Download Diffraction Physics by J.M. Cowley PDF

By J.M. Cowley

The 1st version of this hugely profitable e-book seemed in 1975 and advanced from lecture notes for sessions 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 remodel 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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Here we m e n t i o n only the case that the incident r a d i a t i o n comes from a point source at a finite distance, say RI, from the p e r i o d i c object. Then (26) is r e p l a c e d by gt(x) = C RI~ exp q(X) exp R3, , dX, (34) where the first e x p o n e n t i a l f u n c t i o n r e p r e s e n t s a s p h e r i c a l wave from the point source incident of the object h a v i n g t r a n s m i s s i o n f u n c t i o n q(X) . It is r e a d i l y shown that F o u r i e r images will by m a g n i f i e d by a factor (R + R I)/R 1 and will occur at p o s i t i o n s given by ] l --+ .

E x p { 2 K i ( u X + u a ) }dX [F(v) exp{-2~iux}dv] (-2~iu) F(u) exp{2~iux}dx exp{2~i(,-v) x}dvdx since f exp{2~i(u-v)x}dx = ~(u-v). 3. Multiplication and convolution We add the two important M u l t i p l i c a t i o n theorem relationships, the ~3 If(x) -g (x) ] = F (u) . e. the Fourier transform of a product of two functions the convolution of their Fourier transforms, and the Convolution theorem, ~3 [/'(x) . e. the Fourier transform of the convolution of two functions is the product of their Fourier transforms.

Na s i n (mVau) / (rdVau) ] h (58) Thus the height of each of the d i f f r a c t i o n m a x i m a is p r o p o r t i o n a l to the value of the F o u r i e r t r a n s f o r m of g(x) at that u value. A l t e r n a t i v e l y we c o u l d say that the d i f f r a c t i o n g r a t i n g may be r e p r e s e n t e d by c u t t i n g off a p e r i o d i c t r a n s m i s s i o n fun c t i o n by m u l t i p l y i n g it with a slit f u n c t i o n $(x) of width Na. This is not the same as (56) since in this case we may be using s(x) to cut off a c o n t i n u o u s function.

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