Paraxial design of an optical element with variable focal length and fixed position of principal planes

In this article, we analyze the problem of the paraxial design of an active optical element with variable focal length, which maintains the positions of its principal planes fixed during the change of its optical power. Such optical elements are important in the process of design of complex optical systems (e.g., zoom systems), where the fixed position of principal planes during the change of optical power is essential for the design process. The proposed solution is based on the generalized membrane tunable-focus fluidic lens with several membrane surfaces.