More Zernike modes' open-loop measurement in the sub-aperture of the Shack-Hartmann wavefront sensor

The centroid-based Shack-Hartmann wavefront sensor (SHWFS) treats the sampled wavefronts in the sub-apertures as planes, and the slopes of the sub-wavefronts are used to reconstruct the whole pupil wavefront. The problem is that the centroid method may fail to sense the high-order modes for strong turbulences, decreasing the precision of the whole pupil wavefront reconstruction. To solve this problem, we propose a sub-wavefront estimation method for SHWFS based on the focal plane sensing technique, by which more Zernike modes than the two slopes can be sensed in each sub-aperture. In this paper, the effects on the sub-wavefront estimation method of the related parameters, such as the spot size, the phase offset with its set amplitude and the pixels number in each sub-aperture, are analyzed and these parameters are optimized to achieve high efficiency. After the optimization, open-loop measurement is realized. For the sub-wavefront sensing, we achieve a large linearity range of 3.0 rad RMS for Zernike modes Z2 and Z3, and 2.0 rad RMS for Zernike modes Z4 to Z6 when the pixel number does not exceed 8 × 8 in each sub-aperture. The whole pupil wavefront reconstruction with the modified SHWFS is realized to analyze the improvements brought by the optimized sub-wavefront estimation method. Sixty-five Zernike modes can be reconstructed with a modified SHWFS containing only 7 × 7 sub-apertures, which could reconstruct only 35 modes by the centroid method, and the mean RMS errors of the residual phases are less than 0.2 rad², which is lower than the 0.35 rad² by the centroid method.