| 摘要: | 本研究提出一種適用於類面光源的演算技術，利用單光源在目標平面上的輻射照度、光照度分佈以最小平方法進行函數化成為一個光分佈函數 (light spread function, LSF)，來處理類面光源於近場距離時，輻射強度隨距離而變化的光學設計問題，此光分佈函數為目標面上輻射照度與距離的關係函數，可以藉由數值方法快速計算光源和光源、光源和反射面之間的距離，以達到目標面上的均勻度要求。對於光學設計中反射面的輻射照度分佈計算，我們提出建構虛擬光源的方法，用來近似計算光線經過鋁的鏡面反射面後在目標面產生的輻射照度分佈。在客觀的使用朗伯光源、蝙蝠型光源以及準直光源進行光分佈函數技術的精準度計算，多光源搭配多種排列條件下，比較光分佈函數計算和光學模擬軟體得到的輻射照度分佈，平均絕對誤差百分比 (mean absolute percentage error, MAPE) 可在1.5% 以下，以蝙蝠形光源比較單一以及直角鋁反射面的結果，MAPE可在1% 以下。
為了驗證光分佈函數設計方法的可行性，我們將光分佈函數設計方法應用於設計一款直下式背光燈箱以及兩款平行曝光機，直下式背光燈箱 (direct backlight unit, DBLU)使用36顆蝙蝠型光源，其背光燈箱厚度20 mm，搭配反射率 90% 的鋁反射面，經過光分佈演算法的排列計算後，將演算法所計算參數建入光學模擬軟體中，在不加光學膜片下，均勻度可達99.25%。以相同的參數實際試製一組直下式背光燈箱，比較光分佈計算和實驗試製的結果，MAPE在單一量測方向 x軸 、 y = x 分別為0.64% 、 0.92%，而試製的直下式背光燈箱在九點的均勻度量測下可達96.68%。以光分佈函數法對於步進式和掃描式 UV-LED平行曝光機進行設計，經過光分佈函數法計算後，解決光學設計上對於光源間距、光源旋轉角度以及鋁反射面傾斜角度的問題，使得目標面積內的均勻度可達97%以上，並且平均輻射照度和輻射強度半強角皆可達到曝光機的需求，明顯可見，光分佈函數法計算提供一種準確的設計方法，使得設計者可以解決近場光學的設計問題，並且可以根據設計者需求快速地計算光源陣列和反射面所產生的輻射照度分佈。
;In this thesis, we will propose a method of optical field calculation to accurately calculate the source-to-source spacing and the source-to-reflective-plane spacing of the extended source to obtain uniform illumination into the target plane. A light spread function (LSF) that is composed of a two-term Gaussian function from nonlinear least squares method will be utilized to simulate the illuminance and irradiance distribution of each extended source on the target plane. The LSF will be a function of the illuminance and distance, and the illuminance of the source on the target plane can be derived using the LSF. In the optical system, the energy of the mirror reflected rays can be approximated using a virtual source. Under various arrangement conditions in the optical system, when comparing the results of LSF and optical design software for the entire target plane, the mean absolute percentage error (MAPE) can be lower than 1.5%. The effect of the rays reflected by the sides of a reflective plane and a corner reflective plane was also considered and calculated using the LSF. When comparing the results calculated using the LSF method for the entire target plane with the results from the optical design software, the MAPE can be lower than 1.0%.
Furthermore, to verify the feasibility of illuminance and irradiance calculation for the optical system, a direct backlight unit (DBLU), a step-and-repeat collimated exposure and a scanning collimated exposure were designed using the calculated spacing. Consider a DBLU with 36 batwing sources in a rectangular arrangement with a backlight box thickness of 20 mm. The reflectivity of the backlight box is 0.9. We calculated the uniformity of 9 points without adding any optical films. The illuminance uniformity from LSF was 99.25%. After assembling a prototype of the DBLU with the same parameters, the illuminance uniformity was found to be 96.68%. When comparing the results from the LSF and measured data at y = x and x axis for the DBLU, the MAPE values were 0.92% and 0.46%, respectively. The collimated exposure were designed by the calculated rotation angle of light source and tilt angle of reflective plane. After simulating by the optical design software, the average irradiance and the half angle of radiant intensity can achieve the demand of collimated exposure, and the irradiance uniformity was better than 97%. It is apparent that in the design of a thin DBLU, the LSF calculation provides a more precise design method, which enables designers to simply choose sources and arrangement patterns according to the requirements of an optical system. |
