Least squares fitting of two planar point sets for use in photolithography overlay alignment

Many automated processing systems used in semiconductor manufacturing perform an alignment of one pattern to another, or find the relationship between two coordinate systems by using pairs of measurements of points in both systems. This operation is also performed by other applications in robotics and image processing, such as the hand-eye transform and the stereo model for 3D-point estimation. This paper discusses the alignment and coordinate transform processes and the least squares criteria used in finding the best rotation, translation, and scale change for matching two point sets.