Design of an Optical System for Generating Annular-focused Beams Using a Conical Mirror and a Parabolic Cylindrical Mirror

A reflective optical system is designed for generating annular-focused beams using a conical mirror and a parabolic cylindrical mirror. The parameters of the mirrors are obtained in accordance with the design requirements of the annular beam. The rotation equation of the parabolic cylindrical mirror is derived with the same annular beam diameter, while the apex angle of the conical mirror changes. The uniformity of the annular beam intensity is improved by changing the parabolic cylindrical mirror into a concave-convex parabolic cylindrical integrating mirror, which is designed on the basis of the principles of surface division and beam superposition. The mirrors are processed by single-point diamond turning. An experimental facility is built to analyze the size and uniformity of the beam intensity distribution. The annular beam-width error is less than 3%, and the uniformity is 89%. The surface of the concave-convex parabolic cylindrical integrating mirror is smooth and continuous. The experimental data correspond to the theoretical design.