Illumination optical system for microlithography for guiding illumination light from a primary light source to an object field , - with a mirror array with a plurality of individual mirrors , which can be tilted independently of one another by actuators and are connected to associated tilting actuators , - with a controller for activating the actuators , - with a raster module with a plurality of raster elements for producing a spatially distributed arrangement of secondary light sources, - wherein the raster module is arranged in the region of a plane of the illumination optical system , in which an emergent angle (AR x , AR y ), at which an illumination light part bundle leaves one of the raster elements , is precisely allocated to a location region in the object field , on which the illumination light part bundle impinges on the object field , - wherein the controller is configured in such a way that a specification of a tilting angle for each individual mirror is allocated to a predetermined field-dependent desired course of illumination angle intensity distributions (I 1 (x), I 2 (x), I 3 (x), I 4 (x)), by which object field points distributed over the object field are impinged upon, - wherein the raster module has two raster arrangements , which are arranged one behind another in the beam path of the illumination light , each with a plurality of raster elements , - characterized in that the arrangement and configuration of the two raster arrangements is such that a diameter of the illumination light part bundle , which impinges on one of the raster elements of the second raster arrangement , is smaller than one half of a total entry or impingement face of the raster element of the second raster arrangement . - with a mirror array with a plurality of individual mirrors , which can be tilted independently of one another by actuators and are connected to associated tilting actuators , - with a controller for activating the actuators , - with a raster module with a plurality of raster elements for producing a spatially distributed arrangement of secondary light sources, - wherein the raster module is arranged in the region of a plane of the illumination optical system , in which an emergent angle (AR x , AR y ), at which an illumination light part bundle leaves one of the raster elements , is precisely allocated to a location region in the object field , on which the illumination light part bundle impinges on the object field , - wherein the controller is configured in such a way that a specification of a tilting angle for each individual mirror is allocated to a predetermined field-dependent desired course of illumination angle intensity distributions (I 1 (x), I 2 (x), I 3 (x), I 4 (x)), by which object field points distributed over the object field are impinged upon, - wherein the raster module has two raster arrangements , which are arranged one behind another in the beam path of the illumination light , each with a plurality of raster elements , - characterized in that the arrangement and configuration of the two raster arrangements is such that a diameter of the illumination light part bundle , which impinges on one of the raster elements of the second raster arrangement , is smaller than one half of a total entry or impingement face of the raster element of the second raster arrangement . <EOS>