The Shack-Hartmann wavefront sensor (SHWFS) has been widely used to measure wavefronts; however, its dynamic range and measurement accuracy limit its application. The SHWFS primarily comprises a microlens array and a charge-coupled device (CCD). The dynamic range of the SHWFS depends on the ratio of the maximum allowable offset of the focal spot to the focal length of the microlens because the focal spot generated by each microlens must be located in a predefined sub-aperture region on the detector. In this study, a method based on the Sobel operator and a floating sub-aperture spot-matching algorithm is proposed to solve the problem where the focal spot of the SHWFS exceeds its corresponding sub-aperture owing to large wavefront distortions or pupil tilts.

In this study, a wavefront-reconstruction algorithm for enlarging the dynamic range of the SHWFS is proposed. First, a centroid-estimation algorithm based on the Sobel operator was used to calculate the coordinate positions of all focal spots from an entire spot-array image. This addresses the limitation of the conventional algorithm, in that the spot centroid must be extracted within the sub-aperture range. The focal spots were segmented using the Sobel edge-extraction algorithm, and the centroid of the segmented focal spot region was calculated. Additionally, because centroid extraction was only performed in the focal spot region, a high-precision centroid-extraction algorithm was used. After extracting the centroids of all spots, a spot-matching algorithm based on a floating sub-aperture was established to match the extracted spot centroids with the corresponding sub-apertures. By combining the two algorithms, a wavefront-reconstruction algorithm for a large-dynamic-range SHWFS was established.

The centroid-calculation area of the algorithm proposed in this study is only within the ranges of threshold (Fig. 3) and speck-region-connected domain segmentations (Fig. 4); therefore, the effect of noise is eliminated. When the incident beam features a large oblique aberration, the position of the spot on the CCD is shifted, thus causing the captured spot to be outside the corresponding sub-aperture region. The corresponding relationship between the centroid of the focal spot and the reference centroid was established using the proposed algorithm (Fig. 6), and the focal spot was matched to the corresponding sub-aperture (Fig. 7), thus further expanding the dynamic range of the SHWFS. The performance of the algorithm was analyzed via numerical simulation, where the incident wavefront shows a large tilt and high-order aberration (the RMS and PV values are 4.71λ and 21.76λ, respectively). Additionally, the performance of the proposed algorithm was quantitatively analyzed via numerical simulation (Fig. 9). Compared with the case of the conventional algorithm, the dynamic range of the proposed algorithm is 1.14 to 4.85 times higher.

In this study, a wavefront-reconstruction algorithm for a Shack-Hartmann wavefront sensor with a large dynamic range is proposed, which overcomes the limitation of the conventional algorithm, in that the centroid of the spot must be extracted within the sub-aperture range. Because the centroid-calculation region of the proposed algorithm is only within the spot region of the threshold and connected-domain segmentations, the effect of noise is eliminated. By matching the spot with the sub-aperture based on the floating sub-aperture spot-matching algorithm, the dynamic range is further extended by 1.14 to 4.85 times. The performance of the algorithm was analyzed through numerical simulations, and the effectiveness of the algorithm was further verified experimentally.