Self-calibrated general model-based wavefront sensorless adaptive optics for both point-like and extended objects

The deformable mirror (DM) in conventional model-based wavefront sensorless adaptive optics (WFSless AO) must be calibrated in advance by an additional WFS in order to precisely generate predetermined bias modes with known amplitudes. Although the WFS is unnecessary during correction, it will increase system complexity and may be unavailable in real applications. In this paper, the model-based WFSless AO algorithms, either for point-like or extended objects, are generalized to a unified form and the calibration problem comes down to the measurement of a Gram matrix. We proposed a novel self-calibration procedure to obtain the Gram matrix without using a WFS. The calibrated Gram matrix can be used directly for simultaneous correction if using the influence functions of DM as the bias modes, requiring N+1 images to correct N modes. Alternatively, orthogonal or gradient-orthogonal mirror modes obtained from the eigenvectors of the Gram matrix can be used as the modal basis to implement independent sequential correction that requires 2N images to correct N modes. Simulations and experiments have been done to verify the feasibility of proposed self-calibration and correction methods for both point-like and extended objects in a WFSless AO system.