-
沉浸式HMD一般采用非瞳孔成像结构。该结构更加紧凑轻便,且光阑即为人眼瞳孔,光阑大小随瞳孔大小变化。一般采用逆向光学系统设计的方法,系统入瞳即为实际光学系统的出瞳。
人眼的瞳孔直径随着外界环境的光亮度变化范围约为2mm~8mm,HMD出瞳直径过大,会增加设计难度,增加系统重量,本文中瞳孔直径选取为8mm。一般HMD出瞳距离应不小于12mm,出瞳距离选取为12mm。HMD的视场角越大,沉浸感就越强[14],结合人眼特征,本文中设定光学系统全视场角为90°。
畸变是HMD光学系统的重要参量,与视场呈三次方关系,视场越大,畸变就越大,不同视场角的目视光学系统所允许的畸变值不同,本文中将光学系统最大畸变值设定在10%以内。
调制传递函数(modulation transfer function,MTF)能充分反映光学系统实际成像质量,对于目视光学系统而言,MTF设计值要求在奈奎斯特频率处不小于0.1,为获得较好的成像质量,本文中设计将MTF值设定为不小于0.2。
系统重量和总长也是衡量光学系统的重要指标,本文中将重量控制在50g内,总长(包括出瞳距离)控制在60mm内。
HMD光学系统性能具体参量要求如表 1所示。
Table 1. Performance parameters of HMD optical system
parameter specification wavelength visible light field of view 90° exit pupil diameter 8mm exit pupil distance 12mm total length <60mm distortion <10% MTF ≥0.2@9.31lp/mm weight <50g -
根据光学系统性能参量指标,设计中选用对角线为77.6mm的夏普液晶显示屏作为光学系统图像源,像素尺寸为53.7μm×53.7μm,分辨率为1920pixel×1080pixel,分成相同的左右两部分,分别对应左右眼睛。
由光学系统性能参量指标可知,半视场角为45°,图像源屏幕按左右眼分成完全相同的两块,可计算出每个屏幕的对角线为77.6mm,则半像高为38.8mm。光学系统视场角、有效焦距和图像源半像高之间存在以下关系:
$ h = f \times \tan \theta $
(1) 式中,f为光学系统的有效焦距,若h为图像源的半像高,θ为光学系统的半视场角,根据(1)式可进一步求出系统的有效焦距为38.8mm。
-
非球面采用偶次非球面,相较于奇次非球面,偶次非球面更容易加工,其表达式为:
$ \begin{array}{l} z = \frac{{c{r^2}}}{{1 + \sqrt {1 - (1 + k){c^2}{r^2}} }} + \\ {\alpha _2}{r^2} + {\alpha _4}{r^4} + {\alpha _6}{r^6} + {\alpha _8}{r^8} + \\ {\alpha _{10}}{r^{10}} + {\alpha _{12}}{r^{12}} + {\alpha _{14}}{r^{14}} + {\alpha _{16}}{r^{16}} \end{array} $
(2) 式中,z为表面矢高,c为曲面顶点的曲率,c=1/r0, r0为顶点曲率半径,r为光线与曲面交点的径向坐标;k为二次曲面系数,k=e2; α2, α4, α6, α8, α10, α12, α14, α16为非球面系数。
-
初始结构的选取方法有两种: 一种是运用像差理论方法计算求解得出光学系统的初始结构参量;另一种是直接在已有文献中选择与所需的参量指标相近的结构作为初始结构[15]。
作者从已有资料上选取凯尔纳目镜作为光学系统的初始结构,图 1为初始结构光路图。其半视场为22.5°,出瞳直径为4mm,出瞳距离为22mm,有效焦距为28mm。
显然,初始结构的视场角、出瞳直径和出瞳距离与HMD光学系统性能参量要求具有较大差距,需要对其进一步优化。
-
通过ZEMAX光学软件在初始结构的基础上进行多次结构调整和系统优化,大致可分为以下3个过程。
(1) 将初始结构系统焦距缩放至38.8mm;将系统中S1~S5 5个光学面的曲率半径、透镜1和透镜2的间距以及厚度作为变量,并添加相应操作数控制其范围,如有效焦距操作数控制系统有效焦距大小;通过最大畸变操作数,将系统最大畸变控制在10%内;逐步调整出瞳直径、出瞳距离和视场角,在视场角增加一定程度后手动分离双胶合透镜。
(2) 引入偶次非球面增加系统的变量和自由度,替换玻璃材料,改变材料折射率和阿贝数;继续调整视场角和出瞳距离,添加相应操作数控制系统二次项系数值、表面曲率、表面间距离,非球面系数取到10阶即可,阶数过高会使面型过于复杂。
(3) 添加相应操作数控制系统的像差,进一步提升系统成像质量。如通过子午衍射调制传递函数操作数和弧矢衍射调制传递函数操作数控制系统传递函数值,y方向主光线横向像差操作数和减法运算操作数控制垂轴色差,广义子午场曲操作数和广义弧矢场曲操作数控制场曲。
图 2为最终得到的系统光路图。图 3为光学系统3-D模型切面图。光学系统视场角为90°,出瞳直径为8mm,出瞳距离为12mm,系统总长为59.3mm,单目重量为33.67g,满足光学系统性能参量要求。透镜1为正透镜,透镜2和透镜3为负透镜,S1~S6均为偶次非球面。表 2为光学系统的透镜材料参量。其中COC(copolymers of cycloolefin)为环烯烃共聚物; DKP-A1为以芳香族为原料的聚酯树酯。表 3为光学系统的非球面参量。其中conic为圆锥曲线函数,the nth order为非球面的高阶系数。
Table 2. Material parameters of optical system lens
No. material index abbe density/(g·cm-3) element 1 COC 1.533 56.227 1.020 element 2 OKP-A1 1.649 21.451 1.210 element 3 OKP-A1 1.649 21.451 1.210 Table 3. Optical system aspheric parameters
