Applying multi-focus filtering plane in double-step Fresnel diffraction method for enhanced holographic projection region

Computer-generated holography has been anticipated in augmented reality (AR) since it can fully provide multi-depth 3D information to users, but speckle noises are often accompanied as one of the most significant degradation factors. Since complex amplitude encoding can suppress speckle noises, applying double-phase encoding to a lensless holographic projection system using a double-step Fresnel diffraction (DSF) algorithm has been reported to reduce those noises. However, a single filtering focus at a virtual focal plane might significantly reduce the projection region compared to the maximum diffraction bandwidth of the spatial light modulator. In this paper, we applied multiple foci for the focal plane of the DSF method with off-axis phase encoding, which can expand the projection region and is applicable to display multi-depth images with DSF. Numerical analysis conducted for image quality compared with conventional single focus DSF algorithm shows that the speckle performance does not degrade so much as the number of foci increase. We expect the proposed method to be useful for holographic projection optical systems such as AR head-up display.