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The principal incident beam of circular cross-section reflects at the mirror - telescope input pupil - of elliptical contour defined by ax/ay = 1/ cos i, where i is the incident angle. Thus, for the principal axes of the cylinder, the thickness ratio expands as ty 11 + v 2

which, for a Poisson's ratio v = 1/4, a deviation angle 2 i < 60°, and the first two terms of this expansion, gives an error that deviates of < 6 x 10—3 from unity compared to (5.72a).

4 ^ In the elliptical case, the ellipticity of the outer contour (bx ,by) of the cylinder differs from that of its inner contour (ax,ay). The principal radial thicknesses ty, tx of the cylinder must satisfy t^ay(3 — vaX./ay)=tx3ax(3 — va^/a^) with ax/ay = 1/cosi, (5.73)

where i is the incidence angle of the circular cross-section beam from an object at infinity. Therefore, the radial thickness of the cylinder is the largest at the small axis of the close biplate form.

Table 5.4 displays the ratios ty/tx of the radial thicknesses in the principal directions as a function of Poisson's ratios and beam deviations 2 i at the mirror of elliptical geometry ax/ay = 1/cos i, i.e. ax > ay, corresponding to a principal incident beam of circular cross-section from an object at infinity.

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