a method and a device for processing a light - polymerizable material for building up an object in layers , using a lithography based generative manufacture having a construction platform for building up the object , a projecting exposure unit that can be controlled for locally selected exposing of a surface on the construction platform to an intensity pattern having a prescribed shape , and a control unit prepared for polymerizing overlapping layers on the construction platform in successive exposure steps , each having a prescribed geometry , by controlling the projecting exposure unit , in order to thus successively build up the object in the desired shape , said shape resulting from the sequence of layer geometries . the invention is characterized in that a further exposure unit for exposing the surface of the construction platform is provided on the side opposite the projecting exposure unit , and that the construction platform is designed to be at least partially transparent to light , and that the control unit is designed for controlling the further exposure unit at least while building up the first layer , said layer adhering to the construction platform , for exposing in the prescribed geometry .