Active optics: deformable mirrors with a minimum number of actuators

We present two concepts of deformable mirror to compensate for first order optical aberrations. Deformation systems are designed using both elasticity theory and Finite Element Analysis in order to minimize the number of actuators. Starting from instrument specifications, we explain the methodology to design dedicated deformable mirrors. The work presented here leads to correcting devices optimized for specific functions. The Variable Off-Axis paraboLA concept is a 3-actuators, 3-modes system able to generate independently Focus, Astigmatism and Coma. The Correcting Optimized Mirror with a Single Actuator is a 1-actuator system able to generate a given combination of optical aberrations.