tzN+1 20.000

• Execution of a hyperboloid Cassegrain mirror: Hyperboloid Cassegrain mirrors are classical secondary mirrors for PH or RC telescopes. The active optics apherization was carried out for two sample secondary mirrors of the 90-cm solar RC telescope Themis, f/3.5-f/17, installed in Tenerife [24] (Fig. 6.16). The optical parameters of the telescope main mirrors M1 and M2 are R1 =6,270 mm, R2=1,683mm, k1 = - 1.036, k2 = - 2.62 and their axial separation is M1M2 = 2,465 mm. The telescope tube is equipped with a 1-m enclosure plate for a vacuum. A tip-tilt mirror allows atmospheric corrections for both imaging and spectroscopic modes. This latter mode provides high spectral resolution capabilities.

Fig. 6.16 THEMIS France-Italia-Spain solar observatory (courtesy Cnrs-Cnr-Iac)

Beside the active optics advantage of obtaining a smooth surface secondary mirror, the thin clear aperture area - aspect-ratio 2rN/t0 — 19 - of a vase shell geometry allows a fast thermal exchange by cooling system located inside the vase shell.

Two sample secondaries were hyperbolized by elastic relaxation after spherical figuring under stress. The analytical shell theory in Sect. 6.3.4 with N=10 shell elements, including a simply supported movable base of the outer cylinder N +1, allowed the iterative determination of the normal thickness distribution {tn} of the vase shell where all successive ring-shell elements have a rN/N radial width (Fig. 6.17 and Table 6.8).

From the result of iterations with the shell theory, the active optics superposition law of the surfaces writes, in [mm], zsphe = 0.294684 10-3 r2 + 0.25590 10-10 r4 + 0.4444 10-17 r6 + 0.964 10-24 r8 zFlex = 0.002405 10-3 r2 - 0.68070 10-10 r4 - 0.4441 10-17 r6 - 0.964 10-24 r8 zsum = 0.297089 10-3 r2 - 0.42480 10-10 r4 - 0.3179 10-46 r6 + 0.481 10-50 r8 zOpt = 0.297089 10-3 r2 - 0.42480 10-10 r4 + 0.0000 10+00 r6 + 0.000 10+00 r8

from where we satisfy zSphe + zFlex = zOpt. The dimensionless radius p = r/rN for which dzFlex/dr = 0 is po=1.055. The total flexure sag in the range p e [0; 1 ] is AzFlex=20.98 ¡m. The vase geometry of two Zerodur secondary mirror samples were obtained by computer numerical control diamond turning. After spherical figuring under stress and elastic relaxation, the results from He-Ne interferometric tests showed that the hyperboloid surfaces were obtained within X/12 ptv for each sample.

Fig. 6.17 Left: Design and rear view of the f/3.33 vase shell THEMIS secondary mirror in Schott Zerodur. Right: Fizeau He-Ne interferogram with respect to a sphere after stress polishing and elastic relaxation (Loom)

Table 6.8 Normal thickness distribution {tn} for the hyperbolization of THEMIS f/3.33 vase secondary mirrors. Mirror clear aperture 252 mm. Schott Zerodur E =90.2 GPa. Load q =80kPa. rN = 126mm, tx = 30mm. Ropt = 1,683mm, Rsphe = 1,696.7mm, Rplex = 208,029mm, <R>=1,657 mm

VASE Shell Mirror. Cylinder outer edge radius rOE=150. [Units: mm]

13.16 13.16 13.17 13.18 13.20 13.22 13.24 13.26 13.29 13.31 50.000

6.6.6 Comparison of Various Wide-Field Telescope Designs

Although Schmidt telescopes with refractive corrector plates provide an accurate imaging correction for a 5° sky field, this design suffers from aperture size limitation - due to the difficulty of obtaining homogeneous glass plates larger than 1 or 1.2 m-, spherochromatism residuals and field curvature. Larger Schmidt systems of the all-reflection type similarly suffer from field curvature which is a difficulty for the implementation of a flat and large CCD detector array.

For the purpose of wide-field astronomical sky surveys, typically 1-2° fields with large telescope diameters, various designs in the 2-4 m class have been investigated and some of them have been built. A comparison of possible various wide-field telescope designs show important variations in the overall length and chromatism residual correction (Fig. 6.18).

Fig. 6.18 Comparison of five wide-field telescope designs having the same input beam diameter, focal length and field of view

• (A) Schmidt telescope with refractive corrector plate: The overall length is two times the focal length, L = 2 f. Convex field curvature, cP = 1/ f.

^ Three optical surfaces including one aspheric.

• (B) Mersenne-Schmidt telescope by Willstrop [30]: The overall length slightly exceeds the focal length, L ~ f, when the focal surface is near M1. Flat field curvature, cP = 0. The Sphe3 correction of the spherical tertiary mirror is achieved by deformation of the paraboloid secondary mirror, so the center of curvature of M3 mirror must be located at the M2 vertex.

^ Three optical surfaces including two aspherics.

• (C) Paraboloid and Wynne triplet lens corrector: The overall length is equal to the focal length, L = f. Flat field curvature, cP = 0. For a wide spectral range as XX [350nm-1 ^m] and field of view larger than 1°, this system suffers from chro-matism residuals larger than 1 arcsec. With a moderate spectral range, this system operates at Canada France Hawaii telescope (Cfht) [23].

^ Seven optical surfaces including one aspheric.

