Stigmatic Optics. Rafael G González-Acuña
2.1 From the wave equation, through Helmholtz equation to end with the eikonal equation
2.4 The Snell law from eikonal
2.5 The Fermat principle from eikonal
3 Calculus of variations
4 Optics of variations
4.2 Lagrangian and Hamiltonian optics
4.5 The Fermat principle and Snell’s law
5 Stigmatism and stigmatic reflective surfaces
6 Stigmatic refractive surfaces: the Cartesian ovals
6.2.1 Case I: ro=ri=0,zo→−∞ and zi=f
6.2.2 Case II: ro=ri=0,zo=f and zi→−∞
6.3 Analytical stigmatic refractive surfaces
6.3.1 Case A: ro=ri=0, zo→−∞ and zi=f
6.3.2 Case B: ro=ri=0,zo=f and zi→−∞
6.3.3 Case C: ro=ri=0,zo=∓f and zi=±f
6.3.4 Case D: ro=ri=0,zo=−αf and zi=+f
6.3.5 Case E: ro=ri=0,zo=αf and zi=−f
7 The general equation of the Cartesian oval
7.1 From Ibn Sahl to Rene Descartes