• Acta Optica Sinica
  • Vol. 38, Issue 12, 1212001 (2018)
Xiaoyue Qiao1、*, Xin Chen1、*, Guoqing Ding1, Xiaoyu Cai2, Jiasi Wei2, and Yuan Li2
Author Affiliations
  • 1 School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
  • 2 Shanghai Institute of Measurement and Testing Technology, Shanghai 201203, China
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    DOI: 10.3788/AOS201838.1212001 Cite this Article Set citation alerts
    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 Copy Citation Text show less
    Schematic of positions of grid plate for self-calibration. (a) Initial position; (b) rotation of 90°; (c) translation
    Fig. 1. Schematic of positions of grid plate for self-calibration. (a) Initial position; (b) rotation of 90°; (c) translation
    Schematic of variables for self-calibration
    Fig. 2. Schematic of variables for self-calibration
    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
    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
    Self-calibration results of stage with noise
    Fig. 4. Self-calibration results of stage with noise
    Position combinationRank of ANumber of X
    Initial position2n2+74n2+3
    Rotation of 90°2n2+74n2+3
    Rotation of 180°2n2+74n2+3
    Translation2n2-2n+74n2+3
    Table 1. Rank of relation matrix for one position
    Position combinationRank of ANumber of X
    Initial position+rotation of 90°3.5n2+8.54n2+6
    Initial position+rotation of 180°3n2+94n2+6
    Initial position+translation4n2-2n+74n2+6
    Table 2. Rank of relation matrix for two positions
    Position combinationRank of ANumber of X
    Initial position+rotation of 90°+rotation of 180°3.5n2+11.54n2+9
    Initial position+rotation of 90°+translation4n2+94n2+9
    Initial position+rotation of 180°+translation4n2-n+104n2+9
    Initial position+translation (+x)+translation (-x)4n2-2n+104n2+9
    Initial position+translation (x)+translation (y)4n2+74n2+9
    Table 3. Rank of relation matrix for three positions
    Position combinationRank of ANumber of X
    Initial position+rotation of 90°+rotation of 180°+translation4n2+124n2+12
    Initial position+rotation of 90°+translation (+x)+translation (-x)4n2+124n2+12
    Initial position+rotation of 90°+translation (x)+translation (y)4n2+124n2+12
    Initial position+rotation of 180°+translation (+x)+translation (-x)4n2-n+134n2+12
    Initial position+rotation of 180°+translation (x)+translation (y)4n2+104n2+12
    Initial position+translation (+x)+translation (-x)+translation (y)4n2+104n2+12
    Table 4. Rank of relation matrix for four positions
    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
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