Double amplitude freedom Gerchberg–Saxton algorithm for generation of phase-only hologram with speckle suppression

The Gerchberg–Saxton (GS) algorithm is a widely employed algorithm for the calculation of a phase-only hologram (POH). However, the POH that 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. The peak signal-to-noise ratio can be improved from 14.98 to 33.32 dB after 200 iterations.