Optical System Design for Three Virtual Plane Augmented Reality in Vehicle Head-Up Display

Sijing Wang; Shilei Jiang; Bo Wang; Jin Zhang; Xiaowei Chen; Qiang He; Shaoyin Wang; Xuhang Gong

doi:10.3788/LOP232481

Laser & Optoelectronics Progress, Volume. 61, Issue 10, 1011012(2024)

Optical System Design for Three Virtual Plane Augmented Reality in Vehicle Head-Up Display

Sijing Wang¹, Shilei Jiang^1、*, Bo Wang², Jin Zhang¹, Xiaowei Chen², Qiang He², Shaoyin Wang¹, and Xuhang Gong¹

Author Affiliations

¹School of Opto-Electronical Engineering, Xi'an Technological University, Xi'an 710021, Shaanxi , China

²Foryou Multimedia Electronics Co., Ltd., Huizhou 516005, Guangdong , China

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Abstract Get PDF(in Chinese)

Figures & Tables(22)

Fig. 1. Schematic of three virtual image display

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Fig. 2. Schematic of virtual image size

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Fig. 3. Optimized 3D result

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Fig. 4. Dot-column diagrams at the centre eye point at different virtual image distances. (a) 10 m; (b) 7.5 m; (c) 3.5 m

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Fig. 5. MTF at the centre eye point at different virtual image distances. (a) 10 m; (b) 7.5 m; (c) 3.5 m

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Fig. 6. Grid distortion at the centre eye point at different virtual image distances. (a) 10 m; (b) 7.5 m; (c) 3.5 m

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Fig. 7. Schematic of dynamic distortion

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Fig. 8. Schematic of eyebox deflection

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Table 1. Design parameters of the optical system

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Table 1. Design parameters of the optical system

System parameter	Parameter value
VID /m	Far： 10； Middle： 7.5； Near： 3.5
FOV /［（°）×（°）］	Far： 15×5； Middle： 12×3； Near： 6×1
S_eyebox /（mm×mm）	130×50
Wavelength /nm	550
MTF /（lp·mm^-1）	>0.3@4.7
Distortion /%	<5

Table 2. Fitting data of windshield

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Table 2. Fitting data of windshield

Surface	X1Y0	X0Y1	X2Y0	X1Y1	X0Y2	X3Y0	X2Y1	X1Y2
Fitting data	0	0	-6.319	0.544	-3.658	-0.079	0.102	0.036
Surface	X0Y3	X4Y0	X3Y1	X2Y2	X1Y3	X0Y4	X5Y0	X4Y1
Fitting data	-0.011	0.017	0.039	5.5×10^-3	-9.5×10^-3	-6.7×10^-3	-1.1×10^-3	-8.8×10^-3
Surface	X3Y2	X2Y3	X1Y4	X0Y5	X6Y0	X5Y1	X4Y2	X3Y3
Fitting data	-2.5×10^-3	-4×10^-3	-1×10^-3	-3.4×10^-3	-1.1×10^-3	-1.5×10^-3	-5×10^-3	-1.8×10^-3

Table 3. Optical path structure design

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Table 3. Optical path structure design

Surface	Radius /mm	Thickness /mm	Tilt along X /（°）	Tilt along Y /（°）
Object field	‒	Far： -10000；Middle： -7500；Near： -3500；	‒	—
Windshield	‒	-450	-62.262	4.955
M₂	1034.833	285	-30.00	1.976
M₁	-646.977	Far： -342.416Middle： -310.535Near： -181.094	40.00	-2.909
Image plane	‒	‒	Far： -10.189Middle： 0Near： 0	‒

Table 4. Optimized parameters of M₁

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Table 4. Optimized parameters of M₁

Surface	X1Y0	X0Y1	X2Y0	X1Y1	X0Y2	X3Y0	X2Y1	X1Y2
Fitting data	0	0	23.501	-0.981	13.197	0.130	1.786	-0.981
Surface	X0Y3	X4Y0	X3Y1	X2Y2	X1Y3	X0Y4	X5Y0	X4Y1
Fitting data	0.0027	-0.755	0.268	1.267	1.040	-0.04	-0.406	-1.485
Surface	X3Y2	X2Y3	X1Y4	X0Y5	X6Y0	X5Y1	X4Y2	X3Y3
Fitting data	1.125	-0.949	0.126	-0.657	0.47	0.027	-0.186	-1.492
Surface	X2Y4	X1Y5	X0Y6	X7Y0	X6Y1	X5Y2	X4Y3	X3Y4
Fitting data	0.181	-0.513	0.541	0.154	0.611	-0.214	-0.092	0.571
Surface	X2Y5	X1Y6	X0Y7
Fitting data	0.22	0.138	-0.169

Table 5. Optimized parameters of M₂

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Table 5. Optimized parameters of M₂

Surface	X1Y0	X0Y1	X2Y0	X1Y1	X0Y2	X3Y0	X2Y1	X1Y2
Fitting data	0	0	35.844	-1.691	21.44	0.044	1.716	-0.705
Surface	X0Y3	X4Y0	X3Y1	X2Y2	X1Y3	X0Y4	X5Y0	X4Y1
Fitting data	0.76	0.011	0.249	0.979	1.295	-0.802	-0.106	-0.557
Surface	X3Y2	X2Y3	X1Y4	X0Y5	X6Y0	X5Y1	X4Y2	X3Y3
Fitting data	0.512	-1.135	-0.081	-2.808	0.129	-0.035	-0.085	-1.723
Surface	X2Y4	X1Y5	X0Y6	X7Y0	X6Y1	X5Y2	X4Y3	X3Y4
Fitting data	0.155	-1.094	4.947	0.032	0.171	-0.016	0.0038	1.138
Surface	X2Y5	X1Y6	X0Y7
Fitting data	0.689	0.43	-2.38

