Proper convex function Proper convex function In mathematical analysis (in particular convex analysis) and optimization, a proper convex function is a convex function "f" taking values in the extended real number line such that for at least one "x" and for every "x". That is, a convex function is "proper" if its effective domain is nonempty and it never attains formula_3. Convex functions that are not proper are called "improper convex functions". A "proper concave function" is any function "g" such that formula_4 is a proper convex function. For every proper convex function "f" on R there exist some "b" in R and
Telecentric lens Telecentric lens A telecentric lens is a compound lens that has its entrance or exit pupil at infinity; in the prior case, this produces an orthographic view of the subject. This means that the chief rays (oblique rays that pass through the center of the aperture stop) are parallel to the optical axis in front of or behind the system, respectively. The simplest way to make a lens telecentric is to put the aperture stop at one of the lens's focal points. An entrance pupil at infinity makes the lens object-space telecentric. Such lenses are used in machine vision systems