The disclosure relates to an optical system of an illumination device of a microlithographic projection exposure apparatus, including at least one first light-conductance-increasing element having a plurality of diffractively or refractively beam-deflecting structures extending in a common first preferred direction the light-conductance-increasing element having an optically uniaxial crystal material in such a way that the optical crystal axis of the crystal material is substantially parallel or substantially perpendicular to the first preferred direction.