1. A method for producing data of an original which is used when the original is illuminated by an illumination apparatus and an image of a pattern of the original is projected onto a substrate through a projection optical system, thus forming a target pattern on the substrate, the method comprising: obtaining a two-dimensional transmission cross coefficient based on a function representing a light intensity distribution formed by the illumination apparatus on a pupil plane of the projection optical system and a pupil function of the projection optical system; calculating an approximate aerial image, which is an approximation of an aerial image on an image plane of the projection optical system, based on the two-dimensional transmission cross coefficient and data of a pattern on an object plane of the projection optical system, the calculation using one or more components of the aerial image; and producing data of the pattern of the original based on the approximate aerial image.