A microlithographic apparatus includes an objective that includes a transmission filter that is configured to variably modify a light irradiance distribution in a projection light path. The transmission filter includes a plurality of gas outlet apertures that are configured to emit gas flows that pass through a space through which projection light propagates during operation of the microlithographic apparatus. The transmission filter further includes a control unit which is configured to vary a number density of ozone molecules in the gas flows individually for each gas flow. In this manner it is possible to finally adjust the transmittance distribution of the transmission filter.