基于随机场的全息采样及三维显示

doi:10.3969/j.issn.0372-2112.2020.09.013

电子学报 ›› 2020, Vol. 48 ›› Issue (9): 1755-1761.DOI: 10.3969/j.issn.0372-2112.2020.09.013

基于随机场的全息采样及三维显示

范诚¹, 宋占杰^2,4, 汪火根^3,4, 蔡志森¹, 江朝川¹, 张硕⁵

1. 深圳市泛彩溢实业有限公司, 广东深圳 518104;
2. 天津大学数学学院, 天津 300354;
3. 天津大学电气自动化与信息工程学院, 天津 300072;
4. 天津大学电视与图像信息研究所, 天津 300072;
5. 天津财经大学数学系, 天津 300222

收稿日期:2018-11-13 修回日期:2020-01-20 出版日期:2020-09-25
- 通讯作者:
- 汪火根
- 作者简介:
- 范诚男,1991年毕业于四川大学,获理学博士学位,长期从事全息显示技术的研发工作.现任深圳市泛彩溢实业有限公司董事长.E-mail:drfan@afctech.com
  宋占杰 男,1965年11月生于河北.现为天津大学教授、博士生导师.主要研究方向为随机信号采样、重构与逼近及其应用.E-mail:zhanjiesong@tju.edu.cn
  江朝川 男,1992年毕业于四川大学,获博士学位.现就职于深圳市泛彩溢实业有限公司,长期从事全息显示技术的研发工作.E-mail:ccjiang01@139.com
  蔡志森 男,1979年出生.现就职于深圳市泛彩溢实业有限公司,长期从事全息显示技术的研发工作.E-mail:samchoi@afctech.com
  张硕女,1980年10月生于河北,现为天津财经大学数学系讲师,主要研究方向为随机场局部采样、重构及其应用.E-mail:shuozhang@tju.edu.cn
- 基金资助:
- 国家自然科学基金 (No.91746107，No.61901294）

Holographic Sampling and Holographic Display of Three-Dimensional Space Information Based on Random Fields

FAN Cheng¹, SONG Zhan-jie^2,4, WANG Huo-gen^3,4, CAI Zhi-sen¹, JIANG Chao-chuan¹, ZHANG Shuo⁵

1. AFC Technology CO., LTD., Shenzhen, Guangdong 518104, China;
2. School of Mathematics, Tianjin University, Tianjin 300354, China;
3. School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China;
4. Institution of TV and Image Information, Tianjin University, Tianjin 300072, China;
5. Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, China

Received:2018-11-13 Revised:2020-01-20 Online:2020-09-25 Published:2020-09-25

摘要/Abstract

摘要： 虽然真彩色实时全息显示技术在近几年已经取得了阶段性的发展，如何实现符合人眼视觉条件的理想三维显示是一项具有很有挑战性的工作.本文提出了基于随机场的局部平均采样理论，并借助光子波函数的四维傅里叶变换，搭建了以体像素和空间谱为基本抽样单位的三维空间信息的全息抽样框架，并进一步通过实例将这一新的数学模型成功应用于三维空间信息的离散采样、完整恢复与全息显示.最后借助商用4K平面显示器，结合小透镜阵列和全息功能屏，成功演示了人眼可分辨的典型完美全息三维场.

关键词: 全息采样, 全息显示, 全息功能屏, 体像素, 空间谱, 随机场, 局部平均采样, 四维傅里叶变换

Abstract: Although real-time holographic display technology has been developed in recent years,how to develop an ideal 3D(three dimension) display that meets human visual condition is always a challenging task.Based on the four-dimensional Fourier transforms of the wave function of photons,a holographic sampling theory is proposed for the information of a three-dimensional space with the sampling unit by hoxel and spectrum (spatial spectrum).It is successfully applied to the practice of three dimensional information processing such as discrete acquisition,integral restoration and holographic display of a three dimensional space.Based on a commercial 4K flat-panel displayer and the microlens arrays combined with a holographic functional screen,the perfect holographic three-dimensional displays for human vision is demonstrated.

