Manufacturing aspherical optics using stress polishing^{1} is a mature technique. It was recently used successfully to finish three toric mirrors (TMs)—which combine spherical and cylindrical surfaces—for the Very Large Telescope's Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) instrument. The high contrast required for direct imaging of exoplanets imposes stringent constraints on the optical quality of each surface, especially that of aspherical shapes. Specifications are very tight with regard to form and high-spatial-frequency (HiF) errors to both minimize residual speckles in the image plane and avoid limiting the instrument's detection capabilities.^{2}

In this context, stress polishing is well suited for realization of the three aspherical components in the common optical path. Its principle relies on spherical polishing with a full-sized tool of a warped substrate, which becomes aspherical once unwarped. The main advantage of this approach is the very high optical quality obtained in terms of both form and HiF errors. In addition, the surface roughness can be decreased to a few Ângströms using classical polishing with a large-pitch tool.

Realizing aspherical optics under stress requires minimizing the warping and polishing errors. First, we need to obtain the correct warping function corresponding to the exact inverse of the final, aspherical shape. Analytical calculations based on elasticity theory result in a definition of the blank geometry, and finite-element analysis then allows optimization of the blank shape to increase the optical quality of the warping function. For SPHERE's TMs the blank is warped using two pairs of opposite forces at the end of two orthogonal mirror diameters.^{3} An angular-thickness distribution is machined on the edge of the blank to cancel angular harmonic errors. Figure 1 shows this angular shape on the edge of the Zerodur blank for the first TM (TM1, diameter 133mm) and its deformation system.

**Figure 1. **Zerodur blank shape and deformation system. The angular-thickness distribution on the edge makes it possible to avoid high-order angular harmonics during warping.

Second, spherical polishing must be performed with a full-sized tool (see Figure 2). This very simple polishing process allows the surface to converge quickly to a quasi-perfect sphere with a very low level of form errors and almost no local defects. For TM1 we achieved a polishing form error of 6nm rms on the surface, in addition to 1.7nm rms of higher-order defects. Figure 2 (bottom) shows the final aspherical shape of TM1 after removal of the loads, with a departure from the best sphere of 8μm. We measured a form error of 9nm rms, so that the warping error was 6.7nm rms.

**Figure 2. **(top) Helium-neon interferogram of warped TM1, showing the optical quality resulting from spherical polishing with a full-sized tool. (bottom) TM1 in stress-free state, showing its aspherical shape. Departure from best sphere: 8μm. Low- and high-frequency residuals: 9 and 1.7nm rms, respectively. Roughness: 0.5nm.

We obtained a much better value for the roughness of the final surface. Classical spherical polishing with a large-pitch tool directly leads to superb results. We measured an average roughness for TM1 of 0.5nm rms, while for TM2 (diameter 40mm) we obtained 0.2nm rms for an asphericity of 1μm. Our next step is production of the final TM3, which has a diameter of 366mm and an asphericity of 20μm. Mirror warping has already been achieved, and we expect to achieve similar polishing quality as for TM1 and TM2.

We will also apply this technique to production of off-axis parabolas, for which the warping function must be modified by adding a small coma term. Once mature, this approach will drastically reduce the cost of aspherical mirrors with a superpolished finish.

Emmanuel Hugot, Kacem El Hadi

Laboratoire d'Astrophysique de Marseille

Marseille, France

Marc Ferrari

Institut National des Sciences de l'Univers/CNRS/Université de Provence

and

Laboratoire d'Astrophysique de Marseille

Marseille, France

References:

2.

J. L. Beuzit, M. Feldt, D. Mouillet, C. Moutou, K. Dohlen, P. Puget, T. Fusco, P. Baudoz, A. Bocaletti, S. Udry, D. Ségransan, R. Gratton, M. Turatto, H. M. Schmidt, R. Waters, D. Stam, P. Rabou, A. M. Lagrange, F. Ménard, J. C. Augereau, M. Langlois, F. Vakili, L. Arnold, T. Henning, D. Rouan, M. Kasper, N. Hubin, A planet finder instrument for the VLT, *Proc. Int'l Astron. Union Colloq*. 200, pp. 317-323, 2005. 3.

E. Hugot, M. Ferrari, K. El Hadi, P. Vola, J. L. Gimenez, G. R. Lemaitre, P. Rabou, K. Dohlen, P. Puget, J. L. Beuzit, N. Hubin, Active optics: stress polishing of toric mirrors for the VLT SPHERE adaptive optics system, *Appl. Opt*. 48, no. 15, pp. 2932-2941, 2009.