Phase-shift and phase-contrast images of pancake superconducting vortices

Recently, a Fourier space approach has been developed, which can be fruitfully applied for calculating the phase-shift and phase-contrast transmission electron microscope images of superconducting pancake fluxons in high-T-c layered specimens. in this work, the results obtained by a very simplified model, where the specimen is approximated by three thin layers, are presented and discussed. These model calculations, although oversimplified, can nonetheless give useful hints on the expected images of pancake vortices not piercing the specimen but residing in it or near its surfaces, or pinned by a tilted columnar defect. Furthermore, the model calculations motivate more elaborate and accurate, but time and memory consuming, calculations, which can be carried out by increasing the number of layers.