Final answer:
The technique that provided critical data for the discovery of DNA's double helix structure was x-ray diffraction, with significant contributions from Rosalind Franklin's work.
Step-by-step explanation:
The technique supplied the data that led Watson and Crick to the double helical structure of DNA was x-ray diffraction/crystallography. Rosalind Franklin played a crucial role in capturing X-ray diffraction images that showcased the helical nature of DNA. Watson and Crick used these images, as well as other research such as Chargaff's rules, to formulate the double stranded structural model of DNA, leading to their famous depiction of DNA's iconic helical structure.