# A Fast Computer-Generated Holographic Method for VR and AR Near-Eye 3D Display

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## Featured Application

**The proposed technique has potential for head mounted near-eye VR or AR applications**.

## Abstract

## 1. Introduction

## 2. Methods

_{1A}and p

_{1B}are the projected points of the spatial points A and B on layer

_{1}, respectively. p

_{2A}and p

_{2B}are the projection points of space points A and B on layer2, respectively. The projection of 3D object points on one projection plane forms a projected image corresponding to this projecting angle. In the hologram calculation process, the illumination direction of each point on different projection planes is set as the propagation direction, as shown in Figure 1b. The complex amplitude distribution on the holographic plane H is a superposition of light field from all projection planes. When the hologram is reconstructed, the beamlets in these directions are diffracted from the hologram. Similar to integral imaging 3D displays, the overlapping regions of the different beamlets form a 3D object for 3D display [22,23], where the propagation direction of the beamlets determines the outcome of the 3D display.

_{p}and Y

_{p}are the coordinates of projected point of p on the projection plane. The projected image im

_{i,j}can be expressed as:

## 3. Experiments and Result Analysis

_{i,j}according their positions. Hence in this design, the angular separation between the two adjacent projected images in the x and y directions is set as 0.9°.

_{1}, and the LCoS is illuminated by the reflected light from beam splitter BS. The computer-generated hologram is loaded on the LCoS, and the illumination light is modulated. The modulated light field is filtered by the 4f optical filtering system to form a real 3D image free of zero order and high order image noise finally incident on human eye through the eyepiece lens

_{4}. The lenses used for collimating, 4f optical filtering system and eyepiece are all cemented doublet achromatic lenses with focal length of 50 mm and diameter of 30 mm. In this case, the distance from the LCoS to the eye is less than 25 cm, which means this setup is a relatively compact display system.

_{1}, and then split into two parts through the beam splitter (BS). The transmitted light passes through lens

_{2}to form a convergent spherical wave, which undergoes interference with the plane wave reflected by mirror

_{1}and mirror

_{2}on the holographic material to form the HOE. The laser used for HOE recording is a single mode semiconductor laser with a wavelength of 532 nm and power of 400 mW. The lens

_{2}is a commercially available aspherical mirror with focal length of 40 mm and a diameter of 50 mm (Thorlabs, AL5040M-A, NA = 0.55). The recording material we used in the experiment is a commercial holographic film (Ultimate Holography, U04), which requires an exposure density of ~600 μJ/cm

^{2}[27].

