Partial objective for illumination of an image field in an illuminating device of a microlithographic projection exposure apparatus, arranged between a aperture plane and an image plane. The partial objective comprises a first lens group and a second lens group with a lens with a first aspheric lens surface. The second lens group has at least a first lens with negative refractive power and at least a second lens with positive refractive power. The maximum field height Yimmax within the image field is at least 40 mm; the image-side numerical aperture is at least 0.15. The distribution of the chief ray angles PF over the field heights Yim within the image field is given by a pupil function PF(Yim), which consists of a linear contribution c1·Yim and a non-linear contribution PFNL(Yim), the non-linear contribution PFNL(Yim) being at least +15 mrad for the maximum positive field height Yimmax.