Novel graphical method for the designing of telescopes

Abstract A new way to visualize telescopes for laser beams is presented. Using this novel representation in the complex plane with the already common q-parameter both understanding and designing of telescopes becomes much simpler. This publication incorporates extensive mathematical proofs that the novel representation is correct and based on that a map is derived that even allows the designing of telescopes as a quick back-of the envelope tasks during lab-work. Finally, three telescopes are designed as an example to show how the map works.