AN EXACT ALGORITHM FOR SELF-CALIBRATION OF 2-DIMENSIONAL PRECISION METROLOGY STAGES

We describe an algorithm that can achieve exact self-calibration for h igh-precision two-dimensional (2-D) metrology stages. Previous attempt s to solve this problem have often given nonexact or impractical solut ions. Self-calibration is the procedure of calibrating a metrology sta ge by an artifact plate whose mark positions are not precisely known. By assuming rigidness of the artifact plate, this algorithm extracts t he stage error map from comparison of three different measurement view s of the plate. The algorithm employs the orthogonal Fourier series to expand the stage error map, which allows fast numerical computation. When there is no random measurement noise, this algorithm exactly cali brates the stage error at those sites sampled by the mark array. In th e presence of random measurement noise, the algorithm introduces a cal ibration error of about the same size as the random measurement noise itself, which is the limit to be achieved by any self-calibration algo rithm. The algorithm has been verified by computer simulation with and without random measurement noise. Other possible applications of this algorithm are also discussed. (C) Elsevier Science Inc., 1997.