The theory of dislocations in elasticity goes back to the early years of last century, the 1920’s, mainly due to the work of Volterra. He was concerned with elastic deformations leading to non single-valued displacements. Volterra introduced the basic notion of dislocations. In the 1930’s, dislocations were utilized in a different context, the mechanics of crystalline structures, to explain the mechanisms of plastic deformations. In the 1960’s the use of X-rays made it feasible to visualize the displacement fields surrounding a dislocation by generating the image of carrier fringes that provided the positions of atoms in the region surrounding a dislocation. Later in the last century electron microscopy provided another tool to investigate atom positions in regions of stacking faults. In the present paper techniques developed to analyze displacements fields in solids are applied to signals generated via x-ray electron microscopy. Strain fields in regions where the crystalline structure is distorted are determined.