"Diffraction by helical structures"

Date:
1956-1957
Reference:
PP/CRI/H/2/17
Catalogue details

Licence: In copyright

Credit: "Diffraction by helical structures". Source: Wellcome Collection.

    21/98
    Comparing this with equation (13) y we see that £*,4 ^ J 3 H|J ( ( r ) J a JJTrd f (lb) By the Fourier-Bessel inversion theorem (Titchmarsh or Watson or any standard work) &Q K* (O » f G n W«.) o lote that this analysis is perfectly general for & cylindrical co ordinates, and wo have nowhere used the fact that we are dealing with a helix* The helical symmetry shows itself only in the fact that not all the occur - only those which have £ and n obeying equation (2) occur# When there is no helical or cylindrical symmetry, all will in general he included, Finally in the most general case possible f when there is no axial repeat, the Fourier series in z beomces a Fourier integral. We thus see that to make the Fourier synthesis of electron density we need to .know the individual G 0 (E), that is.the Besse! function terms of various order must first have been unscrambled« M© can then use equation (17) to obtain the (r) t and finally evaluate ç using (15)* It should perhaps be emphasised that if we know only the resultant modulus and phase along a layer line, that is, if we yf, . ^ have F(RfO^ ) - ¿> csn still determine the individual by Fourier«Bessel analysis making use of the orthogonality of Bessel functions of different order ($«€ ¡far mi W c e í&dkmsutk JîaO»T<0 Tp (jnn-r') M =0 ,f nfp ^ Further if n « p, the integral vanishes unless r ~ r*. Hence an b)