<Dd> A S ∫ d r f (r) e i k i n ⋅ r e i k o u t ⋅ (r s c r e e n − r) = A S e i k o u t ⋅ r s c r e e n ∫ d r f (r) e i (k i n − k o u t) ⋅ r (\ displaystyle AS \ int \ mathrm (d) \ mathbf (r) f (\ mathbf (r)) \ mathrm (e) ^ (\ mathrm (i) \ mathbf (k) _ (in) \ cdot \ mathbf (r)) e ^ (i \ mathbf (k) _ (out) \ cdot \ left (\ mathbf (r) _ (\ mathrm (screen)) - \ mathbf (r) \ right)) = ASe ^ (i \ mathbf (k) _ (out) \ cdot \ mathbf (r) _ (\ mathrm (screen))) \ int \ mathrm (d) \ mathbf (r) f (\ mathbf (r)) \ mathrm (e) ^ (\ mathrm (i) \ left (\ mathbf (k) _ (in) - \ mathbf (k) _ (out) \ right) \ cdot \ mathbf (r))) </Dd> <P> which may be written as a Fourier transform </P> <Dl> <Dd> A S e i k o u t ⋅ r s c r e e n ∫ d r f (r) e − i q ⋅ r = A S e i k o u t ⋅ r s c r e e n F (q) (\ displaystyle AS \ mathrm (e) ^ (\ mathrm (i) \ mathbf (k) _ (out) \ cdot \ mathbf (r) _ (\ mathrm (screen))) \ int d \ mathbf (r) f (\ mathbf (r)) \ mathrm (e) ^ (- \ mathrm (i) \ mathbf (q) \ cdot \ mathbf (r)) = AS \ mathrm (e) ^ (\ mathrm (i) \ mathbf (k) _ (out) \ cdot \ mathbf (r) _ (\ mathrm (screen))) F (\ mathbf (q))) </Dd> </Dl> <Dd> A S e i k o u t ⋅ r s c r e e n ∫ d r f (r) e − i q ⋅ r = A S e i k o u t ⋅ r s c r e e n F (q) (\ displaystyle AS \ mathrm (e) ^ (\ mathrm (i) \ mathbf (k) _ (out) \ cdot \ mathbf (r) _ (\ mathrm (screen))) \ int d \ mathbf (r) f (\ mathbf (r)) \ mathrm (e) ^ (- \ mathrm (i) \ mathbf (q) \ cdot \ mathbf (r)) = AS \ mathrm (e) ^ (\ mathrm (i) \ mathbf (k) _ (out) \ cdot \ mathbf (r) _ (\ mathrm (screen))) F (\ mathbf (q))) </Dd>

Determination of crystal structure using x ray diffraction