For hyper numerical aperture (NA) lithographic projection optics, not only scalar aberration but also polarization aberration (PA) should be controlled. Optical interfaces, coatings and intrinsic birefringence of lens materials can induce polarization aberration, so they cannot be ignored at design phase. There are few comprehensive and systematic studies on PA control at design phase for lithographic optics. In this paper, a lithographic projection lens with 1.2 of NA is designed, the root-mean-square of scalar aberration reach 1nm. For PA control of this system, firstly the influence of different subsets of polarization aberration on imaging performance is analyzed. The results indicate that the scalar transmission and diattenuation mainly cause critical dimension error (CDE), and the scalar phase and retardance mainly cause pattern placement error (PE). The results also show the diattenuation is the main controlled object in the process of PA control. Furthermore, a cooperative design strategy for PA control is proposed, which is to cooperate between custom coating design and the optimization of crystal orientation based on optical structure design. Through the cooperative design, the PA can be greatly reduced, especially diattenuation. The simulation results of the final system reveal that the dynamic range of CDE is suppressed from -12.7nm ~ +4.3nm to -0.1nm ~ +0.9nm after PA control, while keeping PE at an acceptable level.