An inverse-polished mirror for wavefront correction of space-based telescopes

In this report we describe our development of a prototype inverse-polished mirror for the passive correction of the static and predictable wavefront errors (WFE) of space-based telescopes, in particular, especially for infrared coronagraphs. An artificial WFE pattern with a root mean square (rms) value of 350 nm was numerically generated to facilitate the design of the prototype mirror. The surface of the mirror is approximately flat, is 50.0 mm in diameter and 15.0 mm thick at the edge. The designed WFE pattern was constructed on the mirror surface by micro-polishing. Both the figure and roughness of the mirror surface were evaluated. The rms value of the measured surface figure was reduced to 135 nm after subtraction of the designed surface figure. The benefit of subtraction to mid-infrared coronagraph performance was simulated, which showed the contrast was improved by a factor of ~100 close to the core (closer than 10 λ/D where λ and D are the wavelength and telescope aperture diameter, respectively) of the coronagraphic image of a point source. An analysis of the power spectrum density shows that the lower frequencies in the WFE are well reproduced on the mirror, while the higher frequencies remain due to the limitations imposed on the controllable spatial resolution by the fabrication process. In this study, inverse-polished mirrors combined with deformable mirrors and their application to ground-based telescopes are also discussed. To fully explore the potential of the inverse-polished mirror, a systematic allocation of the error budget is essential taking into account not only the fabrication accuracy of the mirror but also an evaluation of the telescope and other factors with non-predictable uncertainties.