By Earl J. Kirkland

Preface to moment version a number of new themes were additional, a few small error were corrected and a few new references were further during this version. New subject matters comprise aberration corrected tools, scanning confocal mode of operations, Bloch wave eigenvalue tools and parallel computing innovations. The ?rst version - cluded a CD with computing device courses, which isn't integrated during this version. - stead the linked courses should be on hand on an linked site (currently people.ccmr.cornell.edu/˜kirkland,but could flow as time is going on). I desire to thank Mick Thomas for getting ready the specimen used to checklist the picture in Fig.5.26 and to thank Stephen P. Meisburger for suggesting an enticing organic specimen to exploit in Fig.7.24. back, I make an apology prematurely for leaving out a few undoubtedlyoutstanding r- erences. I additionally express regret for the as but undiscovered mistakes that stay within the textual content. Earl J. Kirkland, December 2009 Preface to First version snapshot simulation has develop into a typical device in HREM (High answer El- tron Microscopy) lately. although, the literature at the topic is scattered between many various journals and convention complaints that experience happened within the final or 3 many years. it truly is dif?cult for novices to start during this ?eld.

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**Example text**

An image simulation may require thousands or millions of operations on each pixel. Therefore during image simulation each pixel should be represented as a floating point number with much more than 8 bits per pixel. Most computer hardware is equipped to handle 32 bit single precision (typically there is one sign bit, 8 exponent bits and 23 mantissa bits) and 64 bit double precision floating point arithmetic. Single precision (32 bits) gives about six decimal digits of accuracy per pixel and is usually sufficient for most image calculations.

If the coherence length is much bigger than the resolution element then the imaging process will be essentially coherent. , the size of the objective aperture). 42) In between these two extremes the image is partially coherent. If the image is coherent then the amplitudes 'I/J of the scattered electrons add and if the image is incoherent then the intensities of the scattered electrons 1'l/J12 add. The final image recording process is only sensitive to the intensity of the electrons and not their amplitudes.

The specific definition of 46 CHAPTER 4. SAMPLING AND THE FAST FOURIER TRANSFORM the Fourier transform FT and its inverse FT- 1 that will be used here is: FT(J(x)] = F(k) = L exp (27rik. 6) X,y FT-l[F(k)] = f(x) = N 1Ny X L exp (-27rik. "k y where x = (x,y) and k = (kx,k y ). The inverse Fourier transform can be written as the complex conjugate of the forward transform of the complex conjugate of F(k). 8) It is only necessary to program one or the other transform (forward or inverse) and the other can be obtained with suitable complex conjugation and scaling.