Download e-book for iPad: Diffraction Physics (North-Holland Personal Library) by J. M. Cowley

By J. M. Cowley

ISBN-10: 0080530397

ISBN-13: 9780080530390

ISBN-10: 0444822186

ISBN-13: 9780444822185

The 1st variation of this hugely profitable booklet seemed in 1975 and developed from lecture notes for periods in actual optics, diffraction physics and electron microscopy given to complicated undergraduate and graduate scholars. The e-book bargains with electron diffraction and diffraction from disordered or imperfect crystals and hired an process utilizing the Fourier rework from the start rather than as an extension of a Fourier sequence treatment.This 3rd revised variation is a significantly rewritten and up to date model which now contains all vital advancements that have taken position in recent times.

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M a k i n g use of the s t a n d a r d integral form exp {-a2x 2 } cos bx dx = --oo /I;1/2 a exp { -b 2 / 4a 2 }, (28 ) we obtain ~/(x) = exp{-ikR} so that the i n t e n s i t y o b s e r v a t i o n is l(x) = e x p { i ~ R X / a 2} cos(2Kx/a), distribution cos 2 (2xx/a) . on the plane (29) of (30) This is i n d e p e n d e n t of R. Hence on any plane of o b s e r v a t i o n at any d i s t a n c e from the object, the i n t e n s i t y d i s t r i b u t i o n will be e x a c t l y the same as at the exit face of the object.

See Fig. 7. 22 A / ' I I ' " / l I/a Fig. 7. The diffraction pattern from a row of circular holes equally spaced in an opaque screen. The widths of the lines are made to suggest their intensities. 3 F O U R I E R TRANSFORMS AND DIFFRACTION: EXAMPLES 47 and the Fourier t r a n s f o r m with respect to y is unity. Hence the Fourier t r a n s f o r m in x and y is a set of straight lines parallel to the v axis and equally spaced at intervals of a -I in the u direction. This distribution will be m o d u l a t e d by m u l t i p l y i n g by the Fourier t r a n s f o r m of O(x,y), namely (ru42/2) J1 (nAU) / (nAU) , where A is the diameter of the holes and U = (u2+v2) I/2 .

28) (60) to obtain exp {-lr2u 2/a 2 }. (61) Hence, if f(x) is a G a u s s i a n of h a l f - w i d t h a -I then its F o u r i e r t r a n s f o r m is also a G a u s s i a n h a v i n g h a l f - w i d t h a/K. e. the = (~/ab) inverse exp {-lr2u 2 (a2+b 2) / (a2b2) }, Fourier transform = (/1;/(a2+b 2) )1/2 e x p { _ (a2b2/(a2+b 2) )x2}, the c o n v o l u t i o n of two G a u s s i a n s is again a Gaussian. 17. FOURIER TRANSFORMS Row circular of AND CONVOLUTIONS CH. 2 holes The e x t e n s i o n to two d i m e n s i o n s a l l o w s the a b o v e r e s u l t s to be a p p l i e d to c a l c u l a t e the d i f f r a c t i o n p a t t e r n s f r o m m a n y s i m p l e t w o - d i m e n s i o n a l d i s t r i b u t i o n s .

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Diffraction Physics (North-Holland Personal Library) by J. M. Cowley


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