Beam shaping of complex amplitude with separate constraints on the output beam

We present a beam shaping technique in controlling the complex amplitude of an optical beam. The constraint on the amplitude of the output beam in the Gerchberg-Saxton algorithm is replaced with constraints both on the amplitude and phase of the output beam in the proposed method. The total areas of the constrained regions and free regions on the complex amplitude of the output beam in the proposed method are maintained. An output beam with arbitrary complex amplitude can be realized with the proposed method. The computing result from the proposed method is a phase-only distribution, which can be fabricated as diffractive optical element for higher diffraction efficiency. Both simulations and experiments are present and the effectiveness of the proposed method is verified.