Spherical aberration free liquid-filled tunable lens with variable thickness membrane

We present an iterative design method for liquid-tunable aspherical lenses capable of diffraction-limited performance over a wide focal length range. The lenses are formed by a thin elastomer meniscus with a variable thickness profile engineered to deform into an ideal asphere under uniform pressure load. Compared to their more conventional counterparts, the proposed lenses significantly reduce spherical aberration over a larger portion of the aperture. The design procedure begins with the semi-analytical calculation of the meniscus thickness profile using large-deflection thin plate theory. This initial profile is then further optimized using coupled finite element analysis and ray-tracing simulations iteratively. We apply the developed method to design a tunable aspherical lens with 3 mm clear aperture and 8 mm optimum focal length, and numerically demonstrate the improvement in optical performance over conventional tunable-lenses over a focal length range from 6 mm to 12 mm. Using 80% of the clear aperture, the lens has better than λ/4 RMS surface error over the focal length range from 7.7 mm to 8.5 mm, corresponding to 10% tuning of focal length with diffraction-limited performance. The sources of potential fabrication errors in a practical implementation of such a lens are also analyzed in detail in terms of their influence on optical performance.