Surface shape realization of deformable mirror based on neural network

Deformable mirror (DM) is a flexible wavefront modulator with a changeable surface. It is traditionally adopted in adaptive optical system for aberration correction. Recently applications in zoom imaging system and interferometer for freeform measurement have been proposed because the improvement in fabrication technique makes larger stroke amount and faster response possible. The order and accuracy of aberration correction are typical wavefront correction characteristics of DMs. Due to the non-linearity, hysteresis and creep characteristic of piezoelectric ceramics, accurate control of piezoelectric type DM remains a challenge. Generally, the surface shape of a DM is changed by altering the voltages applied to different actuators below the DM film. And the shape of the DM can be fitted with Zernike polynomial to better characterize the aberration. So accurate control of the DM surface shape requires a relationship between the control voltage vector and the Zernike coefficients of the surface shape. We adopt neural network for the foundation of the relationship. 3000 set of control-voltage-vector and Zernike-coefficient pairs are experimentally collected based on the data measured with an interferometer and fitted with Zernike polynomials. The neural network is constructed and trained, and the control voltage vectors of new surface shapes can be retrieved with the network. The accuracy of shape realization is finally demonstrated by comparison between measured and predicted voltages.