Surface-Enhanced Raman Imaging of Cell Membrane by Highly Homogeneous and Isotropic Silver Nanostructure

where q is the wave vector and rj represents the spatial coordinates of the j-th center of mass in the pattern. The forward scattering (q = 0) is omitted for consistency with the definition of the ensemble-average structure factor of an infinite point configuration ( ) 1 ( ) S h ρ = + q q in which ρ is the number density, ( ) h q is the Fourier transform of the total correlation function 2 ( ) ( ) 1 h g = − r r and 2 2 ( ) ( ) g g r = r defines the pair-correlation function of the pattern. For homogeneous and isotropic systems we can write r =|r|. For an infinite point pattern, the structure is hyperuniform and shows long-range correlations when 0 lim ( ) 0 S → = q q . In fact, such condition means that the infinite-wavelength density