Phase errors in gossamer membrane primary objective gratings

摘要

A ribbon-shaped primary objective grating (POG) telescope lends itself to deployment in space, because it can be stowed for transport on a roll. Unlike mirrors which need to be segmented for sizes beyond the diameter of the fairing or payload bay, the ribbon is a continuous integral surface transported on a drum and unfurled during deployment. A flat POG membrane abandons a standard three dimensional figure requirement of mirrors and solves the problem of making primary objectives from tensile structures. Moreover, POG telescopes enjoy relaxed surface dimensional tolerances compared with mirrors. We have demonstrated mathematically and empirically that the tolerance for flatness relaxes as the receiving angle increases toward grazing exodus where the magnification of the POG is greatest. At the same time, the tolerance for phase error is worsened as the angle of reconstruction moves toward grazing exodus. The problem will be aggravated by the rigors of the space deployment environment. We give a mathematical treatment for the flatness and phase error. We mention engineering methods that could ameliorate the error.