Does anyone here know any more details? I’m curious as to how this improves on the 2014 work by the same author and others: https://royalsocietypublishing.org/d

Does anyone here know any more details? I’m curious as to how this improves on the 2014 work by the same author and others: https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2014.0608 https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2014... I think this is the new paper (from 2018): https://www.osapublishing.org/ao/abstract.cfm?uri=ao-57-31-9341 https://www.osapublishing.org/ao/abstract.cfm?uri=ao-57-31-9... The introduction to the new paper gives a reasonably clear explanation of how it relates to previous work: > The design of optical systems with aspheric surface has the goal to strongly reduce spherical aberration. Spherical aberration on lenses has been extensively studied by Ref. [1]. Luneberg [2] established a method for computing the shape of the second surface from an initial first surface that introduces spherical aberration, which he described just for special cases. Many authors proposed a lens design with two aspheric surfaces to correct spherical aberration [3,4]. > The problem of the design of a singlet free of spherical aberration with two aspheric surfaces is also known as the Wasserman and Wolf problem [5]. The problem has been solved with a numerical approach by Ref. [6]. Recently, Ref. [7] has shown a rigorous analytical solution of a singlet lens free of spherical aberration for the special case when the first surface is flat or conical. Since its publication, several works inspired by its solution have emerged [7–12], all of them free of spherical aberration. The solution has six different signs; therefore, it is a set of 2^6 = 64 possible solutions, where only one is right. We test the formula provided by those in Ref. [7], when the first surface is not flat or conic, and the equation system does not give correct answers. > In this paper, we present a rigorous analytical solution for the design of lenses free of spherical aberration. The solution presented here has just one sign; therefore, it is a set of just two possible solutions. Our solution is robust because the set of solutions is valid for negative and positive refraction indices. The model allows use of continuous functions, such that the rays inside the lens do not cross each other. This model will compute the second surface in order to correct the spherical aberration produced by the first surface. If I understand this correctly, the key difference is that the earlier paper (referred to as [7] above) only addresses the case where one of the surfaces of the lens is flat or conical. I’m not sure whether this is a serious limitation in practice: I would have thought naively that it’s easier to manufacture a lens with one flat surface. The (new) paper also includes (in Appendix A) Mathematica code to compute and plot the lenses produced by this method.