Acta Optica Sinica, Volume. 38, Issue 12, 1212001(2018)
Scheme for Position Self-Calibration Based on Least Square Method
Figures & Tables(8)
Fig. 1. Schematic of positions of grid plate for self-calibration. (a) Initial position; (b) rotation of 90°; (c) translation
Fig. 3. True values and calculated errors of stage system without noise. (a) Program 1: initial position+rotation of 90°+translation; (b) program 2: initial position+rotation of 180°+translation
Table 1. Rank of relation matrix for one position
View tableTable 1. Rank of relation matrix for one position
Position combination Rank of A Number of X Initial position 2 n 2+ 74 n 2+3Rotation of 90° 2 n 2+ 74 n 2+3Rotation of 180° 2 n 2+ 74 n 2+3Translation 2 n 2- 2n+ 74 n 2+3
Table 2. Rank of relation matrix for two positions
View tableTable 2. Rank of relation matrix for two positions
Position combination Rank of A Number of X Initial position+rotation of 90° 3 . 5n 2+ 8. 54 n 2+6Initial position+rotation of 180° 3 n 2+ 94 n 2+6Initial position+translation 4 n 2- 2n+ 74 n 2+6
Table 3. Rank of relation matrix for three positions
View tableTable 3. Rank of relation matrix for three positions
Position combination Rank of A Number of X Initial position+rotation of 90°+rotation of 180° 3 . 5n 2+ 11. 54 n 2+9Initial position+rotation of 90°+translation 4 n 2+ 94 n 2+9Initial position+rotation of 180°+translation 4 n 2-n+ 104 n 2+9Initial position+translation (+ x )+translation (-x )4 n 2- 2n+ 104 n 2+9Initial position+translation ( x )+translation (y )4 n 2+ 74 n 2+9
Table 4. Rank of relation matrix for four positions
View tableTable 4. Rank of relation matrix for four positions
Position combination Rank of A Number of X Initial position+rotation of 90°+rotation of 180°+translation 4 n 2+124 n 2+12Initial position+rotation of 90°+translation (+ x )+translation (-x )4 n 2+124 n 2+12Initial position+rotation of 90°+translation ( x )+translation (y )4 n 2+124 n 2+12Initial position+rotation of 180°+translation (+ x )+translation (-x )4 n 2-n+ 134 n 2+12Initial position+rotation of 180°+translation ( x )+translation (y )4 n 2+ 104 n 2+12Initial position+translation (+ x )+translation (-x )+translation (y )4 n 2+ 104 n 2+12
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Xiaoyue Qiao, Xin Chen, Guoqing Ding, Xiaoyu Cai, Jiasi Wei, Yuan Li. Scheme for Position Self-Calibration Based on Least Square Method[J]. Acta Optica Sinica, 2018, 38(12): 1212001
Paper Information
Category: Instrumentation, Measurement and Metrology
Received: Jun. 13, 2018
Accepted: Jul. 25, 2018
Published Online: May. 10, 2019
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