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