镜面散射对离轴三反系统成像质量的影响

Effect of Surface Scattering on Imaging Performance for Off-Axis Three Mirror Optical System

针对天文望远镜光学系统中镜面散射对成像质量的影响,提出了一种基于反射镜表面功率谱密度计算离轴三反成像系统像面环围能量比的方法。基于Harvey-Shack散射模型,提出了像面光强分布与反射镜表面功率谱密度的关系,描述了离轴三反系统中的散射在各个反射面的传播过程,并给出了像面光强分布与反射镜表面有效均方根相对于工作波长的比值的关系。通过多手段测量获取1.5m口径加工样件在不同空间频率频段内的表面功率谱密度,利用k-相关模型拟合其全频段一维功率谱密度和二维功率谱密度,加工样件的面形精度有效均方根(在1/D到1/λ范围内)为13.7nm。对比了离轴三反系统在不同工作波长下像面环围能量比的分布,给出在我国某大型空间天文望远镜在考虑散射情况下的加工要求,镜面的有效均方根为10.3nm,其中低频误差均方根小于8nm。

Aiming at the effect of surface scattering on the imaging performance for astronomical telescope optical system, we propose a method of calculating the encircled energy in image plane based on the power spectrum density （PSD） of the mirror surface. The relationship between the intensity distribution of the image surface and the power spectral density of the mirror surface is proposed based on Harvey-Shack scattering model. The propagation of the scattering in the off-axis three mirror optical system on each reflecting surface is described. The relationship between irradiance distribution and the ratio of the effective root-mean-square （RMS） to wavelength is discussed. The surface power spectral density in different spatial frequency bands of 1.5 m-diameter optical surface is obtained by different measurements, and the full band one-dimensional and two-dimensional power spectral density are fitted by k-correlation model. It shows that the effective RMS of surface shape on the processed sample is 13.7 nm. Then the encircled energy distribution of the image plane at different wavelengths is compared. The processing requirements of a large space astronomical telescope in our country including scattering conditions are given： the effective RMS of mirror surface must be less than 10.3 nm, and the RMS of low frequency error needs to be less than 8 nm.