_{2}was tested, and the angular selectivity was within $\pm 5\xb0$. Using the SLM described above, the diffraction angle is within $\pm 1.89\xb0$, which means that most light diffracted by the SLM can be diffracted by HOE in a high efficiency.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Yaras, F.; Kang, H.; Onural, L. State of the art in holographic display: A survey. J. Disp Technol.
**2010**, 6, 443–454. [Google Scholar] [CrossRef] - Matsushima, K.; Arima, Y.; Nakahara, S. Digitized holography: Modern holography for 3D imaging of virtual and real objects. Appl. Opt.
**2011**, 50, H278–H284. [Google Scholar] [CrossRef] [PubMed] - Shi, Y.; Wang, H.; Li, Y.; Jin, H.; Ma, L. Practical method for color computer-generated rainbow holograms of real-existing objects. Appl. Opt.
**2009**, 48, 4219–4226. [Google Scholar] [CrossRef] [PubMed] - Yang, X.; Wang, H.; Li, Y.; Xu, F.; Zhang, H.; Zhang, J.; Yan, Q. Computer generated full-parallax synthetic hologram based on frequency mosaic. Opt. Commun.
**2018**, 430, 24–30. [Google Scholar] [CrossRef] - Cai, X.O.; Wang, H. Study of relationship between recording wavelength and hologram compression. Opt. Commun.
**2006**, 256, 111–115. [Google Scholar] [CrossRef] - Zhang, C.; Yang, G.L.; Xie, H.Y. Information compression of computer-generated hologram using BP Neural Network. In Digital Holography and Three-Dimensional Imaging (DH); Optical Society of America: Miami, FL, USA, 2010; p. JMA2. [Google Scholar]
- Lin, S.; Kim, E. Single SLM full-color holographic 3-D display based on sampling and selective frequency-filtering methods. Opt. Express
**2017**, 25, 11389–11404. [Google Scholar] [CrossRef] [PubMed] - Lin, S.; Cao, H.; Kim, E. Single SLM full-color holographic three-dimensional video display based on image and frequency-shift multiplexing. Opt. Express
**2019**, 27, 15926–15942. [Google Scholar] [CrossRef] [PubMed] - Chang, C.; Xia, J.; Yang, L.; Lei, W.; Yang, Z.; Chen, J. Speckle-suppressed phase-only holographic three-dimensional display based on double-constraint Gerchberg-Saxton algorithm. Appl. Opt.
**2015**, 54, 6994–7001. [Google Scholar] [CrossRef] - Jeon, W.; Jeong, W.; Son, K.; Yang, H. Speckle noise reduction for digital holographic images using multi-scale convolutional neural networks. Opt. Lett.
**2018**, 43, 4240–4243. [Google Scholar] [CrossRef] - He, Z.; Sui, X.; Jin, G.; Cao, L. Progress in virtual reality and augmented reality based on holographic display. Appl. Opt.
**2019**, 58, A74–A81. [Google Scholar] [CrossRef] - Huang, H.; Hua, H. Systematic characterization and optimization of 3D light field displays. Opt. Express
**2017**, 25, 18508–18525. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Huang, H.; Hua, H. Effects of ray position sampling on the visual responses of 3D light field displays. Opt. Express
**2019**, 27, 9343–9360. [Google Scholar] [CrossRef] [PubMed] - Su, P.; Cao, W.; Ma, J.; Cheng, B.; Liang, X.; Cao, L.; Jin, G. Fast computer-generated hologram generation method for three-dimensional point cloud model. J. Display Technol.
**2016**, 12, 1688–1694. [Google Scholar] [CrossRef] - Wei, H.; Gong, G.; Li, N. Improved look-up table method of computer-generated holograms. Appl. Opt.
**2016**, 55, 9255–9264. [Google Scholar] [CrossRef] - Arai, D.; Shimobaba, T.; Murano, K.; Endo, Y.; Hirayama, R.; Hiyama, D.; Kakue, T.; Ito, T. Acceleration of computer-generated holograms using tilted wavefront recording plane method. Opt. Express
**2015**, 23, 1740–1747. [Google Scholar] [CrossRef] [PubMed] - Liu, J.; Liao, H. Fast occlusion processing for a polygon-based computer-generated hologram using the slice-by-slice silhouette method. Appl. Opt.
**2018**, 57, A215–A221. [Google Scholar] [CrossRef] - Ji, Y.; Yeom, H.; Park, J. Efficient texture mapping by adaptive mesh division in mesh-based computer generated hologram. Opt. Express
**2016**, 24, 28154–28169. [Google Scholar] [CrossRef] - Matsushima, K.; Nakahara, S. Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method. Appl. Opt.
**2009**, 48, H54–H63. [Google Scholar] [CrossRef] - Abookasis, D.; Rosen, J. Three types of computer-generated hologram synthesized from multiple angular viewpoints of a three-dimensional scene. Appl. Opt.
**2006**, 45, 6533–6538. [Google Scholar] [CrossRef] [Green Version] - Shaked, N.; Katz, B.; Rosen, J. Review of three-dimensional holographic imaging by multiple-viewpoint projection-based methods. Appl. Opt.
**2009**, 48, H120–H136. [Google Scholar] [CrossRef] - Zhang, Y.; Fu, Y.; Wang, H.; Li, H.; Pan, S.; Du, Y. High resolution integral imaging display by using a microstructure array. J. Opt. Technol.
**2019**, 86, 100–104. [Google Scholar] [CrossRef] - Zhang, H.; Deng, H.; Li, J.; He, M.; Li, D.; Wang, Q. Integral imaging-based 2D/3D convertible display system by using holographic optical element and polymer dispersed liquid crystal. Opt. Lett.
**2019**, 44, 387–390. [Google Scholar] [CrossRef] - Maimone, A.; Georgiou, A.; Kollin, J. Holographic near-eye displays for virtual and augmented reality. ACM Trans. Graph.
**2017**, 36, 8501–8516. [Google Scholar] [CrossRef] - Ting, C.H.; Wokunami, K.; Yamamoto, K.; Huang, Y.P. Reconstruct holographic 3D objects by double phase hologram. Proc. SPIE
**2015**, 9495, 1–5. [Google Scholar] - Zhou, P.; Li, Y.; Liu, S.; Su, Y. Compact design for optical-see-through holographic displays employing holographic optical elements. Opt. Express
**2018**, 26, 22866–22876. [Google Scholar] [CrossRef] [PubMed] - Gentet, P.; Gentet, Y.; Lee, S. Ultimate 04 the new reference for ultra -Realistic color holography. In Proceedings of the 2017 International Conference on Emerging Trends& Innovation in ICT (ICEI), Pune, India, 3–5 February 2017; pp. 162–166. [Google Scholar]

**Figure 1.**The concept of hologram calculation. (

**a**) Projection of 3D object to different layers; (

**b**) the calculation of complex amplitude on holographic plane H.

**Figure 5.**The process of hologram calculation through convolution of corresponding PSF with projected images.

**Figure 8.**Optical reconstructions of second 3D animation model. (

**a**) Both in focus; (

**b**) Coral in focus; (

**c**) Fish in focus.

**Figure 10.**Holographic Augmented Reality (AR) 3D display system. (

**a**) Schematic of display system; (

**b**) Optical display system.

**Figure 11.**Optical experiment results. (

**a**) Fabricated HOE; (

**b**) Focused on Fish (1.2 m); (

**c**) Focused on coral (3 m).

Parameters | Values |
---|---|

SLM horizontal resolution | 1920 |

SLM vertical resolution | 1080 |

SLM pixel size | 8 μm |

LED size | 1 mm × 1 mm |

Center wavelength of LED | 528 nm |

Bandwidth of LED | 28 nm |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yang, X.; Zhang, H.; Wang, Q.-H.
A Fast Computer-Generated Holographic Method for VR and AR Near-Eye 3D Display. *Appl. Sci.* **2019**, *9*, 4164.
https://doi.org/10.3390/app9194164

**AMA Style**

Yang X, Zhang H, Wang Q-H.
A Fast Computer-Generated Holographic Method for VR and AR Near-Eye 3D Display. *Applied Sciences*. 2019; 9(19):4164.
https://doi.org/10.3390/app9194164

**Chicago/Turabian Style**

Yang, Xin, HongBo Zhang, and Qiong-Hua Wang.
2019. "A Fast Computer-Generated Holographic Method for VR and AR Near-Eye 3D Display" *Applied Sciences* 9, no. 19: 4164.
https://doi.org/10.3390/app9194164