Position detecting method and unit, optical characteristic measuring method and unit, exposure apparatus, and device manufacturing method

A position detecting unit which detects a position of a picked-up image by a pick-up unit, the position detecting unit comprising:

• a template-preparing unit connected to the pick-up unit, which prepares a plurality of templates with which correlation values of a picture-element data distribution, as a pick-up result of the image, are calculated and which correspond to same reference images of which center positions are spaced a predetermined distance apart;
• a correlation-computing unit connected to the template-preparing unit, which, by calculating correlation values between the picture-element data distribution and the plurality of templates, obtains position of a maximum template whose correlation value is maximal;
• and
• an image-position calculating unit connected to the correlation-computing unit, which obtains at least one of a curved line function and curved surface function which fit a distribution of correlation values of the correlation values calculated and each are a function of position, the center of the distribution being present in the maximum template's position, and calculates position of the picked-up image based on the at least one function.