1. A projector that projects projection light on a projection object to display an image, the projector comprising: an image formation module that can form a predetermined pattern image for displaying on the projection object; a zoom lens that can change the size of the projected light region on which the projection light is projected; a controller; an imager that images the projection object; and an imaging controller that calculates an exposure calculation value from an imaged image imaged by the imager and adjusts the exposure on the imager such that the calculated exposure calculation value is nearly equivalent to an exposure target value set by the controller, and wherein the controller acquires the imaged image imaged by the imager, and changes an area of a specified color portion represented with a specified color in the pattern image which is formed in the image formation module such that a specified value of a gradient value of a specified color portion represented with the specified color becomes approximately equivalent to a desired gradient value in the acquired imaged image.