The present invention relates to a method for fabricating a LiFePO4 cathode electroactive material for a lithium secondary battery by recycling, and a LiFePO4 cathode electroactive material for a lithium secondary battery, a LiFePO4 cathode, and a lithium secondary battery fabricated thereby. The optical disk further includes a structure management table which stores an attribute for each zone indicating whether the corresponding zone is a recording area which permits rewriting of a recording area that does not permit rewriting. The system control is also programmed to reconstruct a phase contrast image based on the first and second single data sets to correct for spatially-dependent background phase variations.