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The principal outer radii of the elliptical cylinder closing the biplate are alternatively for x and y, bx,y — ax,y + tx,y — ax,y +

Given an elastic material, the eight geometrical quantities t, ax, ay, I, bx, by, tx, ty of the closed vase form and the uniform load q completely determine the as-pherization conditions of an elliptical primary mirror used as input pupil of a non-centered system reflective Schmidt telescope.

• Other applications of an elliptic closed biplate form: The above results for the primary mirror of all-reflective non-centered Schmidts can also apply to mirrors of other optical systems where a parallel beam must be folded by a plane mirror. The aspherization of such elliptical contour mirrors will provide the best results in terms of aberration corrections when a pupil is located near or at this mirror.

5.3.6 LAMOST: A Segmented Bisymmetric Elliptical Primary

Lamost is a giant all-reflective Schmidt, 4-meter clear aperture and 5° field of view, fully dedicated to spectroscopic studies. Its aspherical primary mirror is a bisymmetric elliptical shape segmented into 24 hexagons of 1.1 m in the diagonal. Each segment being flat when at rest, an active optics closed-loop control system generates, through actuators, the required asphericity which is a function of the sky position of observed objects.

Because the Lamost segments are multimode deformable mirrors (MDM) and variably aspherized in-situ at the telescope accounts of these developements are given in Sect. 7.6.4 and Sect. 8.7.3.

5.4 Aspherized Reflective Diffraction Gratings 5.4.1 Active Optics Replication for Grating Aspherization

All diffraction grating manufacturers are well aware of replication techniques. In the basic technique, the optical surface to replicate - or "master" surface - is first coated with a gold layer; then a layer of convenient epoxy resin is pressed onto this surface while slightly heated. After polymerization, the gold layer facilitates the separation of the two surfaces. Low to medium dispersion gratings for astronomical purposes are usually replicas; this allows a substantial decreases of the cost. Furthermore, it has long been known from ancient diamond ruled gratings that a single or even a double replication increases the grating efficiency by removing the sharp edges caused by the diamond.

The active optics replication technique is a straightforward process for obtaining aspherics. Applied to the making of an aspherized grating, this technique uses two replication stages and requires an active optics submaster. Starting for instance from a plane master grating, a first stage provides a plane replica on the submaster; after changing the stress state of the submaster, the second replication stage provides the final aspherized grating replica on a classical rigid substrate.

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