Active Optics—Progress in Modeling of Tulip-like Variable Curvature Mirrors

We present new results obtained from the modeling of a <i>tulip-like</i> variable curvature mirror (VCM) in the case of a central force that reacts to its contour. From Nastran finite element analysis, we shows that 3-D optimizations, using <i>non-linear static flexural option</i>, with an appropriate solution sequence, provide an accurate <i>tulip-like</i> VCM thickness distribution. This allows us to take into account boundary conditions, including the thin outer collarette and its link to a rigid ring. Modeling with a quenched stainless steel chromium substrate provides diffraction-limited optical surfaces. Rayleigh’s quarter-wave criterion is performed over a <i>zoom range</i> from flat up to <i>f</i>/3.5 convexity over a 13 mm clear aperture and 10 daN central force. The optical testing results of a prototype <i>tulip-like</i> VCM elaborated from the previous analytic theory, show quasi-diffraction-limited figures for a zoom range up to <i>f</i>/5. The present modeling results should significantly help in the future construction of such VCMs with a zoom range extended up to <i>f</i>/3.5.