Hybrid gradient and curvature wavefront reconstruction algorithm with higher-order truncation error

Hybrid gradient and curvature zonal wavefront reconstruction algorithm is researched. It is proposed that wavefront reconstruction accuracy can be improved by reducing the truncation error of the reconstruction equation. The mathematical relationship for wavefront values, wavefront gradients and curvatures is calculated using Taylor expansion, obtaining the reconstruction equation whose truncation error is the 5th order of the two adjacent estimated points' interval. Applying the obtained equation to wavefront reconstruction, a new hybrid gradient and curvature wavefront reconstruction algorithm is proposed. The reconstruction error of the proposed algorithm and that of the algorithm published in the past are compared through simulations. It shows that the relative reconstruction error is reduced about two orders of magnitude by the algorithm proposed when measurement noise is ignored; when measurement noise is considered, the algorithm proposed gives apparently smaller relative reconstruction error for the reconstructions of high-order aberrations. Moreover, less calculation is needed for the algorithm proposed, and the algorithm is more appropriate in real-time wave-front measurement.