Infrared and Laser Engineering, Volume. 51, Issue 10, 20211119(2022)
Design method of freeform surface for off-axis reflective head-mounted display optical system
Figures & Tables(20)
Fig. 1. Diagram of three-dimensional direct design method based on Marius's law
Fig. 2. Flow chart of three-dimensional direct design method based on Marius's law
Fig. 3. (a) Define the data points on pupil; (b) Define the feature rays and the starting points of feature rays
Fig. 4. (a) Layout of freeform surface single-mirror optical system in
Fig. 5. Layout of freeform surface two-mirror optical system in
Fig. 6. (a) Sag map of freeform surface fitted; (b) Layout of the optical system; (c) MTF curves of the optical system
Fig. 7. (a) Layout of the single-mirror HMD optical system after optimi-zation; (b) Grid distortion; (c) MTF curves of the optical system
Fig. 8. Layouts of freeform surface two-mirror HMD system. (a) Both F1 and F2 are spheres; (b) F1 is a freeform surface; (c) Both F1 and F2 are freeform surfaces
Fig. 9. Comparison of the average RMS spot diameter between three optical systems
Fig. 10. (a) Layout of the two-mirror HMD optical system after optimi-zation; (b) Grid distortion; (c) MTF curves of optical system
Fig. 11. Surface sag and slope diagram of freeform surface single-mirror HMD system. (a) Surface sag diagram of M1; (b) Surface slope diagram of M1
Fig. 12. Surface sag and slope of diagram of freeform surface two-mirror HMD system. (a) Surface sag diagram of F1; (b) Surface sag diagram of F2; (c) Surface slope diagram of F1; (d) Surface slope diagram of F2
Table 1. Specifications of freeform surface off-axis single-mirror HMD optical system design
View tableView in ArticleTable 1. Specifications of freeform surface off-axis single-mirror HMD optical system design
Parameter Specifications Full field of view/(°) 24(19.12×14.4) Exit pupil diameter/mm 3 Effective focal length/mm 14.25 Pixel size/μm 14.1 Distance of exit pupil/mm >15 Spectral range Visible light band Image quality >30%@35 lp/mm Distortion <5% Size of the micro display 0.25 in(6.35 mm)
Table 2. Zernike polynomial coefficients of freeform surface mirror
View tableView in ArticleTable 2. Zernike polynomial coefficients of freeform surface mirror
Polynomial $ {Z}_{i}(x,y) $ Polynomial coefficients $ {C}_{j} $ $ {Z}_{1} $ 1 $ {C}_{1} $ 18.472 $ {Z}_{2} $ 2 $x$ $ {C}_{2} $ 0 ${{Z} }_{3}$ 2 $ {y} $ $ {{C}}_{3} $ $ 9.011\times {10}^{-2} $ ${{Z} }_{4}$ $\sqrt{3}\left[2\left({{x} }^{2}+{{y} }^{2}\right)-1\right]$ ${{C} }_{4}$ $ -5.269\times {10}^{-3} $ ${{Z} }_{5}$ $2\sqrt{6}{x}{y}$ ${{C} }_{5}$ 0 ${{Z} }_{6}$ $\sqrt{6}\left({{x} }^{2}-{{y} }^{2}\right)$ ${{C} }_{6}$ $ 1.499\times {10}^{-4} $ ${{Z} }_{7}$ $ \sqrt{8}\left[3\left({{x}}^{2}+{{y}}^{2}\right)-2\right]{y} $ $ {{C}}_{7} $ $ 1.149\times {10}^{-5} $ ${{Z} }_{8}$ $ \sqrt{8}\left[3\left({{x}}^{2}+{{y}}^{2}\right)-2\right]{x} $ $ {{C}}_{8} $ 0 $ {{Z}}_{9} $ $ \sqrt{8}\left(3{{x}}^{2}-{{y}}^{2}\right){y} $ $ {{C}}_{9} $ $ 1.748\times {10}^{-6} $ $ {{Z}}_{10} $ $ \sqrt{8}\left({{x}}^{2}-{3{y}}^{2}\right){x} $ $ {{C}}_{10} $ 0 $ {{Z}}_{11} $ $ \sqrt{5}\left[6{\left({{x}}^{2}+{{y}}^{2}\right)}^{2}-6\left({{x}}^{2}+{{y}}^{2}\right)+1\right] $ $ {{C}}_{11} $ $ -6.282\times {10}^{-7} $ $ {{Z}}_{12} $ $ \sqrt{10}\left({{x}}^{2}-{{y}}^{2}\right)\left[4\left({{x}}^{2}+{{y}}^{2}\right)-3\right] $ $ {{C}}_{12} $ $ 3.439\times {10}^{-8} $ $ {{Z}}_{13} $ $ 2\sqrt{10}\left[4\left({{x}}^{2}+{{y}}^{2}\right)-3\right]{x}{y} $ $ {{C}}_{13} $ 0 $ {{Z}}_{14} $ $ \sqrt{10}\left({{x}}^{4}-{6{x}}^{2}{{y}}^{2}+{{y}}^{4}\right) $ $ {{C}}_{14} $ $ -9.838\times {10}^{-7} $ $ {{Z}}_{15} $ $ 4\sqrt{10}\left({{x}}^{2}-{{y}}^{2}\right){x}{y} $ $ {{C}}_{15} $ 0