conic the 2nd order the 4th order the 6th order the 8th order the 10th order S1 37.935 0.000 -1.495×10-5 -2.685×10-7 3.526×10-9 -1.522×10-11 S2 -0.154 0.000 -2.954×10-6 1.508×10-7 -2.170×10-11 1.724×10-12 S3 -11.883 0.000 -2.604×10-5 -7.817×10-9 -2.977×10-11 1.957×10-13 S4 -5.355 0.000 -3.490×10-5 2.005×10-8 -2.722×10-11 -1.532×10-14 S5 -94.629 0.000 2.331×10-5 -2.406×10-8 -1.263×10-11 -8.860×10-15 S6 -0.044 0.000 -1.184×10-5 1.009×10-8 -1.389×10-11 -1.419×10-14 -
光学系统在加工和装配过程中会存在一定的误差,使产品偏离设计结果。为提高产品的成像质量,降低加工装配难度和成本,需要进行合理的公差分配,增加光学系统的可行性[16],因此,光学系统设计完成后,对其进行公差分析具有十分重要的意义。
常用的公差有表面公差和元件公差,具体包括曲率半径、厚度、x/y偏心、x/y倾斜、折射率、阿贝数等公差[17]。此外,通过MATLAB软件对高次非球面的面形精度进行数值分析,建立各面型矢高矩阵,采用非线性最小二乘法拟合出偶次非球面方程,将相应系数输入到ZEMAX中,分析公差对光学系统的成像质量的影响。
公差分配好后,通过ZEMAX光学软件进行Monte Carlo分析。本文中计算分析了200个Monte Carlo样本,实际上每一个样本就是一个模拟加工、装调后的光学系统,通过计算得到光学系统视场内9.31lp/mm处的平均MTF值。表 4为光学系统的公差分配表。表中峰谷值(peak-to-valley, PV)用来表示面型精度。表 5为平均MTF值Monte Carlo分析结果。
Table 4. Tolerance distribution table of optical system
type tolerances surface tolerances radius/mm ±0.01 thickness/mm ±0.05 decenter x/mm ±0.02 decenter y/mm ±0.02 tilt x/(°) ±0.02 tilt y/(°) ±0.02 index ±0.001 abee/% ±0.5 element tolerances decenter x/mm ±0.02 decenter y/mm ±0.02 tilt x/(°) ±0.02 tilt y/(°) ±0.02 surface accuracy PV/μm S2 0.19 S3 0.52 S4 0.41 S5 0.29 S6 0.83 S7 1 Table 5. Monte Carlo analysis results
Monte Carlo analysis MTF value field 1(0°) field 2(13.5°) field 3(22.5°) field 4(31.815°) field 5(38.25°) field 6(45°) >90% 0.33145 0.57739 0.27418 0.35553 0.29823 0.24950 0.21730 >80% 0.33513 0.58377 0.28219 0.36636 0.30420 0.25775 0.23047 >50% 0.3455 0.59278 0.30030 0.38006 0.31381 0.27928 0.26116 >20% 0.35466 0.60065 0.31483 0.38966 0.32330 0.30321 0.30798 >10% 0.35847 0.603317 0.32443 0.39385 0.32805 0.31568 0.33064 表 5中给出了Monte Carlo数据大于90%, 80%, 50%, 20%, 10%的产品所能达到的传递函数。从数据可以看出,按照表 4中的公差分配设置加工、装调后,在9.31lp/mm处,90%以上的产品MTF平均值优于0.33145,90%以上的产品在视场6处的传递函数优于0.21730,均满足光学系统传递函数设计要求值。
沉浸式头戴显示器光学系统设计
Design of immersive head-mounted display optical system
-
摘要: 为了满足虚拟现实头戴显示器大视场、大出瞳和高成像质量等要求,采用非球面透镜设计了1种3片式虚拟现实头戴显示器光学系统,对光学系统进行了公差分析。结果表明,光学系统的平均调制传递函数(MTF)值均满足传递函数的要求;系统视场角为90°、出瞳直径为8mm、系统重量为33.67g、总长小于60mm、频率为9.31lp/mm时的MTF值均优于0.272,最大畸变为8.17%,最大垂轴色差为36.2μm,小于一个像素尺寸;与已有研究相比,增加了视场角、出瞳直径和出瞳距离等参量的信息,提高了成像质量。该研究为沉浸式头戴显示器的光学设计提供了参考。Abstract: In order to meet the requirements of the virtual reality head-mounted display with large field of view, large exit pupil, and high imaging quality, a three-piece virtual reality head-mounted display optical system was designed using aspheric lenses, and the tolerance analysis of the optical system was carried out.The results show that the average modulation transfer function (MTF) value of the optical system meets the transfer function