Lens design uses a calculation of the lens’ surfaces that permits us to
obtain an image from a given object. A set of general rules and laws
permits us to calculate the essential points of the optical system,
such as distances, thickness, pupils, and focal distances, among
others. Now, the theory on which classical lens design is based has
changed radically, as our theoretical foundations do not rely on the
classical ray-tracing rules. We show that with the rules expressed in
a reduced vector analytical solution set of equations, we can take
into account all optical elements, i.e., refractive, reflective, and
catadioptric. These foundations permit us to keep under control the
system aberration budget in every surface. It reduces the computation
time dramatically. The examples presented here were possible because
of the versatility of this theoretical approach.
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