Key words: holographic sampling, holographic display, holographic functional screen, hoxel, spactrum, random field, local average sampling, four dimensional Fourier transforms

中图分类号:

TP302

范诚, 宋占杰, 汪火根, 蔡志森, 江朝川, 张硕. 基于随机场的全息采样及三维显示[J]. 电子学报, 2020, 48(9): 1755-1761.

FAN Cheng, SONG Zhan-jie, WANG Huo-gen, CAI Zhi-sen, JIANG Chao-chuan, ZHANG Shuo. Holographic Sampling and Holographic Display of Three-Dimensional Space Information Based on Random Fields[J]. Acta Electronica Sinica, 2020, 48(9): 1755-1761.

参考文献

[1] KOLMOGOROV A N.The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers[J].The Royal Society,1991,30(4):299-303.
[2] YAGLOM A M.Some classes of random fields in n-dimensional space,related to stationary random processes[J].Theory of Probability & its Applications,1957,2(3):273-320.
[3] YAGLOM A M.Correlation Theory of Stationary and Related Random Functions.Volume I:Basic Results[M].New York:Springer-Verlag,1987.
[4] YAGLOM A M.Correlation Theory of Stationary and Related Random Functions.Volume Ⅱ:Supplementary Notes and References[M].New York:Springer-Verlag,1987.
[5] ZHANG S,SONG Z,LI Y.An advanced inversion algorithm for significant wave height estimation based on random field[J].Ocean Engineering,2016,(127):298-304.
[6] YUE Q,YAO J,Ang A H S,Spanos P D.Efficient random field modeling of soil deposits properties[J].Soil Dynamics and Earthquake Engineering,2018,(108):1-12.
[7] LIEBIG T,PIATKOWSKI N,BOCKERMANN C,MORIK K.Dynamic route planning with real-time traffic predictions[J].Information Systems,2017,100(64):258-265.
[8] SONG Z,SUN W,YANG S,ZHU G.Approximation of weak sense stationary processes from local averages[J].Science in China Series A:Mathematics,2007,50(4):457-463.
[9] SONG Z,SUN W,ZHOU X,HOU Z.An average sampling theorem for bandlimited stationary processes[J].IEEE Transactions on Information Theory,2007,12(53):4798-4800.
[10] HE G,SONG Z.Approximation of WKS sampling theorem on random signals[J].Numerical Functional Analysis and Optimization,2011,32(4):397-408.
[11] HE G,SONG Z.A rate of convergence on sampling of band limited random signals from local averages[J].Chinese Journal of Electronics,2013,22(4):747-750.
[12] ZHANG S,SONG Z,LI Y.Approximation of homogeneous random field from local averages[J].Communication in Statistics-Theory and Methods.2017,46(8):3864-3877.
[13] FAN F C,CHOI S,JIANG C C.Four dimensional fourier transform for wave function and reinvention of holography[A].Holography:Culture,Art,and Information Technology-Proceedings of the Eighth International Symposium on Display Holography[C].Shenzhen,China:River Valley TV,2009.424-452.
[14] SANG X,FAN F C,JIANG C C,et al.Demonstration of a large-size real-time full-color three-dimensional display[J].Optics Letters,2009,34(24):3803-3805.
[15] FAN F C,CHOI S,JIANG C C.Use of spatial spectrum of light to recover three-dimensional holographic nature[J].Applied Optics,2010,49(14):2676-2685.
[16] YU C,YUAN J,FAN F C,et al.The modulation function and realizing method of holographic functional screen[J].Optics Express,2010,18(26):27820-27826.
[17] FAN F C,JIANG C C,CHOI S.Thereinvention of holography[A].Techniques and Principles in Three-Dimensional Imaging:An Introductory Approach[C].Pennsylvania,USA:IGI Global,2014.167-211.
[18] BJELKHAGEN H I.Integral 3-D imaging techniques[A].Techniques and Principles in Three-Dimensional Imaging:An Introductory Approach[C].Pennsylvania,USA:IGI Global,2014.132-149.
[19] SANG X,FAN F C,CHOI S,et al.Three-dimensional display based on the holographic functional screen[J].Optical Engineering,2011,50(9):091303.
[20] LIPPMANN G.La photographie des couleurs[J].C R Hebd Seances Academic Science,1891,(112):274-275.
[21] FAN F C,CHOI S,JIANG C C.Demonstration of full-parallax three-dimensional holographic display on commercial 4K flat-panel displayer[J].Chinese Optics Letters,2016,14(1):010007.
[22] FAN F C,CHOI S,JIANG C.Demonstration of perfect holographic display on commercial 4K plane displayer[A].Digital Holography and Three-Dimensional Imaging[C].Shanghai,China:Optical Society of America,2015.DW3A.4.
[23] FAN F C,CHOI S,JIANG C.Holographic display of digital light field[A].Digital Holography and Three-Dimensional Imaging[C].Jeju Island,South Korea:Optical Society of America,2017.W3A.2.

