By J.M. Cowley

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

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**Example text**

2. G (u) = e x p {-Kiau} But, since from that, 89 + we n o t e - - 8(x that 89 Then - e x p {Kiau} = -2i s i n (~au). (27) G (u) it f o l l o w s = 8(x (27), as = {-2~iu} in e q u a t i o n F(u) = sin F (u), (38), (xau) / (xu) . 6. Straight edge The transmission function is q(x) [F(u)l I ! d q(x) g(x) = (-~ Fig. 2. Derivation of the Fourier transform of a slit function by consideration of its differential. for 38 FOURIER f(x) Using the = TRANSFORMS { 0 if X<0, 1 if x_>0. 5 = df(x)/dx g(x) Then AND C O N V O L U T I O N S CH.

Na sin(~dVau)/(TtNau). 16. the same as (57) or (58) . Gaussian function A G a u s s i a n f u n c t i o n rarely occurs in p r a c t i c e as the t r a n s m i s s i o n f u n c t i o n of an object but is f r e q u e n t l y used as an a p p r o x i m a t i o n , to "round-off" a discontinuity, or to achieve a s u i t a b l e c o n v e r g e n c e of an an a l y t i c function, b e c a u s e of its d e s i r a b l e p r o p e r t i e s in relation to F o u r i e r t r a n s f o r m and convolution.

Thus the second order a p p r o x i m a t i o n is given by r e p l a c i n g ~(r) in the integral by ~(0)(r) + ~(I)(r) and so on. r} e x p { - 2 r d k l r - r'l} 4rc J Ir-r'l 15 (19) exp{-2~ik~ ~(g) Under the usual conditions of a scattering experiment we may assume that the point of observation is at r = R where R is very large compared with the dimensions of the scattering field. t exp {-2rdkoR } [ 4~ R d ~ (/) exp { -2~iq- / } dr'. R } + R -I exp {-2~ik0R } f(q). r}dr. e. that the scattered amplitude is negligibly small.