Logarithmically concave function Logarithmically concave function In convex analysis, a non-negative function is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality for all and . If is strictly positive, this is equivalent to saying that the logarithm of the function, , is concave; that is, for all and . Examples of log-concave functions are the 0-1 indicator functions of convex sets (which requires the more flexible definition), and the Gaussian function. Similarly, a function is log-convex if it satisfies the reverse inequality for all and . Log-concave distributions are necessary for a
Telecentric lens (or "collimated") illuminators, which produce a parallel light flow, often from LED sources. An image-space (or image-side) telecentric lens produces images of the same size regardless of the distance between the lens and the film or image sensor. This allows the lens to be focused to different distances without changing the size of the image. Image-space telecentric lenses have an exit pupil infinitely far in front of the lens; that is, if one looks in the back of the lens, the image of the aperture is very far away. At the film or image sensor, all of the chief rays