R

Q i2 Et0

For a given optical design (R, Q, i) and material (E, v), the latter relation defines the amplitude of the perimeter force per unit length with respect to the central thickness of the cycloid-like mirror (Fig. 3.25-Right).

The final design is achieved by coupling the mirror to a circular outer ring via a collar of thin radial thickness, hence ensuring a simply supported edge boundary (3.17c). This allows using two pairs of opposite point-force and obtaining smooth angular deformations. Mirrors with outer collar and ring are built in to a holosteric piece. Since the ring rigidity is larger than the inner profile, the applied forces and stress level are given by the ring. Developing a half ring into a straight bar and assuming clamped ends, the theory of bars and cantilevers (Lemaitre [21]) provide a convenient strain-stress equivalence if the ring radial thickness is small compared

Fig. 3.25 Configuration providing Astm 3 mode zu = A22 r2 cos 20 by only requiring four axial forces applied at 0 = 0, n/2, n and 3n/2. (Left) CTD class - meniscus form. (Right) VTD class - cycloid-like form
0 0

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