Linear systems

Linear means that two different light signals (or of any other nature, in general) coming from two different points of the object do not interfere with each other. The resulting image of two emitting points is equal to the addition of the images that would arise by measuring the two points separately.

For a mathematical function f(x) to be linear, it must satisfy two properties:

  • Additivity: f(x + y) = f(x) + f(y).
  • Homogeneity: f(c x) = c f(x) for all c.

This linearity doesn't occur in all physical systems, and applying deconvolution to Non Linear images is totally wrong. Deconvolution is based on the idea that the Point Spread Function (PSF) is the basic brick that builds the image up and that the contribution of each part of the image is additive.