Position detecting method and apparatus, exposure method, exposure apparatus and manufacturing method thereof, computer-readable recording medium, and device manufacturing method

摘要

An extracting unit extracts a domain regarding the relative position between a predetermined template and an observation result to be obtained by observing a mark by using an observing unit in which the distribution of correlation coefficients between the observation result and the predetermined template has a single peak from the observation result. A search unit obtains the positional relationship between the predetermined template and the observation result in which the correlation coefficient between the predetermined template and the observation result is maximum in the extracted domain by using a hill climbing method. Based on the obtained positional relationship, a position calculating unit can obtains the position of the mark. Consequently, the position of the mark can be detected with high speed and high precision.