Fig. 10.9 Thickness distribution T = C2/X2 of three cylinders that generates a purely parabolic flexure W = X2 by uniform load only. Length parameters ft = 0.45, 0.90, 1.35. Mirror aspect ratios L/a = 1.092ft shift these poles outside the edge by introducing an additional constant a2 in the flexure function. Assuming a quadratic flexure including only a constant and a x2 term, this parabolic flexure may be represented by

where the mirror aspect ratio is L/a = 2 j and the total sag of the mirror is W(0) -W( j) = j2. From (10.38), the dimensionless thickness is simply the reciprocal function

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