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7.6.3 Non-Centered Systems and Elliptical Vase-Form Primary

Does an elliptical contour allow us to eliminate the arms of an MDM to simultaneously generate the astigmatism Astm3, Astm 5 modes as represented by A22, A42 in (7.49). In fact, we have seen in Chapter 5 that a single vase MDM form cannot provide a solution because the flexure of an elliptical ring having an homothetic geometry with the contour line C of the clear aperture would not satisfy the biharmonic equation V4z = constant. However, a solution to this problem can be obtained by "closed biplate forms" that are made of two identical elliptical vases sealed at their outer ring (cf. Sect. 5.3.5).

7.6.4 In-situ Aspherized Meniscus Segments of LAMOST

With a 4-m aperture, Lamost is by far the largest of all Schmidt telescopes. Compared to other wide-field telescopes also dedicated to spectroscopy, its 5° field of view confers the instrument an outstanding optical etendue (cf. Sect. 1.6.3) which allows obtaining simultaneously spectra of 4,000 stellar or quasi-stellar objects (cf. Sect. 4.3.4 and Sect. 8.7.3).

Lamost is a non-centered system with a segmented primary mirror M1 made of 24 hexagonal meniscus submirrors arranged in a surface of 4.4 x 5.7 meters [64]. The spherical secondary mirror M2 is with 37 segments inscribed in a 6.7-m circular aperture.

The M1 segments are polished flat when in a non-stressed state. A large dedicated machine allows the simultaneous flat polishing of four segments under immersion. The surface reference for optical testing is a plane silicon oil mirror. Then the M1 segments are stressed by 35 force-actuators including 3 displacement-actuators for a pre-calibrated aspherization. Some of the basic features of Lamost are described by Wang, Su et al. [64] and Su, Wang and Cui [61]. At the telescope, starlight sensors and an active optics closed-loop system control the in situ aspherization and ensure the asphericity variation as a function of the alt-az angles of the observed region. Observations for a given declination angle 5 e [—10°, 90°] and integration time of 1.5 hour also require the active optics to generate a variation of the x, y ellipticity of M1. The alignment control maintains the cofocusing of the M1 segments whilst their cophasing is not necessary for spectroscopy. Whatever the declination 5 of the observed field, the central incident beam at M1 is with a circular cross-section of 4 m in diameter. In the y-direction this determines the clear aperture width, 2ymax = 4m, of the primary mirror (Fig. 7.10).

If 1/R is the curvature of M2, (x, z) the telescope symmetry plane, and Q the telescope f-ratio, a first approximation shape for M1 is, from Sect. 4.3.2, z =

0 0

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