A theoretical investigation is carried out in the field of holography. This work presents a study in the topics of holography and computer generated hologram, and it analyzes and implements some existing encoding methods for computer-generated hologram. The operation of computer-generated holograms is used in this research that makes use of the fact that the recorded hologram includes changes in blacking. The produced holograms are binary, are black and white, really opaque and transparent. They are able to construct general wavefronts and images efficiently, and they have high diffraction efficiency of the gratings compared with the holograms which have continuous range of transmittance. This study produces computer generated diffracted optical elements represented by the gratings to produce three types of wavefronts (spherical, conical, and helical wavefronts), these gratings are considered as complete optical elements. The program used to construct these holograms is (visual basic) by using binary synthetic hologram technique. The synthesis holograms based on phase variance. Different numbers of fringes have been used in the construction of the holographic gratings (20, 40, and 80,160) fringes. The reconstruction process of all computergenerated holograms were done by programming software (Matlab).