Polarization smoothing can effectively improve the uniformity of focal spots. In this study, we theoretically and experimentally investigated the polarization synthesis of the focal spot under a birefringent wedge (BW) and speckle under the coupling of the BW and continuous phase plate. Polarization distribution was experimentally obtained using rotating quarter-wave plate measurement under a specific wedge angle. The simulated and experimental results are consistent, demonstrating that the focal spot is in a state of coexistence of elliptical and linear polarizations. In addition, the polarization state is determined by the ratio of the amplitudes and the phase difference between the sub-beams. The simulation results showed that the proportion of linear polarization increased with the separation angle of the sub-beam. In contrast, it decreased with the incident light aperture. This research is crucial for accurately describing the polarization distribution and further understanding the laser–plasma interactions.

An advanced deformable Kirkpatrick–Baez (K-B) mirror system was developed, equipped with high-speed piezoelectric actuators, and designed to induce beam decoherence and significantly enhance the quality of X-ray imaging by minimizing undesirable speckles in synchrotron radiation or free-electron laser facilities. Each individual mirror is engineered with 36 independent piezoelectric actuators that operate in a randomized manner, orchestrating the mirror surface to oscillate at a high frequency up to 100 kHz. Through in situ imaging single-slit diffraction measurement, it has been demonstrated that this high-frequency-vibration mirror system is pivotal in disrupting the coherent nature, thereby diminishing speckle formation. The impact of the K-B mirror system is profound, with the capability to reduce the image contrast to as low as 0.04, signifying a substantial reduction in speckle visibility. Moreover, the coherence of the X-ray beam is significantly lowered from an initial value exceeding 80% to 13%.