Analysis of a two-element optical system composed of membrane fluidic lenses with variable focal length

The problem of determining the basic parameters and third-order aberrations of a two-element thin lens system with variable magnification is analyzed, which consists of two membrane liquid lenses with variable focal length, where the liquid in both lenses has the same refractive index and the curvature of both optical surfaces of the lenses can be changed continuously. Relations are derived to calculate the curvature of the individual optical surfaces of the membrane lenses of the two-element zoom lens for different cases of the third-order aberration (spherical aberration and coma) optimization. The application of the derived relations is shown by several examples.