A-DNA and B-DNA are two secondary molecular conformations (among other allomorphs) that double-stranded DNA drawn into a fiber can assume, depending on the relative water content and other chemical parameters of the fiber. They were the first two forms to be observed by X-ray fiber diffraction in the early 1950s, respectively by Wilkins and Gosling and by Franklin and Gosling. Their corresponding historical diffraction diagrams played an equally crucial role in the discovery of the primary double-helical structure of the DNA molecule by Watson and Crick in 1953. This paper provides a comparative explanation of the structural content of the two diagrams treated on the same footing. The analysis of the diagrams is supported by the optical transform method with which both A-DNA and B-DNA X-ray images can be simulated optically. The simulations use a simple laser pointer and a dozen optical diffraction gratings, all held on a single diffraction slide. The gratings have been specially designed to pinpoint just which of the structural elements of the molecule is responsible for each of the revealing features of the fiber diffraction images. (Contains 9 figures and 2 notes.)