Flexible meniscus/biconvex lens system with fluidic-controlled tunable-focus applications

Hybrid liquid-membrane lenses made by one fixed and one or two active optical components

The paper presents a methodology of calculation of the inner structure of two- and three-component hybrid liquid-membrane lenses with variable focal length that have corrected spherical aberration and coma. Specifically, the formulas for calculation of initial-design inner parameters (radii of curvatures of individual surfaces, axial thickness, and refractive indices of a material of the lens) of a thin-lens system are derived for a hybrid two-component system (doublet) made by one glass and one liquid-membrane lens, and a hybrid three-component lens (triplet) made by one glass lens and two liquid-membrane lenses, which both have variable focal length and corrected spherical aberration and coma for an object at infinity. As optimization during the optical design process requires the starting point be very close to the optimal solution, the presented approach can be successfully used for its calculation, as it is based on fundamental proven formulas of optical aberrations.

Flexible Electrowetting-on-Dielectric Microlens Array Sheet

We have fabricated a fully-flexible, focus-tunable microlens array on a sheet and demonstrated its imaging capabilities. Each liquid lens of the array is individually tunable via electrowetting on dielectric (EWOD) actuation and is situated on a polydimethylsiloxane (PDMS) substrate, which allows the lens array to operate as a reconfigurable optical system. In particular, we observed a significant increase in the field of view (FOV) of the system to 40.4° by wrapping it on a cylindrical surface as compared to the FOV of 21.5° obtained by the array on a planer surface. We also characterized the liquid lenses of the system, observing a range of focus length from 20.2 mm to 9.2 mm as increased voltage was applied to each EWOD lens. A Shack-Hartmann wavefront sensor (SHWS) was used to measure the wavefront of the lens as it was actuated, and the aberrations of the lens were assessed by reporting the Zernike coefficients of the wavefronts.

Dependence of the imaging properties of the liquid lens with variable focal length on membrane thickness

This paper presents the influence of membrane thickness on imaging properties of membrane liquid lenses with variable focal length. Approximate formulas for varying thickness of spherically and parabolically deformed membrane were derived, which allows us to determine their influence on quality of imaging properties of a membrane liquid lens. Furthermore, formulas for wave spherical aberration calculation of a membrane and liquid lens body were derived. It has been shown that the influence of membrane thickness and its changes on wave spherical aberration is negligible from a practical point of view.

Deformation of a prestressed liquid lens membrane

This paper presents a complete model for analysis of the deformed shape of a prestressed circular axisymmetric membrane of a liquid lens. The governing equations are derived using the exact relation between displacements and the Green-Lagrange strains combined with the Saint Venant-Kirchhoff material law, which postulates a linear relation between the Green-Lagrange strains and the second Piola-Kirchoff stresses. A numerical solution based on minimization of potential energy is illustrated by an example, and the dependence of the maximum membrane deflection on material properties and initial prestress is analyzed. The theoretical model is then experimentally validated. It is shown that the model is suitable for large-strain analysis of liquid lens membranes and provides sufficiently accurate results that can be used in further analyses and simulations of imaging properties of active optical elements based on liquid lenses.

Calculation of nonlinearly deformed membrane shape of liquid lens caused by uniform pressure

The paper discusses a numerical calculation of deformation of a circular axisymmetric membrane of a liquid lens caused by the pressure of an optical liquid. Since such deflections of the membrane are many times larger than the membrane thickness, a nonlinear model is applied and generalized relationships are derived that characterize the resulting shape with a high precision and permit an accurate analysis of imaging properties of the lens and of optical aberrations. By comparison with experimental data, it is shown that the presented model is suitable to describe the deformation of the membrane of the lens.

Focus-tunable liquid lens with an aspherical membrane for improved central and peripheral resolutions at high diopters

Liquid lens offers a simple solution to achieve tunable optical powers. This approach, however, suffers from deteriorated resolution at high diopters. In this study, a plano-convex liquid lens with aspherical cross-section is developed. Such configuration allows for the lens profiles at high diopters to be close to spherical shapes by alleviating the edge-clamping effects. Resolution tests of a 6mm lens with optimized asphericity exhibit improved resolutions in both center and peripheral regions at 40 and 100 diopters than the lenses with planar membranes. It shows that aspherical membranes can improve the resolving power of liquid lenses at high diopters, thus providing a new route of optimizing the imaging performance of adaptive liquid lenses for various applications.

Algebraic and numerical analysis of imaging properties of thin tunable-focus fluidic membrane lenses with parabolic surfaces

The theory of third-order aberrations for a system of rotationally symmetric thin tunable-focus fluidic membrane lenses with parabolic surfaces is described. A complex analysis of the third-order design of tunable fluidic lenses is performed considering all types of primary aberrations. Moreover, formulas are derived for the calculation of the change of aberration coefficients of the parabolic tunable fluidic membrane lens with respect to the wavelength. It is shown that spherical aberration of a simple tunable-focus fluidic membrane lens with parabolic surfaces can be corrected, which is not possible with a classical spherical lens. The presented analysis is explained on examples. Derived formulas make possible to calculate parameters of optical systems with fluidic membrane lenses with small residual aberrations.

Simple-structured capillary-force-dominated tunable-focus liquid lens based on the higher-order-harmonic resonance of a piezoelectric ring transducer

This paper proposes a tunable-focus liquid lens implemented with a simple cylindrical container structure and liquid as the lens material. The cylindrical container was constructed using a Pb [Zr(0.52)Ti(0.48)]O(3) (PZT) ring transducer and a polydimethylsiloxane membrane that was attached to a flat side of the transducer. The free surface of the liquid in the cylindrical container can be driven as a static-like convex lens with different curvatures because the higher-order harmonic resonance of the PZT transducer was electrically controlled. Based on a capillary-force-dominant design, the activated liquid lens maintained surface curvature in an arbitrary orientation without a gravitational effect. Profiles of the liquid lenses were characterized with the driving voltages of the transducer ranging from 12 to 60 V peak-to-peak (Vpp) at a resonant frequency of 460 kHz. The temperature effects on the lenses caused by the continuous operation of the transducer were measured. Images showed the various curvatures of the lenses with a range of actuation voltages. A change in focal length of eight times (5.72 to 46.03 cm) was demonstrated within the 10 Vpp variation of the driving voltage. For the characterized liquid lenses, the distortion was less than 2%, and the modulation transfer function reached 63 line pairs per mm (lp/mm) using ZEMAX analysis.