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.