An optimized Gerchberg–Saxton algorithm for speckle suppression with double amplitude freedom

The Gerchberg–Saxton (GS) algorithm is a widely employed algorithm for phase-only hologram (POH) generation. However, the POHs which can strictly satisfy the amplitude constraints on the object and the holographic plane may not exist or be obtained, resulting in speckle noise and reduction of the reconstruction quality. Relaxing the amplitude constraint during the iterations is an effective method to solve the above problem. In this work, a GS-double amplitude freedom (GS-DAF) algorithm is proposed. The amplitude constraint relaxation is realized by both the combined amplitude constraint and the support constraint. The spherical initial phase and oversampling method are applied to further improve the optical reconstruction quality of the GS-DAF algorithm. An enhanced reconstruction quality with less speckle noise has been achieved.