By Peter W. Hawkes, E. Kasper
The 3 volumes within the ideas OF ELECTRON OPTICS sequence represent the first accomplished remedy 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 because of wave size. topics coated include:
Derivation of the legislation of electron propagation from SchrUdinger's equation
Image formation and the inspiration of resolution
The interplay among specimens and electrons
Image processing
Electron holography and interference
Coherence, brightness, and the spectral function
Together, those works include a distinct and informative remedy of the topic. Volume 3, like its predecessors, will offer readers with either a textbook and a useful reference resource.
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Extra resources for Principles of Electron Optics. Wave Optics
Sample text
T h e electrostatic p o t e n t i a l t h e n consists of a large a n d c o n s t a n t acceleration t e r m U a n d a small a t o m i c c o n t r i b u t i o n 1222 56. THE RELATIVISTIC WAVE EQUATION V(r). 12) w i t h o u t loss of generality. 16) λ d e n o t i n g t h e wavelength, g t h e kinetic m o m e n t u m a n d h P l a n c k ' s con s t a n t . 16) is again t h e de Broglie relation. T h e a t o m i c p o t e n t i a l V{r) h a s a short spatial r a n g e a n d is quite of t e n very weak, which m e a n s t h a t | V ( r ) | Forming t h e vector p r o d u c t w i t h t , we find t χ c u r l ( ^ t ) + eB χ t = 0 E x p a n s i o n of t h e curl of a p r o d u c t gives curl(yt) = — t χ g r a d # + g c u r l t a n d so t χ cnn(gt) = g r a d g — ( t · g r a d g)t + gt χ c u r l t T h e rules of vector analysis tells u s t h a t t χ c u r l t = i g r a d ( t · t ) - t V t = -t Vt since t = 1. P u t t i n g all this together, we o b t a i n 2 g r a d g - (t - g r a d g ) t - gt Λ/t = g r a d g - t · V(#£) = - e J B χ t Next we observe t h a t t = dr/ds for t h e t a n g e n t t o t h e curve a n d t h a t £. 18) In t h e wave e q u a t i o n itself, t h e t e r m in V(r) m u s t b e r e t a i n e d b u t , b e c a u s e | V |
