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term, the aberrations become essentially sums over all surfaces of powers of the new variables. However, even in the zero-thickness limit the contribution of a surface in the present formalism is not the same as the corresponding classical Seidel surface contribution.
In the examples, several classical lens design results follow naturally from the new formalism, in some cases with a simpler derivation than the one found in the existing literature. Optimal singlet bending, relaxed doublets and Fulcher configurations can all be understood as a direct consequence of quasi-power equality. Although the thinlens approximation employed here is not intended to yield quantitatively accurate predictions, it can serve as a qualitative model that separates the essential properties of primary aberrations from secondary factors.
When expressed in terms of quasi-powers, spherical aberration becomes independent of the internal surface ordering. This property explains the occurrence in the optimization landscape of large families of local minima through permutation symmetry – a property that is already present at the level of third-order theory. Extensions of this work, including more detailed analyses of the design landscape and higher-order effects, will be addressed in a future publication.
Acknowledgments
The author gratefully acknowledges the use of academic licenses for CODE V and Zemax OpticStudio. The author would also like to thank Kumar Rishav for his assistance with the data presented in Figure 3.
Funding This research was funded by TU Delft.
Conflicts of interest The author has nothing to disclose.
Data availability statement
Test lenses, a CODE V and a Zemax macro, the corresponding outputs and the Zemax lens for the system in Figure 4 are available at https:// doi. org / 10.4121 / ecc198ad-889a-4ea6-aebb- 302303f4e999. References
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