Sixty years after the discovery of the double helix structure of DNA, this iconic symbol of 20th century science continues to fascinate the world. The method of X-ray diffraction for structure determination played a crucial role in the discovery. Unfortunately the original, technical articles remain accessible only to specialized crystallographers. However this need not be so. In the present article we explain the structural meaning of the two X-ray diffraction images of the DNA molecule in its two A and B conformations in a language accessible to a large public. These were the two images which, among many other informations, have substantially helped Crick and Watson to discover both the double helix structure and the mechanism of its genetic function. In view of understanding the content of these two images in terms of molecular structure, we present the results of optical simulation experiments which allow to elucidate which aspect of the molecule corresponds to each of the features of the X-ray patterns.