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使用近眼成像光学结构,可以缩小体积[18]。设计之初先选定图像源,根据像素密度较小的中心视场确定像素水平,如图 2所示。
使用GALAXY S9+手机屏,分辨率为2960pixel×1440pixel,像素大小为47.25μm×47.25μm。图 3和图 4表示瞳距调节的情况。
我国成年人瞳距大多在60mm~75mm,本设计满足大多数用户瞳距调节要求,同时分辨率较高。对于瞳距较小的用户,可以适当减小水平视场。设计时控制镜片最大半径小于30mm,使最小瞳距小于60mm。图 5给出了瞳距调节为60mm时的情况。设计镜头时,单通道图像源如图 6所示。
为便于像质评价,将显示屏作为像面。由显示屏的像素大小可得到Nyquist频率和视场对应的像高,本设计半像高为44.302mm。
系统的理想成像方式是: 无穷远物体经过聚焦,在高斯像面上成像,孔阑是人眼瞳孔。
下式是系统的焦距公式:
$ f^{\prime}=y^{\prime} / \tan \omega $
(1) 式中,f′是焦距,y′是半像高,ω是半视场角。
下式是多光组系统的光焦度公式:
$ \varPhi=\frac{1}{h_{1}} \sum\limits_{1}^{k} h_{k} \varphi_{k} $
(2) 式中,Φ是总光焦度,hk是进入第k个光组的光线高度,φk是第k光组的光焦度。
使用三光组成像,合理分配光焦度。控制远离出瞳的透镜为负透镜,可以增大出瞳距离;因透镜的孔径较大,使其弯向出瞳,减小光线入射角。图 7是光学结构示意图。
图 8是ZEMAX优化后的初始结构。图 9是初始结构的点列图。可以看到,存在严重的色差和像散。图 10是初始结构的调制传递函数(modulation transfer function,MTF)曲线,大视场存在场曲,成像效果不好。
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ZEMAX优化时,需要指定玻璃库,在优化时设置替换。第3片透镜体积较大,应选用密度较小的玻璃材料,防止前重后轻,影响佩戴舒适度。玻璃库使用树脂库,整体重量较轻。将透镜面型设置为偶次非球面,优化曲率半径和非球面系数[19],同时注意控制非球面形状。
本设计中畸变要求较高,畸变与视场的三次方相关,而且慧差和畸变通常难以同时控制得很小。考虑实际使用中孔径光阑较小,对与孔径相关的慧差要求不是很高,可重点抑制畸变。畸变的产生原因是主光线的球差,一般通过最大畸变操作数能很好控制畸变。像散是实际使用中图像模糊的主要原因,需要重点优化。
优化过后,单目光学结构如图 11所示。光学系统的总长为65.7mm,最大镜片半径小于29.6mm,满足瞳距调节要求。
前两片透镜采用的材料是ARTON_D4532树脂(折射率nD=1.513722;阿贝数vD=57.5,下标D指波长为589.3nm的D光),第3片透镜材料是EP-8000树脂(nD=1.661342;vD=20.3729)。单通道光学结构的重量不超过66g。
表 1为优化后的VR HMD镜头数据。表中第2列是指透镜面的曲率半径,第3列是指光学结构各个面之间的距离。
Table 1. Lens data of VR HMD
surface radius/mm thickness/mm glass stop infinity 13 S2 474.488 7.021 ARTON_D4532 S3 -85.193 0.078 S4 29.909 16.612 ARTON_D4532 S5 -110.573 18.214 S6 -56.326 2.8 EP-8000 S7 53.119 7.978 image infinity 表 2为非球面数据。表中第2列是指各个面的圆锥系数,后4列是指非球面的偶次项系数。
Table 2. Aspheric data
surface conic the 4th order the 6th order the 8th order the 10th order S2 25.286 -3.508×10-5 2.056×10-7 -5.665×10-10 6.390×10-13 S3 -99.784 -6.225×10-5 5.667×10-8 -1.783×10-10 3.737×10-13 S4 -2.203 7.508×10-6 -1.759×10-10 -2.201×10-11 -4.208×10-15 S5 18.856 2.790×10-5 1.020×10-7 -3.071×10-10 2.305×10-13 S6 -5.281 -1.144×10-4 1.684×10-7 3.072×10-11 -1.129×10-13 S7 -18.946 -3.930×10-5 6.216×10-8 -4.873×10-11 1.764×10-14 -
设计出瞳直径为8mm,实际使用时,瞳孔直径小于3mm,并伴随眼动情形。
图 12~图 15分别是出瞳为8mm时,光学系统像质评价图。
光学系统的最大畸变为6.1%;垂轴色差很小;随着测试线对空间频率增大,各视场的MTF下降平缓,像差平衡较好。
图 16~图 20分别是出瞳直径为3mm、相对设计出瞳中心不同位置时,上半视场的MTF曲线。
出瞳直径为3mm,眼动范围在-2mm~2mm内,MTF值大于0.3,满足使用要求。
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查阅文献可得到基本公差范围,初步分配公差,一般光线入射角度越大的面公差越严格。对Nyquist频率处的MTF值进行500次Monte Carlo分析,根据仿真结果再分配公差。表 3为公差分配情况。公差要求比较宽松,成品质量也比较好,可根据造价,适当放宽、缩紧公差。
Table 3. Tolerance distribution of optical system
type tolerances surface tolerances radius/mm 0.02 thickness/mm 0.1 decenter x/mm 0.04 decenter y/mm 0.04 tilt x/(°) 0.04 tilt y/(°) 0.04 PV value/μm S2 0.6 S3 0.6 S4 0.6 S5 0.4 S6 0.4 S7 0.4 material index 0.002 Abee/% 1 element tolerances decenter x/mm 0.04 decenter y/mm 0.04 tilt x/(°) 0.04 tilt y/(°) 0.04 表 3中,decenter x是指制作过程中沿x轴的偏移,tilt x是指以x轴旋转的度数,PV(peak-to-valley)是指透镜面各点沿z轴的峰谷值,index是指折射率,Abee是指阿贝数。
