Abstract: An apparatus for detecting a position of a reference pattern or mark formed in a substrate to be aligned with a photomask pattern performs the following functions: scanning a reference pattern having at least two edges and generating a time-serial pattern signal corresponding to the scanned pattern; extracting all scanning positions at which a waveform of the pattern signal has a shape corresponding to an edge of the pattern within a predetermined scanning range including the pattern; selecting one pair from all possible pairs of a plurality of extracted scanning positions in accordance with a degree to which a pattern signal between the two scanning positions defined by each pair satisfies predetermined waveform conditions; and determining as a pattern position a predetermined position at which the interval between the two scanning positions of the selected pair is divided into two intervals by a predetermined ratio.

Abstract: A projection optical apparatus comprises a projection optical system for projecting the image of an object onto a substrate, data collecting means for obtaining data regarding a factor which causes a variation in the optical characteristic of the projection optical system, adjusting means for adjusting the relation between the substrate and the image of the object relative to the variation in the optical characteristic of the projection optical system, means for determining the amount of adjustment by the adjusting means in accordance with a model formula using a predetermined parameter on the basis of the data obtained by the data collecting means, means for independently measuring the variation in the optical characteristic of the projection optical system, and means for correcting the parameter of the model formula on the basis of the result measured by the measuring means.