The precise atomic structure and relative atomic conformation of the individual carbon nanotubes comprising a double wall carbon nanotube (DWCNT) is determined. The DWCNTs are imaged using an aberration corrected high resolution transmission electron microscope (HRTEM) operating at 80 kV. Using processing in Fourier space images of the inner and outer tube of a double-wall carbon nanotube (DWCNT) are analysed. Comparisons of these results with simulated HRTEM images enable the chiral indices and relative atomic correlation of the component tubes of non-commensurate DWCNTs to be determined. This technique is used to reveal the presence of a defect in the inner tube of a (6, 6)@(18, 2) DWCNT.