As a key component of the adaptive optics (AO) system,wavefront corrector plays a crucial role in determining the performance of the AO system.At present,the typical wavefront correctors,including solid deformable mirrors and liquid crystal spatial light modulators,have the common drawbacks of high cost of per actuator channel,and the relatively low stroke deflection (normally less than 50 m) due to the limitation of material and manufacturing technology.In the face of the growing demand for deformable mirrors with large stroke,low power dissipation and low cost,the magnetic fluid based deformable mirror (MFDM) is proposed in this paper.The magnetic fluid has the characteristic of the fluidity of liquid and can be magnetized by an external magnetic field.Therefore,the surface deflection of the MFDM can be controlled by the surrounding magnetic field generated by an array of electromagnetic coils located underneath the magnetic fluid layer.Compared with the conventional deformable mirrors,the MFDM has the advantages of a continuous and smooth mirror surface,large shape deformation,low manufacture cost,and easy extension.The surface dynamics model of MFDM with a circular geometry has been studied previously in the literature.In the present paper, considering the possible applications in the wavefront control of rectangular laser beams,we study the MFDM with a rectangular array of actuators. Firstly,based on the governing equations of the magnetic fluid,derived from the principles of conservation of fluid mass and magnetic field,the dynamics model of surface deflection of the rectangular MFDM is analyzed in Cartesian coordinates under the boundary condition of magnetic field and the kinematic conditions of magnetic fluid.The analytical solutions of the surface movement of the mirror subject to the applied currents in the electromagnetic coils are obtained by properly separating the variables with truncated model numbers.Secondly,based on the derived analytical model, the optimal design procedure for the structure and parameters of the MFDM to obtain the required performance,i.e. the largest stroke and inter-actuator stroke of the mirror,as well as the coupling coefficient of the influence function, is presented.The resulting surface response performance of the designed MFDM is validated by the co-simulation in MATLAB,COMSOL Multiphysics and Tracepro software.Finally,a prototype of square MFDM consisting of the square array of miniature electromagnetic coils,a Maxwell coil and the magnetic fluid filled in a rectangular container is fabricated for experimental evaluation.The experimental results of the surface response of the mirror subject to two adjacent active coils are first presented to validate the stroke performance and linear characteristics of the MFDM. A parabolic surface shape is then further produced in the AO setup system with the MFDM subject to the array of coils driven by the currents calculated from the analytical model.The experimental results verify the accuracy of the established dynamics model and show that the proposed MFDM can be used to effectively control the wavefront of laser beam.