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Deformation Ratio 2110

Deformation Ratio 2110

Fig. 2.6 Comparison of dimensionless load-flexure relations. Left: VTD Type 1 - Uniform load in reaction at the edge. Right: VTD Type 2 - Central force in reaction at the edge a4 q

rcif a2E

where ai are dimensionless coefficients.

2.3 The Mersenne Afocal Two-Mirror Telescopes

The Mersenne two-mirror telescopes, published in 1636 [45, 46], are made of two confocal paraboloid mirrors thus providing afocal systems.

Let us consider a concave paraboloid primary mirror M1 of curvature 1/R1 and two paraboloid secondary mirrors M2a and M2b, all having their focus located at the origin of a cylindric coordinate frame. Their shape is represented by z,

where the suffix i = 1, 2a and 2b characterizes each mirror, and ki are dimension-less parameters defined by ki = 1 , k2a = > O, k2b = - k2a < O,

so that the surfaces of M2a and M2b have opposite curvatures 1 /R2b = — 1 /R2a.

Assuming that each side of M2a and M2b mirrors may be used, Mersenne obtained four distinct afocal forms (Fig. 2.7).

Fig. 2.7 Mersenne afocal two-mirror telescopes. Left: One of the four forms proposed by Mersenne in 1636 [45]. Right: The four forms

• Form 1 uses the convex side of M2a mirror (Cassegrain form),

• Form 2 uses the concave side of M2b mirror (Gregory form),

• Form 3 uses the convex side of M2b mirror (retro-reflective form),

• Form 4 uses the concave side of M2a mirror (retro-reflective form).

Forms 1 and 2 (see also Fig. 1.6) may be used in the paraxial zone as well as in grazing incidences for both mirrors. Retro-reflective forms 3 and 4 preferably applies to rays with large heights at the primary corresponding to conjugates with low heights at the secondary and conversely; however the third-order aberration theory that uses the classical Hamilton/Seidel formulation [53] may not be able to correctly model those two latter forms. Denoting in a general formulation k = R1/R2

the algebraic radius ratio of the two mirrors, and h the height of an incident ray, it can readily be shown that the conjugate height h' of the system emerging ray is a solution of

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