An annealing apparatus and a method of annealing a protection sheet is provided. The annealing method includes disposing the protection sheet in a chamber and injecting high-pressure carbon dioxide (CO2) gas into the chamber or heating the protection sheet at a predetermined temperature in the chamber. In the annealing method a crystalline phase of molecules in the protection sheet is changed to be an amorphous phase of molecules by such that the protection sheet has a refractive index with substantially the same distribution.