requirements. The field of view of the system is 90°, the exit pupil diameter is 8mm, the system weight is 33.67g, the total length is less than 60mm, the MTF value at 9.31lp/mm is better than 0.272, the maximum distortion is 8.17%, and the maximum vertical chromatic aberration is 36.2μm that less than a pixel size, respectively. Compared with the literature, the field of view, exit pupil diameter, and exit pupil distance is respectively increased, and the imaging quality is improved. This study can provide a reference for the optical design of immersive head-mounted displays.
-
Key words:
- optical design /
- head-mounted display /
- virtual reality /
- aspheric surface /
- tolerance analysis
-
Table 1. Performance parameters of HMD optical system
parameter specification wavelength visible light field of view 90° exit pupil diameter 8mm exit pupil distance 12mm total length <60mm distortion <10% MTF ≥0.2@9.31lp/mm weight <50g Table 2. Material parameters of optical system lens
No. material index abbe density/(g·cm-3) element 1 COC 1.533 56.227 1.020 element 2 OKP-A1 1.649 21.451 1.210 element 3 OKP-A1 1.649 21.451 1.210 Table 3. Optical system aspheric parameters
conic the 2nd order the 4th order the 6th order the 8th order the 10th order S1 37.935 0.000 -1.495×10-5 -2.685×10-7 3.526×10-9 -1.522×10-11 S2 -0.154 0.000 -2.954×10-6 1.508×10-7 -2.170×10-11 1.724×10-12 S3 -11.883 0.000 -2.604×10-5 -7.817×10-9 -2.977×10-11 1.957×10-13 S4 -5.355 0.000 -3.490×10-5 2.005×10-8 -2.722×10-11 -1.532×10-14 S5 -94.629 0.000 2.331×10-5 -2.406×10-8 -1.263×10-11 -8.860×10-15 S6 -0.044 0.000 -1.184×10-5 1.009×10-8 -1.389×10-11 -1.419×10-14 Table 4. Tolerance distribution table of optical system
type tolerances surface tolerances radius/mm ±0.01 thickness/mm ±0.05 decenter x/mm ±0.02 decenter y/mm ±0.02 tilt x/(°) ±0.02 tilt y/(°) ±0.02 index ±0.001 abee/% ±0.5 element tolerances decenter x/mm ±0.02 decenter y/mm ±0.02 tilt x/(°) ±0.02 tilt y/(°) ±0.02 surface accuracy PV/μm S2 0.19 S3 0.52 S4 0.41 S5 0.29 S6 0.83 S7 1 Table 5. Monte Carlo analysis results
Monte Carlo analysis MTF value field 1(0°) field 2(13.5°) field 3(22.5°) field 4(31.815°) field 5(38.25°) field 6(45°) >90% 0.33145 0.57739 0.27418 0.35553 0.29823 0.24950 0.21730 >80% 0.33513 0.58377 0.28219 0.36636 0.30420 0.25775 0.23047 >50% 0.3455 0.59278 0.30030 0.38006 0.31381 0.27928 0.26116 >20% 0.35466 0.60065 0.31483 0.38966 0.32330 0.30321 0.30798 >10% 0.35847 0.603317 0.32443 0.39385 0.32805 0.31568 0.33064 -
