1. A projection system for projecting an image onto a projection body by a plurality of projection devices, comprising: an image preparation unit configured to prepare a plurality of imaging images for calibration; a grid point extraction unit configured to extract a set of grid points that indicates a distortion of a projection image for at least one projection device from each of the plurality of imaging images for calibration; a grid point transformation unit configured to execute a transformation between a plurality of images that are imaged in different imaging ranges on the plurality of imaging images for calibration in such a manner that each set of the grid points that are commonly extracted for a subject projection device is provided in a common coordinate system; a grid point synthesis unit configured to produce a set of the grid points that are synthesized for a subject projection device based on a plurality of sets of the grid points in the common coordinate system; and a correction coefficient calculation unit configured to calculate a correction coefficient for a subject projection device based on a set of the synthesized grid points.