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Fig. 10.11 Thickness distribution T = C4/(a2 + p4 — x4) of three cylinders that generates a x4 flexure mode by uniform load only. Length parameters P = 0.45, 0.90, 1.35. Mirror aspect ratios L/a = 1.092 P

Fig. 10.11 Thickness distribution T = C4/(a2 + p4 — x4) of three cylinders that generates a x4 flexure mode by uniform load only. Length parameters P = 0.45, 0.90, 1.35. Mirror aspect ratios L/a = 1.092 P

10.2.5 Thickness Distributions for Tubular Image Transports

Grazing incidence image transport systems are preferably made of a single tubular mirror. Let us consider the basic case were the magnification is M = -1 and the mirror axisymmetric about a z-axis. The stigmatism of the mirror is achieved by use of the tubular central region of an elongated ellipsoid. In a Cartesian z, r frame, the equation of the ellipsoid is z2/a2 + r2/b2 = 1 with the z-axis origin at the middle of the foci. Denoting 21 = fF this distance, we may derive the local representation of the surface in the section x, z of the local frame, where z is now a radial axis whose positive values are towards the ellipsoid axis (cf. Fig. 10.7). This calculation gives z = 2Rx2 + 8R x4 + IW x6 + - , (1°.50a)

where

and b is the height of the mirror at the central symmetry plane. In this latter plane, if we return now to the notation a for the distance from the mid-thickness surface of the cylinder to its axis, and use as previously the dimensionless variable x instead of x, the local shape z(x) of the ellipsoid is represented by

0 0

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