A novel approach to quantitative interpretation of high-resolution electron microscopy images of defects in materials has been developed. The emphasis of this paper is on the methodology, which has been named Computational Fourier Transform Moiré Analysis. The essential principle of this technique is to extract an accurate displacement field about a defect from its near-atomic-resolution picture using digital Fourier transformation procedures. From this data, the displacement gradient can be calculated which yields much information on the experimental deformation mechanics of the material under investigation. As a by-product, we produce the computational Moiré pattern without the need of an external perfect reference lattice image normally associated with the interference phenomena. This method is illustrated using a bounding Frank partial dislocation for a Frank loop of the vacancy type. Results are presented on its strain field, Burgers vector and dislocation core shape and dimensions. Further mention will be made on the types of J-integral calculations that can result from this experimental study.