基于随机场的全息采样及三维显示

Holographic Sampling and Holographic Display of Three-Dimensional Space Information Based on Random Fields

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

[1]	陈光辉, 曾孝平, 焦爽. 基于阵列划分的近场DOA估计算法[J]. 电子学报, 2022, 50(9): 2110-2118.
[2]	任明荣, 孟娟, 王普. MEMS-INS室内行人定位三维地图匹配算法[J]. 电子学报, 2021, 49(1): 111-116.
[3]	张成峰, 王世凯, 华彩成, 李强. 高频返回散射回波到达角探测技术研究[J]. 电子学报, 2020, 48(9): 1868-1872.
[4]	李志丹, 程吉祥, 刘家伟. 基于结构偏移映射统计和多方向特征的MRF图像修复算法[J]. 电子学报, 2020, 48(5): 985-989.
[5]	王泽宇, 吴艳霞, 张国印, 布树辉. 基于空间结构化推理深度融合网络的RGB-D场景解析[J]. 电子学报, 2018, 46(5): 1253-1258.
[6]	练秋生, 宋爽, 陈书贞, 石保顺. 基于高阶马尔可夫随机场及非线性压缩感知的相位恢复算法[J]. 电子学报, 2017, 45(9): 2210-2217.
[7]	刘威, 周婷, 袁淮, 赵宏. 基于多条件随机场模型的图像3D空间布局理解[J]. 电子学报, 2017, 45(2): 328-336.
[8]	周炫余, 刘娟, 卢笑, 邵鹏, 罗飞. 一种联合文本和图像信息的行人检测方法[J]. 电子学报, 2017, 45(1): 140-146.
[9]	赵雪梅, 李玉, 赵泉华. 基于隐马尔可夫高斯随机场模型的模糊聚类高分辨率遥感影像分割算法[J]. 电子学报, 2016, 44(3): 679-686.
[10]	宋婉莹, 李明, 张鹏, 吴艳, 贾璐, 刘高峰. 基于加权合成核与三重Markov场的极化SAR图像分类方法[J]. 电子学报, 2016, 44(3): 520-526.
[11]	陈荣元, 徐雪松, 李广琼, 申立智, 刘星宝. 自适应特征加权的Gibbs随机场影像分割方法[J]. 电子学报, 2016, 44(10): 2351-2356.
[12]	余丽玲, 阳维, 卢振泰, 冯前进, 陈武凡. 乳腺DCE-MRI增强场时间序列和组织形变场的联合估计[J]. 电子学报, 2014, 42(8): 1509-1514.
[13]	张尧烨, 孙正兴, 刘凯, 宋沫飞, 章菲倩. 基于条件随机场的模型特征线提取方法[J]. 电子学报, 2014, 42(3): 498-504.
[14]	杨志伟, 贺顺, 廖桂生, 欧阳缮. 机翼共形阵列的阵元位置估计方法[J]. 电子学报, 2013, 41(10): 1969-1974.
[15]	傅兴玉, 尤红建, 付琨. 基于改进Markov随机场的高分辨率 SAR图像建筑物分割算法[J]. 电子学报, 2012, 40(6): 1141-1147.