Hoffnagle, J.A. and Jefferson, C.M. (2003) Beam Shaping with a Plano-Aspheric Lens Pair. Optical Engineering, 42, 3090-3099.
https://doi.org/10.1117/1.1613957

has been cited by the following article:

• TITLE: Designs of Two-Element Optical Refracting System to Achieve Uniform Laser Beam Profile

  AUTHORS: Abdallah K. Cherri, Nabil I. Khachab, Mahmoud K. Habib

  KEYWORDS: Annular Laser Beam, Refracting System, Lens Design

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.12, December 28, 2017

  ABSTRACT: Various specific laser irradiance distribution outputs are needed in many applications. To fulfill this need, a detailed step-by-step design procedure for split refracting system is proposed for three types of laser beams transformation: 1) Annular-uniform-to-uniform; 2) Annular-Gaussian-to-uniform; and 3) Gaussian-to-uniform to obtain the required laser irradiance distributions. Mathematical expressions of the two Plano-aspheric surfaces are derived for each type. The proposed designs take into account few important parameters such as the system length, the surfaces radii of curvature, the annular beam starting cone angle, and the beams power ratio. Further, the proposed designs are much better than the ones, which were previously reported