, high-resolution electron microscopy has become an increasingly powerful tool for the study of microcrystalline materials. Theoretical descriptions of image production, including the transfer function of the objective lens and the multiple scattering interactions as the electron beam traverses the specimen, have been available for at least a quarter century. Why, then, should there be yet another book on high-resolution electron microscopy, a subject that has been already treated in many sophisticated monographs? The answer is implicit in the book's title.

This book, written by an expert on computer simulations in electron microscopy, shows how the greatly expanded and cheap computer power available nowadays can be used effectively for the interpretation of electron microscope experiments. It discusses how computational methods are optimally designed, a practical approach not encountered in many other texts. Several programs written by the author (*e.g.* the fast Fourier transform) are included in the text and a number of others commonly encountered in simulations are conveniently included in a compact disc to be used on a Macintosh, or PC with Windows 95 or NT. C source code is also provided for Unix-based systems. Although various possible roles of computers in modern electron microscopy are mentioned in the short introductory first chapter, the book is primarily concerned with applications to image simulation.

The second chapter is a brief introduction to the electron microscope as an optical instrument. While much of the discussion treats the conventional transmission electron microscope (CTEM), the author demonstrates quite effectively how the optics of bright-field and dark-field scanning transmission electron microscopes (STEM) are closely related to the CTEM *via* a principle known as reciprocity. Obviously, a major component of the microscope is its objective lens. After a discussion of the relativistic electron wavelength and its dependence on electron accelerating voltage, the spherical aberration of the objective lens and its partial correction by focal changes are encountered. In the third chapter, idealized electron scattering by a weak phase object is introduced to expand the discussion of the objective lens transfer function. Various optimized lens defocus conditions that allow the maximum bandpass of information at the same contrast sign are discussed, including the well known Scherzer focus. The effects of partial coherence or total incoherence of the electron source on the imaging experiment are then introduced in terms of this transfer function.

The very interesting fourth chapter deals with image simulation, particularly the pixel detail needed to visualize various specimen details but also the optimal sampling of the image for transformation to its diffraction pattern or *vice versa*. The concept of the Nyquist limit is introduced, but not specifically in the context of the Shannon sampling theorem. Practical aspects of carrying out discrete Fourier transforms, avoiding artifacts due to image wrap-around, are mentioned, as is the most efficient way to display diffraction patterns as their power spectra. Thin specimen images are then simulated in Chapter 5, again in terms of the weak phase object. The derivation of accurate electron scattering factors is then presented in great detail, including the need for an imaginary form factor for heavier atoms. Steps in the computation of bright-field phase-contrast images are then given with examples for single atoms and a thin crystalline object (silicon). Coherence effects on these images are then reintroduced.

Chapter 6 was of particular value to this reviewer since it discusses multiple-beam dynamical scattering and its influence on images. There are two approaches to modeling multiple beam scattering, the Bloch wave solution (usually in matrix form) and the multislice calculation. Although these methods are physically equivalent, the former is shown to be computationally much more costly than the latter so that the multislice method is most often employed nowadays. Various aspects of these calculations that can lead to error are introduced including the (noncommutative) properties of some operators. Advice for slicing the crystalline specimen into optimal thin layers is given as are tests for validity of the calculation (repeat of slightly different boundary conditions for consistency) and its convergence. The problem of aliasing and bandwith on convolution operations is mentioned. Experimental design for simulating defect-containing crystals is given (the notion of periodic continuation as a superlattice). The next chapter examines a number of crystalline examples. Not only are image simulations shown here but also the production of convergent-beam electron-diffraction patterns, the most reliable way of determining space-group symmetry in crystallography (although that aspect is not mentioned). Finally the problem of quantitative matching of simulated images to experiment is discussed, with several figures of merit recommended.

The final chapter is a user's guide to the programs included in the CD-ROM. One can carry out multislice calculations of dynamical scattering and then simulate images at various degrees of beam coherence. STEM simulations are also included as is the possibility for computing convergent-beam diffraction patterns. Appendices discuss the `shareware' included on the CD for plotting various functions such as the lens transfer function, a list of files on the CD-ROM, a nice demonstration of the central section theorem in diffraction, available sources of electron scattering factors and their parameterization for programs on the CD-ROM, bilinear interpolation and a program giving a perspective view of three dimensions.

In general, I have a very favorable impression of this book. Most of the material is presented reasonably well for someone who is already familiar with the field. (Indeed the preface suggests that the reader might have some previous familiarity with quantum mechanics, Fourier transforms and diffraction.) Again, the major recommendation for the volume is its very practical approach to computational problems, with a voice of experience pointing out where one can easily go astray. I do, however, have a few minor criticisms, even though the scientific presentation is generally first-rate. First, I think that the background section is somewhat uneven. There are some topics, including the Shannon sampling theorem, the resultant limits to transforming accurately to a diffraction pattern of a given resolution, and the issue of wrap-around effects, that could have been discussed in much greater detail, particularly since this book is devoted to image simulation. Certainly much of this information can be found in works cited in the excellent reference list, but it would be more efficient if it were included in this one volume. Since some X-ray crystallographers are becoming interested in high-resolution electron microscopy, it would have been helpful if the relationship between the back focal plane (where the diffraction pattern is found) and the image plane of a lens could have been stated more explicitly, even though the current presentation is not confusing to those already familiar with electron microscopy. Several images and diffraction patterns are poorly reproduced. Details of the convergent-beam patterns on p. 148, for example, are quite badly obscured, as is an illustration of the intensity distribution of an electron probe on p. 141, to name just two of several examples. On a nonscientific level, better editing would have tidied up occasionally appalling grammar and the far too abundant typographical errors. It needs more than a spell-checker to distinguish between `incite' and `insight'! None of the reservations mentioned, however, should obscure the great usefulness of this volume and the software provided with it. It should be on the shelf of any serious electron microscopist interested in the experimental study of crystalline objects at high resolution.

**Douglas L. Dorset**

*Electron Diffraction Department, Hauptman-Woodward Medical Research Institute
Buffalo
NY 14203
USA*

**Copyright © 1999 International Union of Crystallography**