Paraxial ray solution for liquid-filled variable focus lenses

Abstract We propose a general solution for determining the cardinal points and effective focal length of a liquid-filled variable focus lens to aid in understanding the dynamic behavior of the lens when the focal length is changed. A prototype of a variable focus lens was fabricated and used to validate the solution. A simplified solution was also presented that can be used to quickly and conveniently calculate the performance of the lens. We expect that the proposed solutions will improve the design of optical systems that contain variable focus lenses, such as machine vision systems with zoom and focus functions.