Abstract: A projection exposure apparatus which can perform superior observation or projection of a selected mark when the mark is observed or projected through a projection optical system in which a pupil filter is set. The projection exposure apparatus which projects a pattern on a mask through a projection optical system onto a photosensitive substrate held on a substrate stage movable in a plane perpendicular to the optical axis of the projection optical system and which has a pupil filter (optical correction plate) placed on or near the pupil plane of the projection optical system, a reference mark formed on the substrate stage in a scale factor according to the shape of the pupil filter, illuminating means for illuminating the reference mark with illumination light, and light-receiving means for receiving the illumination light having emerged from the reference mark and thereafter having passed the projection optical system.

Abstract: A substrate has a plurality of areas, from which several specific areas are selected. The coordinate positions of the specific areas on a static coordinate system are measured and the coordinate positions of the specific areas on the static coordinate system are calculated by the statistic calculation. For the respective specific areas, the calculated coordinate positions are subtracted from the measured coordinate positions to obtain the respective nonlinear position errors of the specific areas. When there is a peculiar area where the nonlinear position error exceeds an allowed value, the coordinate position of at least one area around the peculiar area is measured to obtain the nonlinear position error thereof.

Abstract: Measured is a coordinate position, on a static coordinate system, of each of some specified areas selected from a plurality of areas on a substrate. The coordinate positions of some specified areas undergo a weighted averaging process by use of such a weight that it decreases with a larger distance between the specified areas. The coordinate position is thereby smoothed per specified area. The weight is given to each of some smoothed coordinate positions, and, thereafter, a statistic calculation is effected. The coordinate position, on the static coordinate system, of the area on the substrate is thereby obtained. The substrate is sequentially located based on the obtained coordinate position, and each area on the substrate is thus aligned to a predetermined position.

Abstract: A method of aligning each of a plurality of processing areas regularly aligned on a substrate according to designed alignment coordinates to a predetermined reference position in a static coordinate system for defining the moving position of the substrate is disclosed. The coordinate positions, on the static coordinate system, of at least three processing areas selected in advance as specific processing areas from the plurality of processing areas are measured. The coordinate positions, on the static coordinate system, of the plurality of processing areas on the substrate are determined by weighting the coordinate positions, on the static coordinate system, of the at least three specific processing areas according to the distances between a processing area of interest and each of the at least three specific processing areas in units of processing areas on the substrate, and executing a statistic calculation using the plurality of weighted coordinate positions.