Multi-plane reconstruction is essential for realizing a holographic three-dimensional (3D) display. One fundamental issue in conventional multi-plane Gerchberg-Saxton (GS) algorithm is the inter-plane crosstalk, mainly caused by the neglect of other planes’ interference in the process of amplitude replacement at each object plane. In this paper, we proposed the time-multiplexing stochastic gradient descent (TM-SGD) optimization algorithm to reduce the multi-plane reconstruction crosstalk. First, the global optimization feature of stochastic gradient descent (SGD) was utilized to reduce the inter-plane crosstalk. However, the crosstalk optimization effect would degrade as the number of object planes increases, due to the imbalance between input and output information. Thus, we further introduced the time-multiplexing strategy into both the iteration and reconstruction process of multi-plane SGD to increase input information. In TM-SGD, multiple sub-holograms are obtained through multi-loop iteration and then sequentially refreshed on spatial light modulator (SLM). The optimization condition between the holograms and the object planes converts from one-to-many to many-to-many, improving the optimization of inter-plane crosstalk. During the persistence of vision, multiple sub-hologram jointly reconstruct the crosstalk-free multi-plane images. Through simulation and experiment, we confirmed that TM-SGD could effectively reduce the inter-plane crosstalk and improve image quality.The proposed TM-SGD-based holographic display has wide applications in tomographic 3D visualization for biology, medical science, and engineering design, which need to reconstruct multiple independent tomographic images without inter-plane crosstalk.

A lensless full-color holographic Maxwellian near-eye display using a single amplitude-type spatial light modulator is proposed in this Letter. The color holographic image is directly projected onto the retina without any eyepiece. The color crosstalk is clearly separated from the signal in the space owing to the encoded spherical wave and carrier wave. An aperture numerical filter and a real polarized filter are used at the pupil plane to accurately stop the crosstalk light. A high-quality dynamic speckless color holographic image was produced in the mid-air within a specific depth range. The horizontal eyebox expansion is achieved simply through multiple spherical wave encoding and verified through an optical experiment. The proposed display is compact and promising as the augmented reality near-eye display.

The holographic Maxwellian display is a promising technique for augmented reality (AR) display because it solves the vergence-accommodation conflict while presenting a high-resolution display. However, conventional holographic Maxwellian display has the inherent trade-off between depth of field (DOF) and image quality. In this paper, two types of holographic Maxwellian displays, the spherical wave type and the plane wave type, are proposed and analyzed. The spherical wavefront and the plane wavefront are produced by a spatial light modulator (SLM) for Maxwellian display. Due to the focusing properties of different wavefronts, the two types of display have complementary DOF ranges. A hybrid approach combining the spherical wavefront and plane wavefront is proposed for a large DOF with high image quality. An optical experiment with AR display is demonstrated to verify the proposed method.

A holographic super multi-view (SMV) Maxwellian display based on flexible wavefront modulation is proposed for the first time, to the best of our knowledge. It solves the issue that the previous holographic Maxwellian displays could not provide depth cues for monocular vision. Different from the previous methods, two or more parallax images are multiplied by quadric phase distributions and converged to the viewpoints existing in the pupil to provide 3-D vision. A time division method is proposed to eliminate the cross talk caused by the coherence of different spherical waves. Experiments demonstrate that the proposed method can accurately reconstruct images at different depth without cross talk. The proposed method inherits the previous holographic Maxwellian display's advantages of flexible viewpoint position adjustment and large depth of field (DOF). Superior to geometric optics based SMV displays, the proposed system is compact without lens aberration since only a single spatial light modulator (SLM) is needed without any additional optical elements.

Conventional holographic stereogram (HS) can be generated through fast Fourier transforming parallax images into hogels. Conventional HS uses multiple plane waves to reconstruct 3D images with low resolution and is similar to the principle of depth priority integral imaging (II). We proposed the concept of resolution priority HS for the first time, which is based on the principle of resolution priority II, by adding a quadratic phase term on the conventional Fourier transform. In the proposed resolution priority HS, the resolution of reconstructed 3D images is much better than conventional HS, but the depth range is limited. To enhance the depth range, a multi-plane technique was used to present multiple central depth planes simultaneously. The proposed resolution priority HS with high resolution and enhanced depth range was verified by both simulation and optical experiment.

We proposed a simple and fast algorithm for computer-generated hologram (CGH) based on pinhole-type II using a look-up table. The method consists of two steps: in the first step, the unity amplitude diffraction pattern of the center pinhole on hologram plane is pre-calculated and stored as many sub-regions. Secondly, diffraction patterns for other pinholes are obtained by simply shifting and tiling the pre-calculated sub-regions, and the final CGH is obtained by adding them all together. The calculation time is short because only addition and multiplication of the stored diffraction pattern are required. In addition, the required memory space is small since only one diffraction pattern is stored. Numerical simulation and reconstruction are performed on both plane object and object with continuous depth profile to verify the proposed method. Result shows that the proposed method can easily achieve real-time hologram generation with several CPU threads running simultaneously.