We introduce a transmissive refractive adaptive optics system featuring a deformable transparent optofluidic wavefront modulator and a sensorless wavefront error estimation algorithm. The wavefront modulator consists of a cavity filled with an optical liquid which is sealed by a deformable elastic polymer membrane. Deformation of the membrane is achieved through electrostatic actuation using 25 transparent indium tin oxide electrodes buried in the cavity. Modulation of the two-dimensional phase distribution generated by the system is performed using open loop control both with and without active wavefront sensing. For the latter, a progressive modal decomposition algorithm is used to estimate and correct distortion in the point-spread function (PSF) of the wavefront arising due to the optical system and other sources of wavefront distortion. Using this control method, we experimentally demonstrate high-fidelity recreation of Zernike modes up to the fourth order, and blind (sensorless) PSF correction in a wide-field microscope.