By Peter W. Hawkes, E. Kasper

ISBN-10: 0123333547

ISBN-13: 9780123333544

The 3 volumes within the ideas OF ELECTRON OPTICS sequence represent the first entire therapy of electron optics in over 40 years. whereas Volumes 1 and 2 are dedicated to geometrical optics, Volume 3 is worried with wave optics and results as a result of wave size. topics coated include:

Derivation of the legislation of electron propagation from SchrUdinger's equation

Image formation and the suggestion of resolution

The interplay among specimens and electrons

Image processing

Electron holography and interference

Coherence, brightness, and the spectral function

Together, those works contain a different and informative remedy of the topic. Volume 3, like its predecessors, will supply readers with either a textbook and a useful reference resource.

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Extra info for Principles of Electron Optics. Wave Optics

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A n d y are t a k e n outside t h e integral, 0 1246 58. 38) We have t o assume here t h a t g φ 0. T h e factor « t h a t we have included will b e useful later; here it is equal to unity. If we now examine t h e behaviour of this integral as ζ —> z , we see t h a t t h e factor h = ζ — z in t h e d e n o m i n a t o r causes huge b u t always i m a g i n a r y e x p o n e n t s , which m e a n s t h a t t h e whole exponential function is a n extremely rapidly oscillating factor. T h e contributions t o t h e integral cancel, unless χ = x /g a n d y = y /gp- T h e a p p r o x i m a t i o n p Q p 0 0 p 0 C(x ,y ) 0 C(x/g y/g ) 0 pi p is therefore justified a n d this factor can t h e n b e t a k e n outside t h e integral.

Curve (A) has t h e above p r o p e r t y a n d r u n s from a fixed s t a r t i n g point Pi t o a fixed t e r m i n a l point P2. Line (B) is a n a r b i t r a r y s m o o t h curve joining t h e same points. 3 THE VARIATIONAL PRINCIPLE a n d satisfying S ( P i , P i ) = 0. 8) a n d using dr = ΪΑ ds o n (A) a n d dr = tj5 ds on ( P ) , we o b t a i n (A) P (B) P 2 S = 2 j\gt · tAds — eA · dr) = j(gt Pi ·i# — · dr) Pi F r o m t h e initial a s s u m p t i o n , we have t = i^? fc-t^ = 1 on line ( A ) , whereas t-ts— cos a Β < 1 on line (B).

31a) 1244 58. 32) T h i s formula is exactly valid within t h e p a r a x i a l a p p r o x i m a t i o n . 33) 2 y o 0 T h i s formula d e m o n s t r a t e s a n i m p o r t a n t difference between t h e wave-optical t h e o r y a n d t h e geometrical approximation. In t h e l a t t e r we have t o choose x(z) a n d y(z) as rays passing t h r o u g h t h e point ( x , y , z ) a n d hence x — χ = ^ ( z — z ), y — y = yj,(^ — z ) . We t h e n o b t a i n t h e well-behaved result 0 0 0 0 0 0 0 S=\go(z-z )(x' +y' ) 2 0 2 0 0 In t h e wave-optical theory, however, t h e coordinate pairs (#, y) a n d ( x , y ) are i n d e p e n d e n t a n d 5 m a y hence become singular &s ζ — z vanishes.

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Principles of Electron Optics. Wave Optics by Peter W. Hawkes, E. Kasper


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