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Classical nonimaging optical designs often use elliptical and hyperbolic flow lines. The transition can be understood by introducing change of gauge in the vector potential.
Roland Winston andLun Jiang
"Gauge invariance in flow line optics (Conference Presentation)", Proc. SPIE 11120, Nonimaging Optics: Efficient Design for Illumination and Solar Concentration XVI, 111200I (9 September 2019); https://doi.org/10.1117/12.2531844
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Roland Winston, Lun Jiang, "Gauge invariance in flow line optics (Conference Presentation)," Proc. SPIE 11120, Nonimaging Optics: Efficient Design for Illumination and Solar Concentration XVI, 111200I (9 September 2019); https://doi.org/10.1117/12.2531844