Holobricks: modular coarse integral holographic displays

Here, we propose and demonstrate a modular holographic display system that allows seamless spatial tiling of multiple coarse integral holographic (CIH) displays called “holobricks”. A holobrick is a self-contained CIH module enclosing a spatial light modulator (SLM), a scanner, and periscopic coarse integral optics. Modular CIH uses a coarse pitch and small area but high-bandwidth SLM in conjunction with periscopic coarse integral optics to form the angularly tiled 3D holograms with large viewing areas and fields of view. The creation of periscopic coarse integral optics prevents the optical system from being larger than the holographic image and allows the holographic fringe pattern to fill the entire face of the holobrick. Thus, multiple holobricks can be seamlessly abutted to form a scalable spatially tiled holographic image display capable of both wide field-of-view angle and arbitrary large-size area. We demonstrate an initial prototype that seamlessly tiles two holobricks each with 1024 × 768 pixels, 40° FOV, full color, 24 fps, displaying 2D, 3D holographic stereograms, and full parallax 3D CGI Fresnel holograms.

the system. In other words, the information BW controlled by the galvanometer (the product of the mirror area size, scan angle, and sweep frequency) was still less than the information bandwidth SLMs was capable of to produce the super-holograms that at video frame rates. Even after allowing overlapping holograms with independent color components for view sequential color, the early dCIH displays can only implemented the SLM'S bandwidth utilization ratio of 53% with the available scanners at the time.

B. Scalable Coarse Integral Holography
To address this issue, various scanning mechanisms were explored that permit better complete utilization of the SLM's BW in the CIH display. The unabridged SLM's bandwidth utilization enabled the CIH display to produce larger, wider FOV holographic images at video frame rates. We investigated three different scanning configurations to increase the bandwidth of the scanning system: two utilizing resonant scanners, with the large mirrors, large deflections, and high but fixed scan frequencies, and a third setup using multiple scanners.
In the first setup, the dCIH added high-frequency resonant scanning in the kHz range as a high-speed vertical dither [2]. This resonant scanner's scan frequency was too high to use for line rate scanning of the horizontal array of holograms to seamlessly abut without gaps. It was therefore used as an auxiliary dither scanner to add a vertical zig-zag dither to the existing horizontal scan, thereby tiling a few holograms in a vertical column for every horizontal row tiling. This arrangement could not increase the number of horizontal hologram tiles, but rather increased the number of vertical tiles, and as a result, increased the display's vertical FOV, and vertical headbox size.
In a second setup, the unutilized SLM bandwidth was exploited by using the dCIH display configuration but replaced the horizontal galvanometer scanner and mirror with a taut-band-based resonant optical scanner (at the identical scanning frequency of 70K Hz) and a larger-size mirror [3]. The exploitation of the wide-angle and large-mirror resonant optical scanner benefited the two-fold increase of the horizontal FOV angle and employed the entire BW of the SLM.
Finally in a third setup, two synchronous scanners were cascaded to enlarge the horizontal viewing angle of reconstructed 3D holographic images and to fully exploit the information BW of the SLM [4].
Using any one of these schemes, the scanners had more than sufficient bandwidth to handle the information in the holograms produced by the SLMs. The scanners were no longer the bottleneck in the system. To further expand the optical extent of the holograms created by the CIH system, another setup used two full-bandwidth holograms produced on two high bandwidth SLMs.
These SLMs spatially tiled onto and scanned by a common large-area taut-band-resonant-based optical scanner (horizontal) and a large-size galvanometric-based scanner (vertical). Then, they angularly tiled by a large integral lens [5]. This results in a full bandwidth dCIH display capable of allowing the two-fold reconstructed holographic image size and twice the viewing angle in the horizontal direction at the same time.

1× Hologram
Hologram Hologram Hologram Hologram Hologram Hologram Hologram replaces the relay 2f-lens in the plain periscope system, (e) the scaled periscope optics using dual lenses achieved the doubling hologram size, (f) the offset periscope optics achieves a doubling hologram size, (g) the array of scaled periscope optical array has two viewing angles, (h) the scaled periscope optics has a triple hologram size, (i) the offset scaled periscope optics obtains a triple hologram size, and (j) the array of the scaled periscope optical array has three viewing angles.

