Fig. 1. Schematics of two dimensional grid structures of (a) micro-graphic array and (b) square aperture micro-lens array
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
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
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
Fig. 5. Experimental devices of small angle measurement system
Fig. 6. Moire fringes under different included angles
Fig. 7. Relationship between included angle and pitch from theoretical calculation
Fig. 8. Relationship between included angle and pitch from experimental measurement
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 /rad | 0.010 | 0.019 | 0.024 | 0.075 | 0.15 | 0.29 | 0.35 | 0.40 | 0.58 | 0.78 |
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/μm | 1200.7 | 1198.3 | 1193.6 | 1159.2 | 1065.2 | 856.3 | 759.5 | 709.2 | 540.9 | 422.8 | 1190.9 | 1187.6 | 1188.7 | 1160.5 | 1058.1 | 834.5 | 752.9 | 712.8 | 536.2 | 435.2 | 1200.2 | 1185.9 | 1191.6 | 1158.6 | 1057.3 | 836.3 | 757.0 | 699.8 | 564.2 | 419.2 | 1200.5 | 1200.4 | 1192.9 | 1159.4 | 1054.9 | 846.5 | 754.8 | 702.8 | 532.4 | 418.6 | 1198.9 | 1196.7 | 1189.8 | 1162.1 | 1060.7 | 837.9 | 758.6 | 689.7 | 534.9 | 410.8 | Average value /μm | 1198.2 | 1193.8 | 1191.3 | 1160.0 | 1059.2 | 842.2 | 756.5 | 702.9 | 541.7 | 421.3 |
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Table 1. Fringe pitch when included angle is in range of 0-0.785 rad
θ /rad | 0.78 | 0.98 | 1.16 | 1.21 | 1.27 | 1.41 | 1.49 | 1.539 | 1.541 | 1.55 |
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/μm | 426.8 | 541.8 | 710.2 | 757.6 | 857.2 | 1059.7 | 1162.3 | 1184.6 | 1197.6 | 1200.8 | 430.2 | 539.4 | 711.8 | 754.4 | 848.5 | 1062.4 | 1161.8 | 1188.9 | 1189.4 | 1196.9 | 419.1 | 544.3 | 708.8 | 756.1 | 842.1 | 1057.3 | 1164.3 | 1190.3 | 1191.2 | 1200.4 | 416.4 | 537.1 | 699.8 | 749.8 | 845.5 | 1059.6 | 1159.6 | 1192.9 | 1198.6 | 1200.2 | 413.8 | 542.9 | 697.9 | 753.6 | 839.8 | 1060.3 | 1163.4 | 1193.8 | 1194.7 | 1199.9 | Average value /μm | 421.3 | 541.1 | 705.7 | 754.3 | 846.6 | 1059.9 | 1162.3 | 1190.1 | 1194.3 | 1199.6 |
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Table 2. Fringe pitch when included angle is in range of 0.785-1.57 rad