Curvature wavefront sensing based on a single defocused image and intensity compensation.

Curvature wavefront sensing usually requires the measurement of two defocused images at equal distances before and after the focus. In this paper, a new wavefront recovery algorithm based on only one defocused image is proposed. This algorithm contains the following four steps: response matrix calculation, establishment of intensity distribution equations, Zernike coefficients solution derived from the least squares method, and defocused image compensation with the solved Zernike coefficients. The performance of the algorithm in a large obscuration ratio and fast focal ratio optical system on axis and the edge of the field of view (FOV) is examined. Two optical systems of the Hubble telescope and a modified Paul-Baker telescope are employed to test the algorithm. The simulations show that the proposed algorithm outperforms in structural simplicity, and applications are expected in the wavefront recovery of the extreme environment (i.e., in space and the Antarctic).