The conditions for transformation with uniform intensity from an annular to a cylindrical beam, as needed for mode control in high-power lasers, are analyzed. The equations for the shapes of the mirrors in two different arrangements are derived and evaluated for feasibility of fabrication. The shape of the inner mirrors as well as the major part of the outer mirrors should present no problem of fabrication. In either system, however, that edge of the outer mirror which reflects to the axis requires a sharp curvature, the machining of which might appear formidable. Nevertheless, recent work with diamond machining has accomplished even sharper curvatures than here required.
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