  Optics for future X-ray telescopes will be characterized by very large
aperture and focal length, and will be made of lightweight materials like glass
or plastic in order to keep the total mass within acceptable limits. Optics
based on thin slumped glass foils are currently in use in the NuSTAR telescope
and are being developed at various institutes like INAF/OAB, aiming at
improving the angular resolution to a few arcsec HEW. Another possibility would
be the use of thin plastic foils, being developed at SAO and the Palermo
University. Even if relevant progresses in the achieved angular resolution were
recently made, a viable possibility to further improve the mirror figure would
be the application of piezoelectric actuators onto the non-optical side of the
mirrors. In fact, thin mirrors are prone to deform, so they require a careful
integration to avoid deformations and even correct forming errors. This however
offers the possibility to actively correct the residual deformation. Even if
other groups are already at work on this idea, we are pursuing the concept of
active integration of thin glass or plastic foils with piezoelectric patches,
fed by voltages driven by the feedback provided by X-rays, in intra-focal setup
at the XACT facility at INAF/OAPA. In this work, we show the preliminary
simulations and the first steps taken in this project.