• (D) Flat-field Ritchey-Chretien and doublet lens corrector: The overall length is about half the focal length, L = f /2. The flat field curvature is achieved by equalizing the curvature of the two mirrors, cP = 0. The null power doublet lens provides the correction of Astm 3. For a wide spectral range and field larger than 1 °, curvature, cP = 0. For a wide spectral range as XX [350nm-1 ^m] and field of view larger than 1°, this system also suffers from chromatism residuals larger than 1 arcsec. For limited spectral ranges, this design was built as a 2.5-m aperture telescope at f/2.5/5 for the Slaon Digital Sky Survey (Sdss) operating at the Apache Point observatory, New-Mexico [28]. Similar form survey telescopes with the Vst and Vista should star observations in 2008.

^ Six optical surfaces including two aspherics.

• (E) Three-reflection Rumsey telescope: The compact three-reflection telescope proposed in 1969 by Norman Rumsey [27] shows an overall length about two-times smaller than the focal length, L ~ f /2, thus is very similar length to design (D). This anastigmatic system provides a null Petzval sum, cP = 0. The design does not suffer from the chromatism residuals inherent to the above lens corrector systems. For good seeing sites, the spherochromatism due to the thickness of the pass-band filters and cryostat window can be made negligible because the image sampling requires a telescope design of low f-ratio, such as f/5. For a large spectral range, this allows obtaining a flat field up to two degrees, i.e. 1.5x1.5° whose aberration residuals can be made smaller than 0.25 arcsec and where the beam baffling and vignetting is similar to design D.

^ Three aspherical surfaces.

other optical designs based on three-mirror concepts with additional corrector lenses are under investigation such as, for instance, the Large Synoptic Survey Telescope (Lsst) project; however these designs are more complex and obtaining both high throughput and large spectral range capabilities from UV to IR is a major difficulty.

From the above five systems, the Rumsey design is a compact system - about 4-times shorter than a Schmidt - which provides the best optical performances for a 2° FoV and large spectral range capability from UV to IR. The central obstruction of the Rumsey is similar to that of the flat-field Ritchey-Chretien (D). We shall see in the next sections that, with a slightly modified Rumsey form, the active optics aspherization of the mirrors provides a high accuracy and important simplifications by figuring only two spherical surfaces for three mirrors.

6.6.7 Modified-Rumsey Three-Reflection Telescope Mirrors

Astronomical sky surveys require the development of dedicated telescopes in large size. As shown above, by comparing several telescope designs, the optical properties of a three-mirror telescope in the Rumsey form [27] provide many significant advantages: (i) the anastigmatic flat field design does not require use of any corrector lens and thus is free from these chromatic residual errors over an extended spectral range, (ii) the system is as compact - and with the same central obstruction - as a flat-field RC with a two-lens corrector but uses three optical surfaces instead of six, and (iii) the primary and tertiary mirrors are on a single disk of glass which provides the advantages of a permanent alignment of these mirrors and less diffraction light by avoiding a spider support.

A modified-Rumsey form was proposed by Lemaitre [16] with active optics apherization of the mirrors. The active process only requires the figuring of only two spherical surfaces for the whole optics. The first one elastically generates the primary and tertiary mirrors whilst the second generates the secondary mirror.

Starting from the Rumsey design where all mirrors are spheroids of the hyperboloid type, and given an effective focal length and output f-ratio, one shows that the eight available free parameters - three curvatures, three conic constants, and two axial separations - can be slightly modified for obtaining the simultaneous aspherization of the primary and tertiary mirrors, M1 and M3, as belonging to a single deformable substrate. This fully retains the anastigmatism properties Sphe 3=Coma 3=Astm 3=0 with a flat-field Petz 3=0 and determines the modified-Rumsey design. Given a focal length, f-ratio and back focal distance there exists one and only one design that satisfies these four conditions.

The basic features of a modified-Rumsey design whose mirrors are generated by active optics aspherizations are the following:

(i) the M1-M3 mirror substrate is made of four concentric zones called a double vase form. Each zone corresponding to the mirror clear apertures have an increasing thickness from center to edge. The link zone between M1 and M3 is a narrow ring not used optically - of larger axial thickness than those of the reflective zones - for which the flexural continuity conditions also apply. The outer zone surrounding M1 is a thick cylinder as for usual vase forms,

(ii) the elastic aspherization of Mi and M2 mirrors are simultaneously generated by the same uniform load. The axial reaction to the load is only exerted at the basis of the outer cylinder of the double vase form.

(iii) the optical aspherization alternatives for M1 and M2 mirrors are stress figuring at the laboratory or in situ stressing at the telescope.

• Telescope optical design: The modified-Rumsey design is of interest for developing large space- and ground-based survey telescopes in ultraviolet, visible, or infrared. In order to validate the active optics aspherization methods the design and construction of two identical telescopes Minitrust-1 and -2, f/5, 1.5 x 1.5° FoV, were carried out by Lemaitre et al. [18,19]. The hyperbolizations ofM1 andM3 mirrors were simultaneously obtained by in-situ stressing of a double vase form. The hyperbolization of M2 was obtained by stress figuring of a tulip form (see Sect. 3.3.5 for this latter mirror).

The elasticity continuity conditions for the slope and sag variations in the area of the intermediate ring linking M1 to M3 lead to cross optimizations between optical and elasticity designs. From these optimizations, and setting the Minitrust input pupil on M2, we obtain an optical design which leads to an optimal balance of the M1 and M3 clear aperture areas (Table 6.9 and Fig. 6.19).

• Double vase shell primary and tertiary mirrors - In situ stressing: The elasticity design of a double vase shell as the common substrate of M1 and M3 mirrors requires that the aspherization process - hereafter carried out by in situ stressing -

Table 6.9 Modified-Rumsey telescope optical design - MINITRUST f/5-1.5 x 1.5° FoV - XX [3801,000 nm] - Efl=2,265.6mm. [Units: mm]






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