表 4是蒙特卡洛运行结果。从蒙特卡洛运行结果可知,本光学系统满足像质和加工要求。
Table 4. Probability after Monte Carlo operation
probability/% MTF value(average) 98 0.33392437 90 0.34511044 80 0.35272703 50 0.36683301 20 0.37892665 10 0.38500852
大视场虚拟现实头戴显示器光学结构设计
Optical structure design of virtual reality head-mounted display with large-field
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摘要: 为了满足用户对虚拟现实头戴显示器大视场和高分辨率的需求,采用逆向设计方法,通过理论计算与软件仿真,设计了一种同轴大视场虚拟现实型头戴显示器的光学结构。结果表明,每个通道采用3片非球面透镜,全视场角为90°,出瞳直径为8mm,出瞳距离为13mm,在奈奎斯特频率10.58lp/mm处调制传递函数大于0.3,最大畸变为6.1%;与参考文献相比,此结构分辨率高、畸变小、像差平衡合理。该设计为优化大视场头戴显示器的光学结构提供了参考。Abstract: In order to meet the needs of users for large-field of view angle and high resolution of virtual reality head-mounted displays, the initial structure of the optical system was calculated by using reverse design method, and the optical design software was used for simulation analysis optical structure of coaxial large field of view virtual reality head-mounted display. The results show that three aspheric lenses are used in each channel, and the full field angle is 90°, the exit pupil diameter is 8mm, the exit pupil distance is 13mm, the modulation transfer function is greater than 0.3 at Nyquist frequency of 10.58lp/mm, and the maximum distortion is 6.1%, respectively. Compared with the reference, the resolution is higher, the distortion is reduced and aberration balance is reasonable. The design provides a reference for optimizing the optical structure of large field of view head-mounted display.
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Table 1. Lens data of VR HMD
surface radius/mm thickness/mm glass stop infinity 13 S2 474.488 7.021 ARTON_D4532 S3 -85.193 0.078 S4 29.909 16.612 ARTON_D4532 S5 -110.573 18.214 S6 -56.326 2.8 EP-8000 S7 53.119 7.978 image infinity Table 2. Aspheric data
surface conic the 4th order the 6th order the 8th order the 10th order S2 25.286 -3.508×10-5 2.056×10-7 -5.665×10-10 6.390×10-13 S3 -99.784 -6.225×10-5 5.667×10-8 -1.783×10-10 3.737×10-13 S4 -2.203 7.508×10-6 -1.759×10-10 -2.201×10-11 -4.208×10-15 S5 18.856 2.790×10-5 1.020×10-7 -3.071×10-10 2.305×10-13 S6 -5.281 -1.144×10-4 1.684×10-7 3.072×10-11 -1.129×10-13 S7 -18.946 -3.930×10-5 6.216×10-8 -4.873×10-11 1.764×10-14 Table 3. Tolerance distribution of optical system
type tolerances surface tolerances radius/mm 0.02 thickness/mm 0.1 decenter x/mm 0.04 decenter y/mm 0.04 tilt x/(°) 0.04 tilt y/(°) 0.04 PV value/μm S2 0.6 S3 0.6 S4 0.6 S5 0.4 S6 0.4 S7 0.4 material index 0.002 Abee/% 1 element tolerances decenter x/mm 0.04 decenter y/mm 0.04 tilt x/(°) 0.04 tilt y/(°) 0.04 Table 4. Probability after Monte Carlo operation
probability/% MTF value(average) 98 0.33392437 90 0.34511044 80 0.35272703 50 0.36683301 20 0.37892665 10 0.38500852 -
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