目标图像结构和噪声对相关哈特曼-夏克波前传感精度的影响

以空间频谱描述图像结构,以图像灰度起伏的方均根值与噪声方均根值之比表示信噪比,系统分析了目标图像结构和噪声对相关哈特曼-夏克波前传感精度的影响。理论分析表明,两个子图像的相关函数峰值位置的亚像元插值误差等于其各离散频率成分的相关函数峰值位置插值误差的加权平均;相同功率下,低频成分的加权系数较小,高频成分的加权系数与亚像元偏移量有关。一维窄带图像的统计仿真表明,无噪声时,低频成分和接近奈奎斯特频率成分的误差较大,中频成分的误差较小;有噪声时,噪声对高频成分的影响低于低频成分。对典型频谱的32×32图像仿真表明,图像起伏信噪比为2∶1时,子图像平移量计算误差约0.03~0.11像元,与无噪声时相比增加不大。

Influence of Scene Structure and Noise on Precision of Correlating Hartmann-Shack Wavefront Sensing

Influence of the observed-scene structure and noise on the precision of correlating Hartmann-Shack wavefront sensing is systematically analyzed, where the scene structure is described with spatial spectrum, and the signal-noise-ratio (SNR) is described with the ratio of the root-mean-square (RMS) of image grey variance to the root-mean-square of noise. Theoretical analysis shows that the subpixel interpolation error of correlation function at peak value of two subimages is equal to the weighted average of the correlation function interpolation error (CFIE) at peak value of their discrete frequency components. With the same power, the weighting coefficient of the low-frequency components is less, and the weighting coefficient of the high-frequency components is related with the subpixel shifts. Statistical simulations of one-dimensional narrow-band images show that, in zero-noise case, the CFIEs of the frequency components near the zero frequency or Nyquist frequency are relatively larger compared with the middle-frequency components. And the influence of noise on the high-frequency components is lower than that on the low-frequency components. Simulations of broad-band images with a typical spectrum and 32×32 pixels show that, The calculating error of sub-image shift is 0.03～0.11 pixels under the signal-to-noise ratio (SNR) of 2∶1, which only has a small increase in error compared with the zero-noise case.