An illumination optical apparatus for illuminating a pattern on a mask with illumination light, the illumination optical apparatus comprising: an optical integrator arranged in an optical path of the illumination light, the optical integrator being a fly's eye lens or micro fly's eye lens; and a distribution forming optical element for forming a light intensity distribution in a region on a pupil plane of the illumination optical apparatus, the distribution forming optical element being arranged in the optical path on an incidence side of the optical integrator and being configured to be capable of forming the light intensity distribution in its far field, the region on the pupil plane being away from an optical axis of the illumination optical apparatus; characterized in that: the apparatus further comprises a polarization transforming element which is arranged in the optical path between the distribution forming optical element and the optical integrator, the polarization transforming element being made of an optical material with optical activity and being configured to provide different thicknesses of the optical material in a direction of the optical axis at different azimuthal positions about the optical axis so as to change a polarization state of the illumination light, being incident on the polarization transforming element in a linearly polarized state, so that a polarization direction of the illumination light in the region is substantially coincident with an azimuthal direction about the optical axis, and the polarization transforming element is arranged so that a direction of an optic axis of the optical material is substantially coincident with a direction of the optical axis. an optical integrator arranged in an optical path of the illumination light, the optical integrator being a fly's eye lens or micro fly's eye lens; and a distribution forming optical element for forming a light intensity distribution in a region on a pupil plane of the illumination optical apparatus, the distribution forming optical element being arranged in the optical path on an incidence side of the optical integrator and being configured to be capable of forming the light intensity distribution in its far field, the region on the pupil plane being away from an optical axis of the illumination optical apparatus; characterized in that: the apparatus further comprises a polarization transforming element which is arranged in the optical path between the distribution forming optical element and the optical integrator, the polarization transforming element being made of an optical material with optical activity and being configured to provide different thicknesses of the optical material in a direction of the optical axis at different azimuthal positions about the optical axis so as to change a polarization state of the illumination light, being incident on the polarization transforming element in a linearly polarized state, so that a polarization direction of the illumination light in the region is substantially coincident with an azimuthal direction about the optical axis, and the polarization transforming element is arranged so that a direction of an optic axis of the optical material is substantially coincident with a direction of the optical axis. the apparatus further comprises a polarization transforming element which is arranged in the optical path between the distribution forming optical element and the optical integrator, the polarization transforming element being made of an optical material with optical activity and being configured to provide different thicknesses of the optical material in a direction of the optical axis at different azimuthal positions about the optical axis so as to change a polarization state of the illumination light, being incident on the polarization transforming element in a linearly polarized state, so that a polarization direction of the illumination light in the region is substantially coincident with an azimuthal direction about the optical axis, and the polarization transforming element is arranged so that a direction of an optic axis of the optical material is substantially coincident with a direction of the optical axis.