基于本征正交分解基的实时波前重构方法

气动光学畸变波前可近似表示为低阶本征正交分解(POD)基与时间系数的相乘叠加形式。当本征正交分解基已知时,如何实时获取各阶时间系数则是能否对波前进行有效低阶近似重构的关键。从波前低阶近似表达式出发建立了时间系数、基函数的空间导数与探测光束偏折角所满足的线性方程组,通过求解该方程组得到系列低阶时间系数。对实验测量的畸变波前时间序列的分析表明,该方法求解的时间系数和直接波前本征正交分解分析得到的时间系数能够较好地吻合,并且与基函数的组合也能较好地重构出波前。由于只需测量波面上稀疏布局的探测光束的偏折角,并且求解的方程组包含方程数量少,因此该系数获取方法更具有实时性,从而实现对高频变化的气动光学畸变波前的实时重构。

Real-Time Wavefront Construction Approach Based on Proper Orhtogonal Decomposition Basis Function

Aero-optical aberration wavefront can be represented as a multiplicative summation of the proper orthogonal decomposition(POD)basis functions and time coefficients.So if the basis functions are known,how to obtain the time coefficients real-timely is the key in construction the wavefront.Based on the wavefront's low order approximation expression,the linear equations set that the time coefficients,basis function's spatial derivative and the jitters of probe beams are met is established.By solving the linear equations set,the series coefficients are obtained.This approach is applied in the aberration wavefront induced by a heated jet.The results indicate that coefficients obtained by this approach are coincided with those by directed POD analysis of the wavefront time series. The coefficients combined with POD basis functions can reconstruct the wavefront effectively.Because only a few jitters need to be measured among the beam apertures and a few equations need to be solved,so the approach has the potential for real-time coefficients obtaining,sequentially for the fast wavefront reconstruction.