tailieunhanh - New Approaches in Automation and Robotics part 14

Tham khảo tài liệu 'new approaches in automation and robotics part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The Wafer Alignment Algorithm Regardless of Rotational Center 383 The alignment space is on 2D the alignment procedure carries out translation and rotational motion. The movement can be described by rigid body transformation and the coordinate after the motion can be calculated simply by multiplying matrices. The notation of the translational matrix usually has a T the rotational matrix has an R and the center of rotation has a C . Then the transformation is formulated by equation 2 . P T R P - C C 2 TR matrices in the wafer alignment system can be derived as equations 3 and 4 which are 4 X 4 matrices. 10 0 Ax 0 0 10 0 0 0 1 3 cos Ad - sin Ad 0 0 sin Ad cos Ad 0 0 0 0 1 Ad 0 0 0 1 Basic alignment algorithm Kim et al 2006 The wafer has marks for alignment. The ideal mark position Pt is stored when the wafer is perfectly aligned. Misalignment is calculated from the current position Pc. The vision system inspects the location of the mark on the screen. These mark positions can be defined as follows. Pt xt yt dt 1 T Pc Xc yc dc 1 T 5 When the current position of the mark is deviated from the ideal one the resulting displacement can be defined as 4. The mark position in the machine can be obtained from the target position and the displacement by equation 6 . Pc P A xc Ax yc Ay 6C Ae 1 T 6 If the current position is compensated with an arbitrary value a a x a y a 0 0 the mark will be located at the target position. So an alignment algorithm f x can be written by equation 7 . f Pc a - Pt 0 7 f Pc a can be replaced with the equation from the rigid body transformation. The result is shown as 8 . The T and R have the unknown compensation variable for the current position. 384 Desktop New Approaches in Automation and Robotics T R PC - C C - Pt 0 8 The plus direction between the mathematical coordinate and vision can be reverse and the relation can be written by vision direction matrix Dv whose diagonal terms have a value of either 1 or -1 and the other terms are zero. T R