成像與非成像光學系統之光學傳遞函數分析與應用

Abstract

對於當今的光學儀器與光電消費性產品而言，除了被要求微型化系統設計之外，追求更優質的影像品質和高光學效率以及細緻的解析度畫質亦是未來光電產品的重要趨勢與主流。在成像光學系統的領域中，全幅對焦技術(EDOF, extending the depth of focus) 已然成為一個非常重要的光學設計議題。本論文利用光學傳遞函數 (OTF, optical transfer function) 和照明分布函數，開發出一套解析和半解析式數學模型，並將此方法應用於非同調成像光學系統之成像與非成像光學品質的評估與分析。由於照明光場會改變待測物的反射光強度分佈，因此我們不能再假設一成像系統中，待測物的光學傳遞函數值為一。所以，我們利用光闌方程式 (pupil function) 中的振幅穿透方程式 (一個描述非成像光學特性的項)和波像差方程式(一個描述成像光學特性的項)，深入地探討光學傳遞函數和照明光分布之間的相互關係。本論文的學術貢獻之ㄧ，是在一光學系統的光學傳遞函數計算中，加入一”非成像光學”的有效因子，進而能夠完整地分析與評估光學系統的成像品質。我們也進一步地提出一種新的全幅對焦光學技術，並驗證於非同調成像光學系統之中。此技術利用在非成像系統中，設計一個空間光學調變器來產生一個結構光束(structured light)，如數位微鏡片元件(DMD, digital micromirror device)或是發光二極體陣列裝置(LED array module)，以提供一動態可程式化變形光闌 (a dynamically programmable shaped pupil)，並將此變形光闌投影在成像光學系統的孔徑位置。我們使用自行開發的光學傳遞函數之半解析式數學模型，驗證此新技術可以有效地補償光學像差，如失焦、球差和彗差等，同時亦可提升光學系統的成像解析力。我們的研究是連結和整合成像與非成像光學系統的特性，開發出一新全幅對焦光學技術，應用一嵌入式照明調變器，達到提升傳統非同調光學系統的成像光學品質以及擴展其光學系統的對焦深度，並將此技術應用於光導管、攝影機、顯微鏡和投影機等光學系統中。

Today’s optical instruments and electro-optical consumer products demand high imaging quality, optical efficiency and high resolution with the volume of the machine, nevertheless, being compact. At the same time, extending the depth of focus (EDOF) in an imaging system has been a long-standing issue in optical designs. This thesis develop either an analytical or a semi-analytical model by the use of optical transfer function (OTF) and illumination formations on the study of imaging and non-imaging qualities in the incoherent imaging system. Since the illumination light could vary the intensity distribution of the reflective light from an object, we could no longer assume the OTF of the object equal to unity in an imaging system. Hence, we make the in-depth investigation into the relationship between OTF and the illumination light distribution by calculating the OTF using the pupil function with the amplitude transmittance function which is the term given to the characteristic of a non-imaging system, and the wave aberration function which is the term given to the characteristic of an imaging system. One of main contributions of this thesis is to implement and demonstrate the effective factor of the non-imaging system (i.e., illumination light) in OTF calculation for assessing and specifying the performance of an imaging system. Then, a new approach for EDOF in an incoherent imaging system has been demonstrated. It provides a programmable shaped pupil using structured light which is generated by a non-imaging system with a spatial light modulator such as the digital micromirror device (DMD) or the light-emitting-diode (LED)-array module. The semi-analytical results using the OTF indicate that the limiting resolution of an imaging system with a specific defocus coefficient, and the specific coefficients for spherical aberration and coma aberration can be improved significantly with a binary shaped pupil. The proposed structured light on aperture stop from the non-imaging system can offer a dynamically programmable approach for aberration compensation in an incoherent imaging system. Our proposed research provides the connection between non-imaging and imaging systems for extending the depth of focus and further enhancing the image quality in the conventionally incoherent imaging systems for light pipe, camera, microscope and projector with embedded illumination modulator.