S2. Computer-generated hologram (CGH) generation algorithm for holobricks
In the holobrick display system, the periscope optical array is used to relay the hologram on the DMD plane to the holobrick face. There is not a Fourier lens to reconstruct the holograms of Here, we use Pn to express the Fourier holographic pattern, Pn=FFT(Gn). Fourth, each depth hologram is attached by a computed holographic lens as: (S1) This method is a layer algorithm when the depth information is considered. The "attached" holographic lens is computed as part of the hologram, and scanned with the SLM into the array, removing the need for a coarse integral optics' lenslet array as well. The generation algorithm is shown in Supplementary Fig. S13

S3. The occlusion or accommodation for the holobrick system
Same as the other holographic displays, holograms can produce the accommodation depth cues and occlusions. These two features have a direct relationship with the hologram generation algorithm. A holographic display system can provide the capability of these two effects. With the same capability as our previous scalable full-bandwidth dCIH systems, our graphics rendering approach for the presented holobrick system allows the incorporation of all appropriate depth cues and occlusion in the generated holograms for angular tiling. The presented holobrick system can display holographic images with accommodation cues. This accommodation cue capability is the same as our previous scalable full-bandwidth dCIH systems. A significant feature of the CIH systems is the trade-off between the resolution of accommodation cue and hologram generation calculation speed. Under the acceptable calculation consumption, the accommodation cue resolution is determined by the object and the human visual system. For example, a total depth of an object is 10 cm. When the layer number is 10~20, the depth resolution is 5 mm~10 mm. The depth resolution can satisfy the eye accommodation and the system can provide smooth accommodation cues. In our holobrick system, the nature of angularly tiled CIH holograms can be fully utilized to produce view-dependent holograms. Each sub-hologram generated by our layer-based algorithm can project a voxel emitting light isotropically within its small FOV zone. The tileable coarse integral optics can provide angularly tiled view zones independent of each other. The independence of the view zones allows each sub-hologram to be computed separately, independently of other sub-holograms for efficient and parallel computation. This allows us to render and display occlusion /disocclusion effects, to view dependent shading and lighting, as well as to prevent layering artifacts with off-axis viewing of layered holograms. Our computergenerated imagery color and depth renderings of the 3D model from different viewpoints can provide view-dependent lighting, occlusion/disocclusion handling, and layer slicing.

S4. Objective evaluations of the holobrick display system
We also objectively evaluate display system performance using the following several measurements. Firstly, the reconstructed holographic image quality from the holobrick system is measured by eight parameters: contrast, edge intensity (EI), average gradient (AG), entropy, variance, luminosity, homogeneity, and mean structural similarity index (MSSI). Table S1 shows the measurement results at different FOV positions. From the measure results, the reconstructed images can obtain high performance in terms of contrast, EI, AG, entropy, variance, luminosity, homogeneity, and MSSIM. For example, the reconstructed and original images have a similar performance in the contrast. These measurement results indicated that the proposed system can achieve a high display performance.  [8] is widely used for the MTF evaluation of an optical system. However, this method is suitable for general optical systems and not for a holographic display system. Here, we utilize speckles from the holographic images as point sources to measure the MTF. Fig. S17 shows the measured MTF curve. From the measurement results, the display system exhibited a good MTF performance. At the normalized frequency of 0.5, the MTF can achieve 0.44. This value represents the high optical performance of the holographic system. Finally, we also analyze other performances regarding the optical efficiency, the smallest viewing-angle matching, and color size matching for the holobrick system.

S5. A video record example of holographic displays with different FOV angles for a holobrick system
We demonstrated a video record example of holographic displays with different parallax images for the holobrick system. This example also showed a complete holographic display flow from the hologram generation and holographic displays for a holobrick system. Figure S18 shows the complete record process of the holographic display with different viewing angles (i.e., parallax) using a camera. First, we use 3ds Max to design a 3D object model to produce different parallax images. The 3D object model is a curved surface composed of 16 sub-surfaces. Each sub-surface is designed with a capital letter. Each sub-surface has a small viewing angle of 2.5°. Thus, the total FOV angle of the designed 3D object is 40°. Second, each angular-view hologram is calculated from its image Fourier transformation using the hologram generation algorithm. Third, all sub-holograms are presented on the SLMs of the tiled holobrick system. The sub-scanning system of the holobrick can scan low SBP sub-holograms to form the hologram array for the integral optics. Fourth, we placed a camera in front of the holobrick system to record the holographic image display process at the different FOV positions. In the recording process, the camera is moved along the perpendicular direction of the optical axis from the left FOV to the right FOV. The holographic images of different viewing angles are recorded. A recorded video is shown in Supplementary video materials. From the video, we can observe the different parallax holographic images at different times.