1. An image processing apparatus for use in a projector which projects and displays an image on a projection surface, the image processing apparatus comprising: an adjustment image producing section that produces an adjustment image from adjustment image data for adjusting a focus of a projected image to be displayed on the projection surface; and an imaging section that images the adjustment image projected on the projection surface and outputs an image signal according to a captured adjustment image, wherein the adjustment image producing section changes the adjustment image data to be produced, such that a grayscale pattern of the captured adjustment image obtained by imaging is close to a grayscale pattern of the adjustment image.