An apparatus for exposing a substrate to an energy in a vacuum includes a substrate stage having a mirror surface; a mirror configured to deflect a light into a Z axis direction; a measuring device configured to measure the stage position in the Z axis direction with the light in which the mirror surface is irradiated; a driving device configured to move the measuring device so that the mirror surface is irradiated with the light; an optical system configured to project the energy onto the substrate; and a cooling device including a radiation plate (arranged between the optical system and the stage in the Z axis direction and having a first opening which the energy passes and a second opening which the light passes), including a cooler configured to cool the first radiation plate, and configured to perform radiation cooling of the substrate.