[1] ZHAO Q P. Virtual reality review[J]. Science in China, 2009, F39(1): 2-46(in Chinese). [2] ZHANG Zh Y, WANG H, ZHU H X, et al. Design and realization of adaptive training system for immersive military battlefield[J]. Journal of Ordnance Equipment Engineering, 2018, 39(6): 24-26(in Chin-ese). [3] SANJOG J, KARMAKAR S, PATEL T, et al. Towards virtual ergonomics: Aviation and aerospace[J]. Aircraft Engineering and Aerospace Technology, 2015, 87(3): 32-37. [4] JIANG J, ZHI L, XIONG Z. Application of virtual reality technology in education and teaching[C]//2018 International Joint Conference on Information, Media and Engineering (ICIME). New York, USA: IEEE, 2018: 300-302. [5] JAVAID M, HALEEM A. Virtual reality applications toward medical field[J]. Clinical Epidemiology and Global Health, 2019, 8(2): 600-605. [6] HE J. Application of virtual reality technology in industrial design[J]. Journal of Physics, 2019, 1345(6): 062013. [7] CRUZ-NEIRA C, FERNÁNDEZ M, PORTALÉS C. Virtual reality and games[J]. Multimodal Technologies and Interaction, 2018, 2(1): 2010008. [8] CHENG D W, WANG Y T, CHANG J, et al. Design of a lightweight and wide field-of-view HMD system with free-form-surface prism[J]. Infrared and Laser Engineering, 2007, 36(3): 309-311(in Chinese). [9] CHENG D W, WANG Y, HUA H, et al. Design of a wide-angle, lightweight head-mounted display using free-form optics tiling[J]. Optics Letters, 2011, 36(11): 2098-2100. doi: 10.1364/OL.36.002098 [10] LV X B, WANG Zh, WEI Zh F. Lightweight design of a helmet-mounted display optical system[J]. Acta Optica Sinica, 2015, 35(10): 1022007 (in Chinese). doi: 10.3788/AOS201535.1022007 [11] CHEN J K. Design of virtual reality optical system based on human eye characteristics[D]. Suzhou: Soochow University, 2018 : 23-35(in Chinese). [12] LU Ch H, LI H F, GAO T, et al. Virtual reality head-mounted display with large field of view based on stitching[J]. Acta Optica Si-nica, 2019, 39(6): 0612002(in Chinese). doi: 10.3788/AOS201939.0612002 [13] WANG Zh Q, WANG Y, QUAN W. Design of aspheric FFA camera based on eye model[J]. Optics and Precision Engineering, 2010, 18(7): 1511-1519(in Chinese). [14] MENG X X, LIU W Q, ZHANG D L, et al. Design of wide field-of-view head-mounted display optical system with double freeform surfaces[J]. Infrared and Laser Engineering, 2016, 45(4): 189-194(in Chinese). [15] GAO X Y, CHEN P B, LI M F, et al. Design of wide angle wide depth double telecentric system[J]. Laser Technology, 2017, 41(2): 182-186(in Chinese). [16] SUN Y X, XIA Zh T, HAN H B, et al. Design and tolerance analysis of infrared off-axis three-mirror optical system with large aperture[J]. Journal of Applied Optics, 2018, 39(6): 803-808(in Chin-ese). [17] DOU X X, ZHU J W, DING G L. Design of optical system of mobile phone lens and simulation of stray light[J]. Laser Technology, 2016, 40(4): 500-505(in Chinese).