*Article* **Filtered Influence Function of Deformable Mirror for Wavefront Correction in Laser Systems**

**Yamin Zheng 1,2 , Ming Lei <sup>3</sup> , Shibing Lin 1,2, Deen Wang 1,2,4, Qiao Xue <sup>4</sup> and Lei Huang 1,2,\***


**Abstract:** An influence function filtering method (IFFM) is presented to improve the wavefront correction capability in laser systems by curbing the correction performance degradation resulted from the IF measurement noise. The IFFM is applied to the original measured IF. The resulting filtered IF is then used to calculate the wavefront control signal in each iteration of the closed-loop correction. A theoretical wavefront correction analysis model (CAM) is built. The impact of the IF measurement noise as well as the improvement of the IFFM on the wavefront correction capability are analyzed. A simulation is set up to analyze the wavefront correction capability of the filtered IF using Zernike mode aberrations. An experiment is carried out to study the effectiveness of the IFFM under practical conditions. Simulation and experimental results indicate that the IFFM could effectively reduce the negative effect of the measurement noise and improve the wavefront correction capability in laser systems. The IFFM requires no additional hardware and does not affect the correction speed.

**Keywords:** adaptive optics; influence function; wavefront correction
