Off Axis Segments of a Conicoid Mirror

The shape of large primary mirrors of presently large segmented telescopes are either a sphere (Het, Salt), a hyperboloid slightly deviating from a paraboloid (Keck, Gtc) or an actively controlled pseudo-plane-aspheric surface (Lamost). For the next telescope generation - which will have aperture diameters in the class 25-50 m -, it is useful to determine the shape of a segment for a conicoid primary mirror which may appreciably deviate from a paraboloid.

Still representing the optical shape of a segment by zOpt = XOnmpn cosm0, we give hereafter the result of the analysis by Nelson and Temple-Raston [51], also including a small correction in one of them. The Onm coefficients are derived by substituting the conicoid shape into the equation set (7.27) and expanding them by modes similarly as in the previous subsection. These optical sags are

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