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The various loading delays are concerned with two cases: (A) stress figuring with removing and without removing the loading each day, (B) quasi-permanently stressed optics i.e. in situ active optics. All stresses have been calculated from a103sec using the law (5.19b) with p = 14. [t] Tensile ultimate strengths from manufacturers and corresponding to a103s. [*] These values are a1s in (5.19b).

N.B.: For safety in active optics methods, in long duration processes it is customary to not overpass the tensile maximum stress aTmax = 5 aW3 s or 5 aW3 s.

each (p = 2). More than 50 corrector plates of 4-10 cm clear apertures at f-ratios from f/2 to f/1.1 have been realized with n = 1 and outer zone loadings smaller than 0.3 bar for the fastest ones, working also with the less conservative rule ault/2. This was mainly for space experiments in the UV and conventional ground-based spectrographs, such as, for example, with the Scap flights, Janus flights, Skylab mission cameras by Courtes et al. [7] and semi-solid Schmidt Pediscou spectrograph of Haute Provence observatory. The aspheric correction is analyzed from a He-Ne plate-test interferogram formed by the light reflected from each plate face (Fig. 5.6).

At the instigation of Fehrenbach [9], the method has been developed for making the 62-cm clear aperture plate of the f/3.3 Franco-Belgium Schmidt telescope at Haute Provence observatory which was further extensively used with a 62-cm Fehrenbach normal dispersion biprism for radial velocity measurements in the

Fig. 5.6 Fizeau interferograms of 5-cm clear aperture fused silica corrector plates aspherized by plane figuring and two-zone partial vacuum. An f/1.1 corrector plate is shown on the right (Lemaitre [13]) (Loom)

slitless spectroscopy mode (cf. Sect. 1.12.7). In Fehrenbach's method the radial velocity of a star is derived from the relative shift of two spectra recorded on the same plate with opposite dispersions. This is obtained by a 180° in-plane rotation of the biprism and a slight lateral telescope depointing avoiding fuzzy spectra that would be caused by a full superposition.

The active optics aspherization of the plate required the construction of a dedicated surfacing machine with a rigid steel table rotating onto a hydrostatic pad. A metal-oil-plastic pad provided a low friction rotating table avoiding ball bearing deformation errors. A preliminary result with this 1 m surfacing machine was the stress aspherization of a 50-cm BK7 plate for the f/2.7 Schmidt of Lyon observatory (Lemaitre [15]). After a fine grinding of the two sides by use of a central suction disc, the plate was directly supported by a finely ground ring that emerged from the table after an in-situ lathe-type operation removing 0.3-0.4 mm on each side of the ring. For the Haute Provence observatory, similar preparations were carried out with a UBK7 glass plate and rotating table support ring. The design parameters were 2a = 2rm =620mm, b/a = 1.2542,n = 4, q2 = 0.85bar, v = 1/5, E = 82GPa, R =4,170 mm, p= 2, and t =24.14 mm. This plate replaced the previous one made by the classical method of zonal tool polishing. Off-focus star images showed that the optical quality is clearly in favor of the active method (Fig. 5.7).

The previous analysis has been carried out by considering constant thickness plates, but this is not exactly the case since the plates are slightly thinner at the clear aperture edge than at their center. In fact, a finer analysis would show that the active methods provide, at least, a Sphe 5 coefficient of the right sign for higher-order corrections of the spherical aberration.

During the period 1968-2005, the two-zone stress figuring method was extensively used at Loom where more than 60 corrector plates have been produced this way for space- and ground-based telescopes and spectrographs.

Fig. 5.7 Comparison of the same intrafocus patterns of a star image before and after replacement of the 62-cm corrector plate of the f/3.3 Franco-Belgium Schmidt telescope in Haute Provence observatory. (A) Former plate made by the classical method of zonal tool figuring. (B) New plate made by two-zone stress figuring method and full-size tool. The latter images show smooth and uniform patterns conferring the telescope with an excellent optical quality (Loom)

Fig. 5.7 Comparison of the same intrafocus patterns of a star image before and after replacement of the 62-cm corrector plate of the f/3.3 Franco-Belgium Schmidt telescope in Haute Provence observatory. (A) Former plate made by the classical method of zonal tool figuring. (B) New plate made by two-zone stress figuring method and full-size tool. The latter images show smooth and uniform patterns conferring the telescope with an excellent optical quality (Loom)

5.2.5 Glass Rupture and Loading Time Dependance

During the figuring of small and fast aperture corrector plates - which is useful with the flat tool method - a breakage may happen. This was the case for some of the

Fig. 5.8 Fracture figure of two corrector plates at f/1 and f/1.2 that arose during the flat polishing of the second face (p = 2, v = 1/6, b/a = 1.4888, fused silica). The rupture starts from the support ring of radius r = a = rm, and propagates along this circle before reaching the edge, thus forming an O-shaped line (Loom)

Fig. 5.8 Fracture figure of two corrector plates at f/1 and f/1.2 that arose during the flat polishing of the second face (p = 2, v = 1/6, b/a = 1.4888, fused silica). The rupture starts from the support ring of radius r = a = rm, and propagates along this circle before reaching the edge, thus forming an O-shaped line (Loom)

4-10 cm aperture plates when aspherizing them at f/1. This allows verifying that the maximal stress formula, as given by or(a) in (5.18), is valid. The rupture line starts at the supporting circle r = a, and continues along this circle line before joining the edge (Fig. 5.8).

The roughness being higher during the grinding, one could suppose, at first, that the breakage occurs during this part of the figuring. In fact this is not so and the breakage may also appear during the polishing. The grinding process is always relatively fast compared to the polishing delay, and the rupture stress of glass is very dependent upon the loading time. This phenomenon of glass mechanics is known by glass manufacturers but poorly described in the literature.

Rupture tests using rectangular glass plates bent onto cylinders of various curvature have been carried out. About 40 rectangular samples were cut from Kodak photographic plates that come polished on each side and are of the borosilicate type, probably in a somewhat quenched state. The elastic constants of the glass, such as given by Kodak, were E = 7.5 GPa and v = 0.24. The thicknesses t of the samples were within a 0.60-0.75 mm range. Each sample was bent for two hours onto successive cylinders of curvature radii Rx = 414, 377 and 350 mm. The latter curvature provided the rupture for all samples having passed the two previous curvatures for two hours each. The rupture stress arupt was calculated with the formula orupt = Et/2(1 -v2)Rx. The result of these tests can be modelled by asymptotic-type laws (Fig. 5.9).

Let us consider two possible rupture laws. The first is of the form

where p is a constant and t the loading time. From our rupture tests with Kodak plates we obtain oult = 57.22MPa, odyna = 18.77MPa and p = 654 x 106. This curve is denoted [28] in Fig. 5.9. For t = 0, orupt could be defined as an instantaneous stress which is substantially larger than oult. When the loading time t ^ orupt becomes equal to oult which is too optimistic with respect to our results on ruptures happening after 1-2 hours loading.

The second law, mentioned by Haward [10], is more realistic. It may be written as

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