具多圈電極之液晶變焦透鏡及發展其成像品質評估方法

Abstract

本論文完成具多圈電極之液晶變焦透鏡應用於手機相機的設計。以液晶分子在電場作用下的動態理論做為基礎理論設計，並藉由模擬與分析達到電極圈數的最佳化設計。近年來，由於手機相機搭載自動對焦與變焦系統的趨勢更為彰顯，若液晶變焦透鏡能取代傳統手機鏡頭模組中的透鏡，則可使手機相機同時具備自動對焦與變焦系統並且更為輕巧與降低成本。因此，本文首先根據液晶變焦透鏡的變焦效能來計算實際可取代傳統手機鏡頭模組做為自動對焦與變焦系統的程度。相較於一般手機相機，其鏡頭模組特別需要較短的焦距(約8公分)與較大的孔徑(大於3公厘)，然而這也是目前液晶變焦透鏡無法達成的規格。本文為使改善目前液晶變焦透鏡對於手機相機的應用，而建立一套方法可設計具多圈電極之較大孔徑的液晶變焦透鏡。不僅如此，本文針對液晶變焦透鏡的成像品質亦發展其評估方法，基於點擴散函數與調制轉換函數的光學理論計算而成。藉此成像品質評估方法對具多圈電極之液晶變焦透鏡的電極寬度與圈數做最佳化設計，以達成所需之成像品質的要求。而在此設計之中，液晶變焦透鏡的電極圈數得首先決定，再依據其所需電壓與透鏡半徑位置的斜率變化比例關係來設計多圈電極寬度。最後本文以三圈電極之液晶變焦透鏡做為最佳化設計結果，依據其電極圈數持續增加至七圈時的成像品質無明顯提升。而此三圈電極之液晶變焦透鏡的成像品質，其調制轉換函數分別在65%與48%時可解析至5LP/mm與7LP/mm。

The liquid crystal (LC) lens with multi-ring electrodes for cameras in cell phones is designed in this study based on theoretical analysis, simulations and optimization. As the auto-focusing and zooming systems for cameras in cell phones become popular, the applications of a liquid crystal lens to cameras in cell phones provide the advantages such as compact, lightweight, and inexpensive, by replacing the indispensible moving lenses in the traditional lens module. This study starts with the calculations to show that a substantial size reduction of a lens module can be offered by an insertion of LC lens. As compared to conventional cameras, the lens module in phone cameras particularly requires shorter focal length (around 8cm) and larger aperture (greater than 3 mm). The currently available LC lenses, however, fails to provide both the above capabilities. To remedy the problem, the method to design a large-aperture LC lens with multi-ring electrodes is developed in this study, and a new quality-assessment method is developed to evaluate the designed multi-ring LC lens via point spread function (PSF) and modulation transfer function (MTF). The number and widths of the ring-type electrodes are further optimized to reach certain required levels of PSF and MTF for the LC lens. This is achieved by designating a finite number of ring electrodes first and then assigning the width of each electrode proportional to the slope of the required applied voltage along the radius of the LC lens. Optimization results show that the three-ring LC lens with ring widths particularly designed reached satisfactory MTF of 65% for 5 and 48% for 7 line pairs per millimeter, which are not increased significantly even with the ring number increased to seven.