The polygon-based method is grounded in the basic concept of computer graphics (CG), where a 3D object is discretized into multiple polygons, such as triangles or quadrangles. Each polygon is a 2D structure, but with different directional normals, resulting in a continuous 3D surface of the object. 

However, the one-to-many nature of the holographic problem makes the polygon-based method different from CG, where it can be rendered pixel by pixel, whereas the field distribution of a tilted polygon in the holographic plane needs to be described in the frequency domain. 

Various acceleration algorithms for generating polygon-based holograms have been proposed, which can be divided into two main categories: numerical-based methods for obtaining spectra by FFT and interpolation, and analytic-based algorithms for obtaining spectra by analytic functions.

[Ref. 1] Fan Wang (2023). Polygon-Based Hologram Calculation Methods. In: Shimobaba, T., Ito, T. (eds) Hardware Acceleration of Computational Holography. Springer, Singapore.

[Ref. 2] Y Zhang, H Fan, F Wang, X Gu, X Qian, TC Poon, Applied Optics 61 (5), B363-B374

[Ref. 3] Matsushima K. Introduction to Computer Holography: Creating Computer-Generated Holograms as the Ultimate 3D Image[M]. Springer Nature, 2020. 

In this study, we propose a comprehensive rendering pipeline for computing holograms. The pipeline starts with 3D object modeling, then processes complex occlusion issues, implements smooth shading, and finally generates holograms through an acceleration algorithm. The proposed accelerated method using wavefront recording plane introduces a speedup of more than hunderds times compared to conventional methods, which is a great jump for the polygon-based holograms. The improved smooth shading method achieves highly realistic lighting effects at an economical computational cost. The proposed occlusion-culling method combines techniques in computer graphics to implement complicated hidden surface removal with no additional workload, enhancing the 3D perception of holographic reconstructions.

The proposed polygon-based comprehensive hologram high-speed rendering pipeline is capable of computing any complex three-dimensional object, and numerical and optical reconstructions confirm the pipeline's generalizability. These advances stand on the development of polygon hologram over the past 20 years and are a new beginning in developing more practical holographic display technologies based on polygonal holograms.

[Ref. 1] F Wang, T Ito, T Shimobaba, Photonics Research 11 (2), 313-328

[Ref. 2] F Wang, H Shiomi, T Ito, T Kakue, T Shimobaba, Optics and Lasers in Engineering 160, 107235

[Ref. 3] F Wang, H Shiomi, T Ito, T Kakue, T Shimobaba, Optics and Lasers in Engineering 160, 107235

The point-based methods are good at presenting object details, polygon-based methods are good at efficiently rendering high-density surfaces with accurate occlusion. The point-polygon hybrid method (PPHM) takes advantage of both point-based and polygon-based methods, which combines the strengths of both methods and eliminates their weaknesses to achieve higher computational efficiency. The PPHM utilizes a low-polygon approximation of the original 3D polygonal meshes and leverages the computational advantages of the wavefront recording plane and look-up table methods to generate high-resolution holograms with smooth focal cues quickly. The proposed PPHM algorithm is validated to present continuous depth cues and accurate occlusion with fewer triangles, implying high computational efficiency without quality loss.

[Ref.] F Wang, D Blinder, T Ito, T Shimobaba, Optics Letters 48 (12), 3339-3342

Utilizing computer-generated holograms is a promising technique because these holograms can theoretically generate arbitrary waves with high light efficiency. In phase-only spatial light modulators, encoding complex amplitudes into phase-only holograms is a significantissue, and double-phase holograms have been a popular encoding technique. However, they reduce the light efficiency. In this study, our complex amplitude encoding, called binary amplitude encoding (BAE), and conventional methods including double-phase hologram,iterative algorithm and error diffusion methods were compared in terms of the fidelity of reproduced light waves and light efficiency, considering the applications of lensless zoomable holographic projection and vortex beam generation. This study also proposes a noise reduction method for BAE holograms that is effective when the holograms have different aspect ratios. BAE is a non-iterative method, which allows holograms to be obtained more than two orders of magnitude faster than iterative holograms; BAE has about three times higher light efficiency with comparable image quality compared to double-phase holograms.

[Ref. 1] T Shimobaba, F Wang, J Starobrat, A Kowalczyk, J Suszek, T Ito, Applied Optics 62 (28), 7471-7479

[Ref. 2] Tomoyoshi Shimobaba et al 2020 J. Opt. 22 045703