@article{WANG2026, 
author = {Rui WANG and Bingfang YANG},
title = {EXTREMUM PROBLEM OF OPTICAL PATH IN IMAGING BY A SINGLE SPHERICAL SURFACE UNDER NON-PARAXIAL CONDITIONS},
year = {2026},
journal = {Physics and Engineering},
volume = {36},
number = {2},
pages = {142-151},
keywords = {Fermat's principle, non-paraxial conditions, type of extremum, spherical surface imaging},
url = {https://www.sciopen.com/article/10.26599/PHYS.2026.9320222},
doi = {10.26599/PHYS.2026.9320222},
abstract = {Fermat's principle indicates the characteristic that the actual optical path always takes an extremum. Based on this, it is possible to further determine the specific type of extremum. Single-spherical-surface imaging, as a typical example of curved-surface imaging, has a constant actual optical path in paraxial ideal imaging. However, for the non-paraxial case, the type of extremum of the actual optical path has not been specifically discussed in the literature. This paper uses the mathematical method of finding higher-order derivatives to focus on discussing the type of extremum of the actual optical path corresponding to a given image point after reflection or refraction of light rays emitted from a given object point on the principal axis under non-paraxial conditions, deepening the understanding of non-paraxial imaging and Fermat's principle.}
}