曲面型微透鏡陣列、環境友善頭燈及利用流體成型製造透鏡之光學研究

Abstract

本論文探討彼此間具有密切關聯性之光學研究主題。首先，我們探討如何將相機結構結合曲面型微透鏡陣列以及毫米(mm)尺寸之單透鏡。微透鏡陣列中的每個子透鏡皆為單一通道，並各自獨立進行成像。利用此多通道成像原理，進而引發出火車頭燈研究主題，即設置於燈殼中之各個LED芯片所發出之光線，可視為各自獨立之照明光斑，如同前項主題當中，光線於多通道行進的過程，用以探討頭燈的照明。至於在首項主題所使用mm尺寸之單透鏡，則早已廣泛應用於光學設計中，並於光學研究中佔有相當大的重要性。故此，我們於最後一項主題探討如何高速自製mm尺寸透鏡之方式。 於曲面型微透鏡陣列之相機鏡頭研究中，其成像系統乃是基於人眼以及由生物啟發之多焦距人工複眼的原理，所製作出之光學結構。人造複眼是類似於昆蟲複眼之曲面六邊形微透鏡陣列，其中每個人造小眼以小角度接受入射光，而圓弧形陣列則有助於本研究來實現具有廣視野且結構緊湊之相機模組。在模擬設計中所提出之系統僅使用兩個透鏡，即一個半球形透鏡和一個圓弧彎曲之六邊形微透鏡陣列，用以實現廣視場攝相系統。接著，本研究以實驗來印證模擬設計，但為避免在實際生產中，因設置個別獨立光學元件而產生之公差積累，故本研究將半球形透鏡與彎曲之六邊形微透鏡陣列合併成單一透鏡元件。 其次，本研究提出了一種使用雙半圓形拋物面鍍鋁反射器之火車頭燈系統，每個半圓形反射器包含五個高效率、小封裝之發光二極體（LED）芯片，且此兩個半圓形反射器承180°旋轉對稱。頭燈照明必需符合美國聯邦法規之交通安全規範，為了預測照明模式，本研究針對垂直於LED芯片之中心所發出的光線光路，進行了分析推導。該光線代表從LED芯片所發出的主光線，並會落於由LED光源所投射至屏幕上之光斑的最大照度處。接著，本研究進行系統性地分析設計，以確定反射器中LED芯片的位置應如何擺設，方可達到最少電力的消耗，又同時滿足交通法規安全規範之限制。相較於典型的火車頭燈系統，白熾燈或鹵素燈需要耗能幾百瓦，而本研究所提出的系統僅使用20.18W即可滿足法規要求。此外，於延伸討論中，本論文也提出多面形反射器火車頭燈系統之探討構想，有利於照射光斑更接近圓形，以增進光線聚焦效果。 最後，本論文提出了一種利用彈性模具來製造光滑非球面透鏡的方法，該彈性模具是由注入受控氣泡於液體聚二甲基矽氧烷（PDMS）後硬化而成。PDMS的表面張力為成形氣泡提供了所需之壁張力(wall tension)，為使壁張力達到最小化，氣泡將會被擠壓成非球面形狀。藉由控制氣泡之體積，我們可以使氣泡生成不同的曲率半徑。在製作好彈性體模具後，我們接著將UV光固化光學膠填充到模具中，即可複製出本研究所需要的鏡片。若需通過傳統精密鏡片成型工藝來製造透鏡，不僅製作設備難以取得、且所需使用之設備價格昂貴，一般研究人員難以利用此法自製透鏡。利用本研究之製作方式，不僅設備成本低廉，且藉由同一模具還可翻模出相同外型之透鏡，如此複製品便能夠實現相同的光學性能。因此，本研究能以快速且低成本的方式來製造出許多具有相同形狀的鏡片。最後，本研究呈現將自製透鏡結合智慧型手機，而成為可攜式顯微鏡之應用方式。

This dissertation presents works of the optical research with significant relationships. The first topic talks about an imaging system that combines a multichannel structure with a main lens. The multichannel structure is realized by a curved hexagonal microlens array (MLA). With this architecture, each microlens of the array transmits a segment of incident rays. Therefore, partial images can be recorded in separate channels. It inspires us to create a multichannel projection system for a train headlamp system in the second topic. That is, the light emitted on the screen by each light-emitting diode (LED) chip disposed in the lamp housing can be regarded as an independent illuminated spot. After adjusting the positions of the LED light sources in the train headlamp, the illuminated spots can be combined into a desired pattern. Furthermore, the main lens used in the first topic is a millimeter length scale, which is a popular lens scale for optical applications. It inspires us to invent a method of lens fabrication for millimeter-scale lenses in the third topic. The first topic is to perform optical studies of a camera using a biologically inspired artificial compound eye with multiple focal lengths and all spherical surfaces. This structure is based on the principles of both the human eye as well as the insect’s compound eye. The artificial compound eye is similar to an ommatidial array in which each artificial ommatidium collects light with a small angular acceptance. The curved hexagonal array helps us to achieve a compact and wide field-of-view camera module. In simulation design, the proposed system uses only two lenses which are a hemispherical lens and a curved hexagonal MLA to achieve a wide full field-of-view. Next, we design an experiment specifically for simulation modeling. In order to avoid tolerance build-ups due to setting independent optical elements in actual production, we combine the hemispherical lens with the curved hexagonal array into a single lens element. Moreover, we propose a train headlamp system using dual half-circular parabolic aluminized reflectors. Each half-circular reflector contains five high-efficiency and small-package LED chips. And the two halves are 180 degrees rotationally symmetric. For traffic safety, the headlamp satisfies the Code of Federal Regulations. To predict the pattern of illumination, an analytical derivation is developed for the optical path of a ray which is perpendicular to and emitted from the center of an LED chip. We then systematically analyze the design to determine the locations of the LED chips in the reflector that minimize electricity consumption while satisfying the reliability constraints associated with traffic safety. Compared to a typical train headlamp system, with an incandescent or halogen lamp needing several hundred watts, the proposed system uses only 20.18 W to achieve the luminous intensity requirements. In addition, in order to make the shape of the illuminated pattern more circular and improve the focusing performance, more design ideas about combined multiple parabolic aluminized reflectors can be found in the extended discussions. Last but not least, we propose a fabrication method of making a smooth quasi-spherical lens using an elastomeric mold which is hardened after a captive bubble injected into the liquid polydimethylsiloxane (PDMS). The surface tension provides a necessary wall tension for the liquid PDMS to form a bubble. The tendency to minimize wall tension pulls the bubble into an aspherical shape. By controlling the volume of the bubble, we can make many bubbles with different radii of curvature. After preparing the elastomeric molds, we can fill the UV-curing optical adhesive into the molds and duplicate the lenses of different shapes we need. Suppose that if an exact copy lens is made by a precision lens molding process then the duplicate should be able to achieve the same optical capabilities. This allows researchers to manufacture many lenses with a same lens shape for experimental usage. Furthermore, we present an application for the homemade lens by integrating it with a smartphone to be a portable digital microscope.