Fig. 1. Illustration of holographic AR displays with two different types of optical combiners. (a) Traditional coaxial design. Light from the SLM is reflected onto a curved partial mirror by a BS and then reflected toward the human eye. (b) Proposed off-axis design. Light from the SLM hits the HOE in an oblique incidence angle and then gets reflected and converged toward the human eye.

Fig. 2. Overview of tilt-SGD and tilt-CITL. (a) Hologram generation with the tilted plane setting. The initial phase hologram loaded on the SLM is a random phase to avoid getting stuck in local optimum during iteration. The reference plane is parallel to the SLM and set for propagation between two parallel planes. Two coordinate systems are used in the propagation model: one is the (x,y,z) SLM coordinate, while the other one is the (x′,y′,z′) or (x^,y^,z^) reference coordinate. Note that the tilted plane can either rotate the reference plane around the x^ axis or the y^ axis. (b) Camera-calibrated hologram optimization. The phase is represented by a green frame and the amplitude is represented by a black frame. The initial hologram loaded on the SLM is also a random phase. Similar to the pipeline of tilt-SGD, the reference plane field can be obtained through the propagation of the SLM field by ASM, and the tilted plane field is obtained by applying the transformation matrix T into the reference plane field. Note that tilt-CITL needs to capture the virtual imagery in a dark environment.

Fig. 3. Simulation results (PSNR, in dB). For each set (left to right): simulation results with SGD, perspective-SGD, tilt-SGD.

Fig. 4. Schematic diagram of the proposed HOE (a) fabrication and (b) reconstruction procedure. The (x,y,z) HOE coordinate is established to analyze the fabrication and reconstruction process better. Suppose the coordinates of the viewpoint are (0,0,zv). (c) Fabricated HOE by a 532 nm laser. The HOE consists of a layer of photopolymer and a glass substrate. The glass substrate size is about 50  mm×40  mm, and the thickness is 1 to 2 mm. (d) The viewpoint was formed by illuminating the HOE with a 532 nm laser.

Fig. 5. Analysis of HOE diffraction efficiency. (a) Diffraction efficiency distribution according to exposure time. The exposure intensity is fixed at 0.3  mW/cm2. (b) Effects of incident light angle deviation on the measured diffraction efficiency. Please note that the diffraction efficiency is normalized.

Fig. 6. System design and setup of the implemented prototype. (a) Optical schematic: CL, collimating lens; LP, linear polarizer; BS, beam splitter; SLM, spatial light modulator; L1, lens 1; L2, lens 2; HOE, holographic optical element. L1 and L2 form a 4f system for magnifying the image. (b) Bench-top holographic AR display prototype. The light emitted from the fiber-coupled laser meets CL, LP, SLM, and 4f system, and constructs an image at the HOE plane through the eyepiece. A physical cube is placed behind the HOE as the reference. (c) Zoom-in details of the eyepiece and the full-color HOE. The distance between the HOE and the eyepiece is 30 mm, which is also the eye relief.

Fig. 7. Comparison of SGD and tilt-SGD results. (left to right) Captured results and optimized holograms of SGD and tilt-SGD when the target image is located at 10 cm. The main purpose is to illustrate the effect of the proposed algorithm, so these results are not calibrated by the camera, and there will be other distortion issues besides stretch distortion.

Fig. 8. Comparison of results using tilt-SGD and tilt-CITL in the VR-mode holographic display. The 2D resolution of captured images is 1600×880. For each set (left to right): target images, phase patterns by tilt-SGD, captured results of tilt-SGD, phase patterns by tilt-CITL, and captured results of tilt-CITL, respectively. The target image is set at 10 cm away from the SLM plane. The PSNR metrics are reported. The phase patterns of full-color target image are created by superimposing holograms from three separate color channels. Note that these captured images are normalized for visualization purpose.

Fig. 9. Acquired AR results at two focusing distances. (a) Near focus, with the camera focusing at the real object “Physical Cube.” (b) Far focus, with the camera focusing at the real object “Head Model.”

Fig. 10. Diagram of the experimental setup used for HOE fabrication. M1, M2, M3, M4: mirrors; DM1 and DM2: dichroic mirrors; BS: beam splitter; CL: collimating lens; HOE: holographic optical element.