Design of freeform mirrors using the concentric rings method.

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.