离焦像边界对曲率传感精度影响研究

Influence of defocused image boundary on curvature sensing accuracy

大口径大视场望远镜主动光学系统,需要基于离焦星点像完成波前探测与系统闭环。为了实现系统的有效运行,本文对离焦星点像边缘区域与波前传感精度之间的关系开展了相关研究。首先,根据电磁波的传输方程介绍了曲率传感算法。接着,以像散与彗差为例从理论上分析了典型边界条件对波前解算的影响。然后,分析比较了不同像元分辨率对信息完备性的影响。最后,在极限采样率下,对波前重建误差进行了仿真分析。实验结果表明在连续边界的情况下,单位圆边缘引入的误差约为35%(未进行迭代);离焦星点像在100个像元以下时,其携带信息的能力迅速下降;在接近100个像元时,对彗差的检测误差为0.08个波长,与400个像元时相比约下降14%。因此,在时-空分辨率要求较低,即采样率不高的情况下,考虑闭环主动光学的误差收敛效应,忽略边界效应也可以满足主动光学波前传感需要,但在高时-空分辨率测量的情况下,边缘的影响不可以忽略。

In the active optics(AO)system of large closed-looped survey telescopes,wavefront sensing based on defocused star images is necessary.To realize the effective operation of the AO system,this study investigates the relationship between the boundary area of a defocused image and wavefront sensing accuracy.First,a curvature sensing(CS)algorithm is introduced according to the irradiance transport equation of an electromagnetic wave.Then,by considering astigmatism and coma as examples,the influence of typical boundary conditions on wavefront sensing is theoretically investigated.Subsequently,the influence of different pixel resolutions on the completeness of information is analyzed.Finally,under the limit sampling rate,the wavefront reconstruction error is simulated and analyzed.The experimental results show that the error introduced on the edge of a unit circle is approximately 35%(without iteration).When a defocused star point image is below 100 pixels,its ability to carry information rapidly decreases.When it is close to 100 pixels,the detection error of the coma is 0.08 wavelength,which is approximately 14%lower than that at 400 pixels.Therefore,considering the error convergence effect of closed-loop active optics and ignoring the boundary effect can satisfy the requirement of active optical wavefront sensing in the case of a low time-spatial resolution,that is,at a low sampling rate.However,in the case of measurements with a high time-spatial resolution,the influence of the edge cannot be ignored.