Q

r m which links the mirror thickness t (r) to the central force F40.

For instance, the all-reflective Schmidt telescope Faust at f/1.5 has been built for an ultraviolet space survey of extended objects. A stainless steel Fe87Cr13 primary of 18 cm clear aperture has been built and polished flat at rest. The thickness distribution was dimensioned by to = 5.6 mm. Its edge was simply supported by a radially thin cylindrical collar linked to a rigid ring of thicknesses tz = 25 mm and tr = 14 mm. Interferograms of Fig. 5.13 display the result of flexure for each mode and their superposition. Figure 5.14 displays the theoretical images of the Faust rocket program (Monnet et al. [27], Cohendet [5]) and the improvement in image quality during the aspherization process.

Fig. 5.13 {Left) View of a circular primary mirror designed in the VTD class with k = 0. The stainless steel mirror for the FAUST experiment is shown without its deforming cell. The dimensionless thickness T40 =

allows one to compensate for aberrations at f/1.5 with a beam deviation of 30°. (Right) He-Ne interferograms of the elastic aspherization with respect to a plane. (1) Sphe 3 mode achieved by a central force F40 in reaction with the outer ring. (2) Astm 5 mode achieved by two equal axial forces F42 applied on the perimeter ring at 9 = 0,n in reaction with two forces —F42 at 9 = ±n/2. (3) Superposition of the two modes [16] (Loom)

Fig. 5.14 (Up-left) Ray traces of a reflective Schmidt in four angular sections with i = 15°, f/1.5, and field angles q = 0°, 1.25° and 2.5° from the axis. The ray traces are on the best curved focal surface. (Up-right) FAUST reflective Schmidt telescope at f/1.5, FOV=5°, F = 270mm, beam deviation 2i = 30°, primary mirror designed with k = 0 and 180 mm circular aperture. (Down) Evolution of the image quality during the in situ aspherization. The first image at the Gauss focus corresponds to the unstressed state. The measured resolution was 50 line pairs/mm over a 2.5° field diameter (Loom)

Fig. 5.14 (Up-left) Ray traces of a reflective Schmidt in four angular sections with i = 15°, f/1.5, and field angles q = 0°, 1.25° and 2.5° from the axis. The ray traces are on the best curved focal surface. (Up-right) FAUST reflective Schmidt telescope at f/1.5, FOV=5°, F = 270mm, beam deviation 2i = 30°, primary mirror designed with k = 0 and 180 mm circular aperture. (Down) Evolution of the image quality during the in situ aspherization. The first image at the Gauss focus corresponds to the unstressed state. The measured resolution was 50 line pairs/mm over a 2.5° field diameter (Loom)

5.3.5 Bisymmetric Elliptical Primary Mirror with k = 3/2 - Vase Form - Biplate Form

• Non-centered systems: All-reflective Schmidts generally provide better images with a primary of bi-axial symmetry (Sect. 4.3). Considering incident beams of circular cross section, a constant thickness plate with an elliptical contour allows simultaneously to compensate for Cv 1, Sphe 3 and the astigmatism modes Astm 3 and Astm 5 determined by (7.49) in Chap. 7. The elliptical contour of the mirror - telescope pupil - is defined by the incidence angle i of the principal beam. It is of interest to aspherize such primary mirrors by active optics methods. This simple process can also be used for other systems than Schmidts requiring aberration corrections on elliptical mirrors preferably used as pupil mirrors.

In order to directly obtain affine curvilinear flexures with meridian profiles defined by k = 3/2, we will see that a vase form must be modified into a "biplate form" made of two identical elliptical vases that are sealed together at their outer ring.

• Flexure of an elliptical plate in a vase form: Let us consider the system coordinates of an elliptical plate as shown in Fig. 5.15 and denote n the normal to the contour C of the optical clear aperture; the equation of C is represented by

ax ay

The differential equation of a flexure generated by a uniform load q, is

V4z = d4z/dx4 + 2 d4z/dx2dy2 + d4z/dy4 = q/D. (5.26)

With boundary conditions defined by a clamped edge, i.e. the origin z|c — 0 and curvilinear slope dz/d«lC = 0 of the flexure along the contour C of the ellipse (ax, ay), the bilaplacian equation is satisfied if the flexure is represented by (Bryan [2], Love [26], Timoshenko and Woinovsky-Krieger [30a])

The flexural sag z0 is obtained from substitution in the biharmonic equation

0 0

Post a comment