• Acta Optica Sinica
  • Vol. 38, Issue 2, 0205002 (2018)
Sanchao Zheng, Sumei Zhou*, Gaokun Huang, and Xiaoming Yang
Author Affiliations
  • School of Physical Science and Technology, Southwest University, Chongqing 400715, China
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    DOI: 10.3788/AOS201838.0205002 Cite this Article Set citation alerts
    Sanchao Zheng, Sumei Zhou, Gaokun Huang, Xiaoming Yang. Micro-Angle Measurement Based on Two-Dimensional Moire Fringes Generated by Square Aperture Micro-Lens Array[J]. Acta Optica Sinica, 2018, 38(2): 0205002 Copy Citation Text show less
    Schematics of two dimensional grid structures of (a) micro-graphic array and (b) square aperture micro-lens array
    Fig. 1. Schematics of two dimensional grid structures of (a) micro-graphic array and (b) square aperture micro-lens array
    Schematics of moire fringes generated by combination of square aperture micro-lens array and micro-graphic array. (a) First kind of fringe; (b) second kind of fringe
    Fig. 2. Schematics of moire fringes generated by combination of square aperture micro-lens array and micro-graphic array. (a) First kind of fringe; (b) second kind of fringe
    Relationship between moire fringe pitch and included angle. (a) a=0.2, b=0.1; (b) a=0.3, b=0.2; (c) a=0.2, b=0.2; (d) a=0.3, b=0.3; (e) a=0.2, b=0.3; (f) a=0.3, b=0.4
    Fig. 3. Relationship between moire fringe pitch and included angle. (a) a=0.2, b=0.1; (b) a=0.3, b=0.2; (c) a=0.2, b=0.2; (d) a=0.3, b=0.3; (e) a=0.2, b=0.3; (f) a=0.3, b=0.4
    Relationship between pitch variation and variation of included angle under different initial included angles. (a) (c) Variation of B1; (b) (d) variation of B2
    Fig. 4. Relationship between pitch variation and variation of included angle under different initial included angles. (a) (c) Variation of B1; (b) (d) variation of B2
    Experimental devices of small angle measurement system
    Fig. 5. Experimental devices of small angle measurement system
    Moire fringes under different included angles
    Fig. 6. Moire fringes under different included angles
    Relationship between included angle and pitch from theoretical calculation
    Fig. 7. Relationship between included angle and pitch from theoretical calculation
    Relationship between included angle and pitch from experimental measurement
    Fig. 8. Relationship between included angle and pitch from experimental measurement
    Theoretical and experimental pitch value of moire fringes when included angle is in range of (a) 0-0.1 rad and (b) 1.47-1.57 rad, respectively
    Fig. 9. Theoretical and experimental pitch value of moire fringes when included angle is in range of (a) 0-0.1 rad and (b) 1.47-1.57 rad, respectively
    θ /rad0.0100.0190.0240.0750.150.290.350.400.580.78
    B1 /μm1200.71198.31193.61159.21065.2856.3759.5709.2540.9422.8
    1190.91187.61188.71160.51058.1834.5752.9712.8536.2435.2
    1200.21185.91191.61158.61057.3836.3757.0699.8564.2419.2
    1200.51200.41192.91159.41054.9846.5754.8702.8532.4418.6
    1198.91196.71189.81162.11060.7837.9758.6689.7534.9410.8
    Average value /μm1198.21193.81191.31160.01059.2842.2756.5702.9541.7421.3
    Table 1. Fringe pitch when included angle is in range of 0-0.785 rad
    θ /rad0.780.981.161.211.271.411.491.5391.5411.55
    B2 /μm426.8541.8710.2757.6857.21059.71162.31184.61197.61200.8
    430.2539.4711.8754.4848.51062.41161.81188.91189.41196.9
    419.1544.3708.8756.1842.11057.31164.31190.31191.21200.4
    416.4537.1699.8749.8845.51059.61159.61192.91198.61200.2
    413.8542.9697.9753.6839.81060.31163.41193.81194.71199.9
    Average value /μm421.3541.1705.7754.3846.61059.91162.31190.11194.31199.6
    Table 2. Fringe pitch when included angle is in range of 0.785-1.57 rad
    Sanchao Zheng, Sumei Zhou, Gaokun Huang, Xiaoming Yang. Micro-Angle Measurement Based on Two-Dimensional Moire Fringes Generated by Square Aperture Micro-Lens Array[J]. Acta Optica Sinica, 2018, 38(2): 0205002
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