1. A method for generating a pattern of a mask to be used for illuminating the mask with an illumination optical system and projecting an image of the pattern of the mask onto a substrate through a projection optical system, the method comprising the following steps being performed by a processor: setting a pattern on an object plane of the projection optical system; shifting a pupil function representing a pupil of the projection optical system in accordance with a position of a point light source at coordinates on a pupil plane of the projection optical system for individual point light sources on the pupil plane, and generating shifted plural pupil functions; defining a matrix containing the generated plural pupil functions; calculating an image of the pattern on the object plane by generating a vector obtained by transposing and complex-conjugating a vector containing, as components, values of the pupil functions at origin coordinates on the pupil plane from among components of the matrix, and performing convolution integral between the pattern on the object plane and a Fourier transform of a product of the vector and the matrix; and generating, using the calculated image, an assist pattern for the pattern on the object plane, and generating a pattern of the mask including the pattern on the object plane and the assist pattern.