Table 3. Specifications of freeform surface two-mirror HMD optical system design
View tableView in ArticleTable 3. Specifications of freeform surface two-mirror HMD optical system design
Parameters Specifications Micro display Micro display OLED Size 0.61 in (12.36 mm×9.36 mm) Resolution/pixel 800×600 Pixel size/μm 15 Head-mounted display system Structure Off-axis two-reflective system Exit pupil diameter/mm 8 F/# 4 Distance of exit pupil/mm >30 Full field of view/(°) 28(23×16) Performance MTF >0.4@30 lp/mm，with a 4 mm exit pupil Maximum distortion <5%
Table 4. Tolerance data for freeform surface single-mirror HMD optical system
View tableView in ArticleTable 4. Tolerance data for freeform surface single-mirror HMD optical system
Manufacture tolerance Alignment tolerance Shape error PV/λ Air thickness /mm Decenter X /mm Decenter Y /mm Tilt X/(°) Tilt Y/(°) Tilt Z/(°) M1 1/4 - ±0.2 ±0.2 ±0.2 ±0.2 ±0.2
Table 5. Tolerance data for freeform surface two-mirror HMD optical system
View tableView in ArticleTable 5. Tolerance data for freeform surface two-mirror HMD optical system
Manufacture tolerance Alignment tolerance Shape error PV/λ Air thickness /mm Decenter X /mm DecenterY /mm Tilt X/(°) Tilt Y/(°) Tilt Z/(°) F1 1/4 ±0.2 ±0.2 ±0.15 ±0.2 ±0.2 ±0.2 F2 1/4 ±0.2 ±0.2 ±0.1 ±0.2 ±0.2 ±0.25
Table 6. Tolerance analysis of freeform surface single-mirror HMD optical system
View tableView in ArticleTable 6. Tolerance analysis of freeform surface single-mirror HMD optical system
Field X field /(°) Y field /(°) Theoretical MTF avg Toleranced MTF avg MTF change 1 0 0 0.378 0.368 2.7% 2 0 7.2 0.416 0.405 2.6% 3 0 −7.2 0.495 0.482 2.6% 4 6.76 0 0.407 0.401 1.5% 5 6.76 7.2 0.356 0.338 5.1% 6 6.76 −7.2 0.535 0.530 0.9% 7 9.56 0 0.455 0.438 3.7% 8 9.56 7.2 0.328 0.315 3.9% 9 9.56 −7.2 0.532 0.528 0.7%
Table 7. Tolerance analysis for freeform surface two-mirror HMD optical system
View tableView in ArticleTable 7. Tolerance analysis for freeform surface two-mirror HMD optical system
Field X field /(°) Y field /(°) Theoretical MTF avg Toleranced MTF avg MTF change 1 0 0 0.516 0.478 7.4% 2 0 8 0.560 0.506 9.6% 3 0 −8 0.574 0.533 7.1% 4 11.5 0 0.453 0.397 12.4% 5 11.5 8 0.579 0.539 6.9% 6 11.5 −8 0.407 0.370 9.1% 7 5.75 0 0.569 0.526 7.6% 8 5.75 8 0.738 0.687 6.9% 9 5.75 −8 0.505 0.462 8.5%
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Congshan Rui, Chunmei Zeng, Zhiqiang Feng, Chengliang Xia, Yang Hong. Design method of freeform surface for off-axis reflective head-mounted display optical system[J]. Infrared and Laser Engineering, 2022, 51(10): 20211119
Paper Information
Category: Optical design
Received: Dec. 29, 2021
Accepted: --
Published Online: Jan. 6, 2023
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