The method of operating a microlithographic projection objective of a projection exposure apparatus and the apparatus

One kind of a projection objective of a microlithographic projection exposure apparatus (10), the wavefront correction means (42) comprises, comprising: a first refractive optical element (44) and the second refractive optical element (54). The first refractive optical element comprising a first optical material, the apparatus for the operating wavelength, said first optical material decreases with increasing temperature having a refractive index. The second refractive optical element comprises a second optical material, for the operating wavelength of the device, with the second optical material having a refractive index temperature increases. The correction means (42) in the calibration mode, a first heating means (46; 146) and may generate a non-uniform temperature distribution in a first variation of the first optical material, the second heating means (56; 156 ) non-uniform and may vary in a second temperature distribution of the second optical material.