Adaptive micro-lenses enable the design of very compact optical systems with tunable imaging properties. Conventional adaptive micro-lenses suffer from substantial spherical aberration that compromises the optical performance of the system. Here, we introduce a novel concept of liquid micro-lenses with superior imaging performance that allows for simultaneous and independent tuning of both focal length and asphericity. This is achieved by varying both hydrostatic pressures and electric fields to control the shape of the refracting interface between an electrically conductive lens fluid and a non-conductive ambient fluid. Continuous variation from spherical interfaces at zero electric field to hyperbolic ones with variable ellipticity for finite fields gives access to lenses with positive, zero, and negative spherical aberration (while the focal length can be tuned via the hydrostatic pressure).

Optofluidics is a rapidly growing versatile branch of adaptive optics including a wide variety of applications such as tunable beam shaping tools, mirrors, apertures, and lenses. In this review, we focus on recent developments in optofluidic lenses, which arguably forms the most important part of optofluidics devices. We report first on a number of general characteristics and characterization methods for optofluidics lenses and their optical performance, including aberrations and their description in terms of Zernike polynomials. Subsequently, we discuss examples of actuation methods separately for spherical optofluidic lenses and for more recent tunable aspherical lenses. Advantages and disadvantages of various actuation schemes are presented, focusing in particular on electrowetting-driven lenses and pressure-driven liquid lenses that are covered by elastomeric sheets. We discuss in particular the opportunities for detailed aberration control by using either finely controlled electric fields or specifically designed elastomeric lenses.

By means of numerical simulations, using a computational fluid dynamics software together with an optical ray tracing analysis platform, we show that we can tune various optical aberrations by electrically manipulating the shape of liquid lenses using one hundred individually addressable electrodes. To demonstrate the flexibility of our design, we define electrode patterns based on specific Zernike modes and show that aspherical, cylindrical and decentered shapes of liquid lenses can be produced. Using different voltages, we evaluate the tuning range of spherical aberration (Z11), astigmatism (Z5 and Z6) and coma (Z7), while a hydrostatic pressure is applied to control the average curvature of a microlens with a diameter of 1mm. Upon activating all electrodes simultaneously spherical aberrations of 0.15 waves at a pressure of 30Pa can be suppressed almost completely for the highest voltages applied. For astigmatic and comatic patterns, the values of Z5, Z6 and Z7 increase monotonically with the voltage reaching values up to 0.06, 0.06 and 0.2 waves, respectively. Spot diagrams, wavefront maps and modulation transfer function are reported to quantify the optical performance of each lens. Crosstalk and independence of tunability are discussed in the context of possible applications of the approach for general wavefront shaping.

We propose a new design for tuning the astigmatism of liquid micro-lenses using electric field and hydrostatic pressure as control parameters. We explore the feasibility and operating range of the lens with a self-consistent numerical calculation of the electric field distribution and the shape of the two-phase interface. Equilibrium shapes, including surface profiles parallel and perpendicular to a stripe electrode, are extracted to determine the astigmatism. The wavefronts are decomposed into Zernike polynomials under zero defocus conditions using a commercial ray-tracing software. We observe that the global curvature of the lens is primarily controlled by the hydrostatic pressure, while asphericity and astigmatism are controlled by the electric field. For optimized electrode geometries and simultaneous control of pressure and electric fields the astigmatism can be tuned from Z6 = 0…0.38 μm with minor changes in the focal length.

Abstract:In this work, we use the numerical simulation platform Zemax to investigate the optical properties of electrically tunable aspherical liquid lenses, as we recently reported in an experimental study [K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, "Optofluidic lens with tunable focal length and asphericity," Sci. Rep. 4, 6378 (2014)]. Based on the measured lens profiles in the presence of an inhomogeneous electric field and the geometry of the optical device, we calculate the optical aberrations, focusing in particular on the Z11 Zernike coefficient of spherical aberration obtained at zero defocus (Z4). Focal length and spherical aberrations are calculated for a wide range of control parameters (fluid pressure and electric field), parallel with the experimental results. Similarly, the modulation transfer function (MTF), image spot diagrams, Strehl's ratio, and peak-to-valley (P-V) and root mean square (RMS) wavefront errors are calculated to quantify the performance of our aspherical liquid lenses. We demonstrate that the device concept allows compensation for a wide range of spherical aberrations encountered in optical systems.