Optical EngineeringSimplified model of an O-ring-driven liquid-filled lens for calculating focal length
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The purpose of this study was to develop a mathematical model that could be used to obtain the approximate focal length of O-ring-driven liquid-filled lenses. An O-ring-driven liquid-filled lens is composed of a base plate, a glass-covered liquid reservoir, a pliable membrane, an O-ring, a spring, and three actuators. The movement of the ring changes the focal length or the focus position. In previous studies, the commercial software ANSYS was used to find the membrane deformation and ZEMAX was used to find the focal length. The procedures used in those previous studies are complicated and generally require considerable design work. The proposed mathematical method employs the principle of liquid volume conservation to simplify the calculations that approximate the focal length of the lens. The result is confirmed on ZEMAX to ensure that the method is practicable. Consequently, focal lengths of lenses with different ring thicknesses, radii, and squeezing depths to contact the membrane can be calculated immediately.