A projection objective of a microlithographic projection exposure apparatus has a high index refractive optical element with an index of refraction greater than 1.6. This element has a volume and a material related optical property which varies over the volume. Variations of this optical property cause an aberration of the objective. In one embodiment at least 4 optical surfaces are provided that are arranged in at least one volume which is optically conjugate with the volume of the refractive optical element. Each optical surface comprises at least one correction means, for example a surface deformation or a birefringent layer with locally varying properties, which at least partially corrects the aberration caused by the variation of the optical property.