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16 Q2

This determines the execution conditions of the deformable submaster for focal ratios slower, say, than f/2.5. At the built-in edge ro, the junction to a thick outer ring is achieved by a quarter-circle of curvature 1/t. Metal submasters such as q r m chromium stainless steel are preferred for linearity and safety when applying several atmospheres inner air pressure. The shrinkage effect of epoxy resins during the polymerization process is corrected at the final aspherization process of replication by a slight overload Aq that usually is Aq/q ~ 4%. This also requires use of a minimal resin quantity; hence the rigid Zerodur substrate of the final grating replica must be given a slightly concave spherical shape before the replication where the thickness of the resin is minimum even at center and edge.

• Variable thickness submasters for fast focal ratio cameras: The design of active submasters for making gratings of fast f-ratio spectrographs requires use of the power series (5.76a) for a higher-order correction of spherical aberration modes. With an active optics submaster made of a plate built-in to a thick outer ring, we show hereafter that these corrections lead to an active plate thickness slightly decreasing from center to edge.

The static equilibrium of the plate is derived from the radial bending moment, tangential bending moment, and shearing force. These are defined by the equation set (Sect. 2.1.2)

r dr

Qr = -2nr/orq2nrdr = -2 qr■ After substitution of Mr, Mt, and Qr, the equilibrium equation becomes dD id2z v dz\ d i d2z 1 dA = 1 dr V dr2 r dr I dr 1 dr2 r dr I 2

where the flexure of the submaster plate is, from (5.76a) and (5.77),

0 0

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