Deterministic figure correction of piezoelectrically adjustable slumped glass optics

Thin x-ray optics with high angular resolution (≤ 0.5 arcsec) over a wide field of view enable the study of a number of astrophysically important topics and feature prominently in Lynx, a next-generation x-ray observatory concept currently under NASA study. In an effort to address this technology need, piezoelectrically adjustable, thin mirror segments capable of figure correction after mounting and on-orbit are under development. We report on the fabrication and characterization of an adjustable cylindrical slumped glass optic. This optic has realized 100% piezoelectric cell yield and employs lithographically patterned traces and anisotropic conductive film connections to address the piezoelectric cells. In addition, the measured responses of the piezoelectric cells are found to be in good agreement with finite-element analysis models. While the optic as manufactured is outside the range of absolute figure correction, simulated corrections using the measured responses of the piezoelectric cells are found to improve 5 to 10 arcsec mirrors to 1 to 3 arcsec [half-power diameter (HPD), single reflection at 1 keV]. Moreover, a measured relative figure change which would correct the figure of a representative slumped glass piece from 6.7 to 1.2 arcsec HPD is empirically demonstrated. We employ finite-element analysis-modeled influence functions to understand the current frequency limitations of the correction algorithm employed and identify a path toward achieving subarcsecond corrections.