For instance from Table (1.10), comparing a Zerodur vitroceram (where atmax = 22 MPa and E = 90.2 GPa), with a quenched stainless steel Fe87Cr13 (where atmax = 1.4 x 103MPa and E = 201 GPa), the gain in elastic deformability is ~ 28-times in favor of this metal alloy; taking into account the Poisson ratio would lead to a gain ~ 25.

Other linear alloys usable for mirrors, such as Ti90Al6V4 or Be95Cu5, could also provide large gains in elastic deformability, but their practical machining to the convenient geometry of a VTD seems more difficult. For large zoom range VCMs, stainless steel Fe87 Cr13 in a quenched state has been found preferable.

2.6.2 Zoom Range and Choice of a Thickness Distribution

For a small zoom range, the design of a VCM using a VTD is straightforward. With the examples in Fig. 2.6, if the zoom range is corresponding to a variation of [ f/c»-f/7 ] with VTD Type 1 or a variation of [ f/^-f/5 ] for VTD Type 2, the stressstrain relations are quasi-linear and any thickness profile T20 provides accurate curvatures which are affine paraboloids.

For a large zoom range such as [f/^-f/2.5], it is not possible to obtain affine paraboloids all over the range. Assuming that the VCM is polished flat or slightly convex at an f-ratio Q0 close to infinity when at rest, and that the zoom range varies down to Qmin, a balance of the surface deviation to a paraboloid can be obtained if the thickness T20 is determined for an Q-value such as Q e [Q0, Qmin ]. In this range the full sag variation is subdivided into four equal segments and the optimal design f-ratio Q for the calculation of T20 is determined for the junction of the last two segments by using the balance criterion

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