Fast focusing of electrowetting liquid lenses driven by model-based feedforward voltage waveforms

Electrowetting-based liquid lenses (EWLLs) are widely applied in adaptive optics systems requiring rapid zooming. To improve the dynamic response of a specific EWLL for faster adaptability of optics systems, adjusting its driving voltage waveform (DVW) is an effective approach, which, however, lacks a method to determine the waveform automatically without pre-tuning and calibration. This paper proposed a dynamic model-based feedforward controller to generate adaptive DVWs for fast focusing of EWLLs. The dynamic model of EWLL was derived from the Onsager variational principle to describe the motion of the liquid-liquid interface in the lens under different voltages. It was experimentally validated that the model provides an accurate formulation of the voltage-motion relationship, which is the basis for calculating appropriate DVW for arbitrary trajectories. Then, an inverse-dynamics feedforward controller based on the dynamic model was designed to adaptively generate suitable DVW for fast focusing at different optical powers. Test results for a specific step change of optical power showed that the proposed method reduces response time by 63% compared to the conventional method using step-shaped DVW. Test results for random changes of optical power were also given to exhibit that the method has consistent performance across the entire voltage range, requiring no case-by-case experimental pre-tuning, amplitude-dependent calibration and without additional sensor feedback.