Table 6. Optimized results of lower perspective
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Table 6. Optimized results of lower perspective
D_VI /m θ /（°）
3.5 5.5
7.5 3
10 -1.5

Table 7. Radius RMS at the centre eye point at 10 m
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Table 7. Radius RMS at the centre eye point at 10 m
Field 1 2 3 4 5 6 7 8 9
Radius RMS 9.613 23.725 15.192 22.226 30.569 13.570 27.186 18.552 15.225

Table 8. Radius RMS at the centre eye point at 7.5 m
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Table 8. Radius RMS at the centre eye point at 7.5 m
Field 1 2 3 4 5 6 7 8 9
Radius RMS 19.874 9.247 15.287 28.702 19.134 15.955 17.981 6.407 10.717

Table 9. Radius RMS at the centre eye point at 3.5 m
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Table 9. Radius RMS at the centre eye point at 3.5 m
Field 1 2 3 4 5 6 7 8 9
Radius RMS 19.251 16.764 13.975 26.247 23.951 20.004 25.098 24.248 21.905

Table 10. Dynamic distortion at 10 m of projected distance

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Table 10. Dynamic distortion at 10 m of projected distance

Position	P1	P2	P3	P4	P5	P6	P7	P8	P9
Config2-Config1	0.27	0.60	1.22	0.44	1.82	1.02	0.61	1.70	0.63
Config3-Config1	0.87	0.97	1.94	1.04	2.43	1.07	0.53	1.86	0.63
Config4-Config1	0.23	0.34	1.13	0.62	1.91	1.27	1.02	2.14	1.79
Config5-Config1	1.48	1.74	1.94	1.66	1.81	1.40	0.31	0.80	0.14
Config6-Config1	0.58	0.41	0.46	0.13	0.30	0.35	1.12	0.58	1.33
Config7-Config1	0.64	0.95	1.04	0.66	2.32	0.97	1.23	2.25	0.95
Config8-Config1	1.86	2.40	2.87	2.11	3.21	1.72	0.54	2.02	0.55
Config9-Config1	1.08	1.28	1.85	1.35	2.75	1.27	1.30	1.80	0.56

Table 11. Dynamic distortion at 7.5 m of projected distance

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Table 11. Dynamic distortion at 7.5 m of projected distance

Position	P1	P2	P3	P4	P5	P6	P7	P8	P9
Config11-Config10	1.03	1.45	1.28	0.76	1.12	0.79	1.17	1.19	0.97
Config12-Config10	1.40	0.81	1.05	0.99	0.89	0.34	1.23	1.21	0.81
Config13-Config10	1.24	0.81	1.21	1.01	1.11	1.26	1.05	1.54	1.11
Config14-Config10	1.24	1.91	1.43	0.83	1.68	1.06	0.79	0.96	1.01
Config15-Config10	0.10	0.36	0.22	0.95	0.41	1.08	1.23	0.80	1.22
Config16-Config10	1.37	0.55	1.08	1.59	1.07	1.43	2.27	1.54	2.24
Config17-Config10	1.97	3.24	2.07	1.02	2.38	1.51	0.53	1.76	0.51
Config18-Config10	0.92	1.81	1.64	1.29	2.01	0.58	2.07	1.45	1.34

Table 12. Dynamic distortion at 3.5 m of projected distance

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Table 12. Dynamic distortion at 3.5 m of projected distance

Position	P1	P2	P3	P4	P5	P6	P7	P8	P9
Config20-Config19	0.67	1.62	1.81	0.73	1.71	1.99	0.80	1.86	2.29
Config21-Config19	1.37	1.60	1.18	1.44	1.70	1.31	1.52	1.85	1.55
Config22-Config19	0.66	1.59	1.82	0.70	1.70	2.07	0.73	1.89	2.43
Config23-Config19	1.33	1.59	1.60	0.76	1.01	1.12	0.63	0.32	0.29
Config24-Config19	0.42	0.25	0.32	0.42	0.25	0.30	0.58	0.38	0.38
Config25-Config19	1.50	1.52	1.39	1.54	1.60	1.45	1.74	1.81	1.70
Config26-Config19	1.17	1.96	2.07	0.66	1.61	1.77	1.19	1.86	1.99
Config27-Config19	2.42	2.57	2.04	2.12	2.26	1.72	1.64	1.95	1.43

Table 13. System tolerance allocation

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Table 13. System tolerance allocation

Parameter	Windscreen	M₁	M₂
Radius of curvature /mm	1	1	1
Spacing /mm	0.2	0.2	0.2
X direction offset /mm	0.2	0.2	0.2
Y direction offset /mm	0.2	0.2	0.2
Amount of rotation on the X axis /（°）	0.2	0.2	0.2
Amount of rotation on the Y axis /（°）	0.2	0.2	0.2

Table 14. Results of Monte Carlo analysis

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Table 14. Results of Monte Carlo analysis

Percentage	MTF at 10 m virtual image distance	MTF at 7.5 m virtual image distance	MTF at 3.5 m virtual image distance
90%	0.55338520	0.59094188	0.58008748
80%	0.55858614	0.59510540	0.58269619
50%	0.56767183	0.60199468	0.58722231
20%	0.57532117	0.60751383	0.59075959
10%	0.57775279	0.60992915	0.59234608

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Sijing Wang, Shilei Jiang, Bo Wang, Jin Zhang, Xiaowei Chen, Qiang He, Shaoyin Wang, Xuhang Gong. Optical System Design for Three Virtual Plane Augmented Reality in Vehicle Head-Up Display[J]. Laser & Optoelectronics Progress, 2024, 61(10): 1011012

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