González-García Jorge, Santiago-Alvarado Agustin, Cruz-Félix Angel S
Physics and Mathematics Institute, Technological University of the Mixteca, Carretera a Acatlima km 2.5, Huajuapan de León, Oaxaca C. P. 69000, Mexico.
Postgraduate Studies Division, Technological University of the Mixteca, Carretera a Acatlima km 2.5, Huajuapan de León, Oaxaca C. P. 69000, Mexico.
Heliyon. 2023 Mar 3;9(3):e14229. doi: 10.1016/j.heliyon.2023.e14229. eCollection 2023 Mar.
Through the methodology of optical surface design based on concentric rings, this paper proposes the design of freeform mirrors, initially by employing segmented rings, each of them with different spherical radii of curvature, and then by employing segmented conic rings with different conic constants in each of the segments. These surfaces will then produce the desired images. For the case of segmented spherical rings, mathematical expressions were deduced to obtain the image points as a function of the radii of curvature. Furthermore, it is shown that in the case where conic rings were used, there is a decrease in spherical aberration, which allows the manipulation of the generated image. Finally, several proposals are presented for the design of mirrors to generate both the desired size of the image and the desired distribution of energy, together with their analyses.
通过基于同心环的光学表面设计方法，本文提出了自由曲面镜的设计方案，首先采用分段环，每个分段环具有不同的球面曲率半径，然后采用各段具有不同圆锥常数的分段圆锥环。这些表面将产生所需的图像。对于分段球环的情况，推导了数学表达式以获得作为曲率半径函数的像点。此外，结果表明，在使用圆锥环的情况下，球差会减小，这使得可以对生成的图像进行操控。最后，针对生成所需图像尺寸和所需能量分布的镜子设计提出了几种方案，并进行了分析。
