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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。
The structure of the image is described by spatial spectrum, the signal-to-noise ratio is represented by the ratio of the root mean square value of the image gray level to the root mean square of the noise, and the influence of the target image structure and noise on the accuracy of the related Hartmann-Shack wavefront sensing is analyzed. Theoretical analysis shows that the sub-pixel interpolation error at the peak position of the correlation function between the two sub-images is equal to the weighted average of the interpolation error at the peak position of the correlation function of each discrete frequency component. Under the same power, the weighting coefficient of the low-frequency component is small, The weighting factor is related to the sub-pixel offset. The statistical simulation of the one-dimensional narrow-band image shows that the error of the low-frequency component and the near-Nyquist frequency component is larger and the error of the mid-frequency component is smaller when there is no noise; when there is noise, the influence of noise on the high-frequency component is lower than that of the low- . The 32 × 32 image simulation of the typical spectrum shows that the calculated error of the sub-image translation is about 0.03-0.11 pixels when the signal-to-noise ratio of the image is 2: 1, which increases little compared with that without noise.