• Acta Optica Sinica
  • Vol. 38, Issue 5, 0522002 (2018)
Hailong Chen1, Yang Gao1, Dewen Cheng1、2、*, Yifan Huang1, and Yongtian Wang1、2
Author Affiliations
  • 1 Beijing Aerospace Institute of Metrology and Measurement Technology, Beijing 100076, China
  • 1 School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China
  • 2 Beijing Engineering Research Center for Mixed Reality and Advanced Display Technology, Beijing 100081, China
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    DOI: 10.3788/AOS201838.0522002 Cite this Article Set citation alerts
    Hailong Chen, Yang Gao, Dewen Cheng, Yifan Huang, Yongtian Wang. Optical Description and Design Method of Annularly Piecewise Surface[J]. Acta Optica Sinica, 2018, 38(5): 0522002 Copy Citation Text show less
    Schematic of surface transformation
    Fig. 1. Schematic of surface transformation
    Structural diagram of phone lens
    Fig. 2. Structural diagram of phone lens
    ERMS curves under different numbers of segments. (a) 2-6; (b) 6-13; (c) 13-20
    Fig. 3. ERMS curves under different numbers of segments. (a) 2-6; (b) 6-13; (c) 13-20
    Optical path of initial structure
    Fig. 4. Optical path of initial structure
    (a) Optical path when overlap of rays exists; (b) optical path when overlap of rays is solved
    Fig. 5. (a) Optical path when overlap of rays exists; (b) optical path when overlap of rays is solved
    System after optimization of aspherical surface. (a) MTF curve; (b) distortion grid
    Fig. 6. System after optimization of aspherical surface. (a) MTF curve; (b) distortion grid
    Layout of optical system with ultra-short projection lens
    Fig. 7. Layout of optical system with ultra-short projection lens
    System after optimization of annularly piecewise surface. (a) MTF curve; (b) distortion grid
    Fig. 8. System after optimization of annularly piecewise surface. (a) MTF curve; (b) distortion grid
    ParameterValue
    Digital micro-mirror device size (diagonal)16.51 mm
    Screen size (diagonal)2032 mm
    Projection distance /mm590
    Throw ratio0.29
    F number3
    Distortion<2%
    Modulation transfer function>30%@66 lp/mm
    Telecentricity /(°)<3
    Table 1. Performance parameters of ultra-short projection lens
    Segmentation methodUniformCurvatureFeedback
    ERMS /mm1.14×10-47.23×10-53.85×10-5
    Table 2. ERMS for three piecewise methods
    Number of segmentsabcd
    11.123117×10-41.371715×10-23.148854×10-3-6.005532
    29.837807×10-51.233221×10-21.755533×10-2-6.041083
    31.825474×10-46.737111×10-31.059625×10-1-6.449983
    44.177199×10-51.088035×10-28.125299×10-2-6.538591
    59.082783×10-57.099632×10-31.767819×10-1-7.332781
    61.945387×10-4-2.278891×10-34.592208×10-1-10.165570
    74.156418×10-4-2.611475×10-21.316245-20.442780
    88.242289×10-4-7.619679×10-23.362841-48.325430
    91.610584×10-3-1.809737×10-18.017051-1.172477×102
    Table 3. Polynomial coefficients of each piecewise surface
    Hailong Chen, Yang Gao, Dewen Cheng, Yifan Huang, Yongtian Wang. Optical Description and Design Method of Annularly Piecewise Surface[J]. Acta Optica Sinica, 2018, 38(5): 0522002
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