Patent ID: 7190456

Claim:
An apparatus for determining positions of a plurality of regions formed on a substrate based on positions of a plurality of sample regions sampled from the plurality of regions, said apparatus comprising: stage configured to hold and move the substrate; an alignment optical system configured to measure a position of each of the plurality of the sample regions sampled from the plurality of regions on the substrate held and moved by said stage; and a processor configured to control operation of said stage and said alignment optical system so as to obtain positions of the plurality of the sample regions sampled from the plurality of regions, to calculate a first conversion parameter for converting designed positions of the plurality of regions into first determined positions of the plurality of regions based on designed positions of the plurality of the sample regions and positions of the plurality of the sample regions measured by said alignment optical system, to control operation of said stage and said alignment optical system so as to obtain a position of an additional sample region sampled from the plurality of regions to increase the plurality of the sample regions, to calculate a second conversion parameter for converting designed positions of the plurality of regions into second determined positions of the plurality of regions based on designed positions of the increased plurality of the sample regions and positions of the increased plurality of the sample regions measured by said alignment optical system, and to determine whether to finish the position determinations based on a difference between the first conversion parameter and the second conversion parameter.