本論文主要針對固態光源與反射杯式車燈之設計、比較與分析並 提出以線性位移不變系統的概念，結合相關性與捲積運算進行光形疊 加之光學模擬方式，並探討了二次光學系統的線性位移不變範圍，以 便透過脈衝響應對該範圍做捲積來得到一等效於朗伯面光源的成像 結果。本研究中透過定義反射式機構在光源面的線性位移不變範圍， 並以該特性來做一理想的假設，以兩軸上之線性位移不變區間來假設 整個光源面上之線性位移不變範圍，試圖尋找二次光學系統中線性位 移不變區域的區間，並以此證實了即使在機構較複雜的照明系統中， 仍存在有一定範圍的線性位移不變系統。在證明了線性位移系統在照明系統的可行性之後，我們亦提出了一個簡易的線性位移不變範圍的劃分方式，即以等宮格方式劃分光源面，藉此假設能表現出系統特性的線性位移不變範圍。將光源切分為100 等宮格，並將 100 宮格中每一等份以點光源的形式取代並且放置於中心處，各別對兩款反射杯進行模擬，其結果與等效面積之方形朗伯面光源比較之 NCC 值可達到 99.06 %以上。而利用影像處理技術，我們可以減少劃分的宮格數量與模擬需要的光線數量，並大幅的提高 運算速度。以目前的計算時間只需要朗伯面光源模擬的 1%的時間。 本論文提出一個基於固態照明光源之高效率標示牌設計，透過高效率 遠距離投射燈之設計，並搭配合歸反射結構及擴散片，可以使標示牌 被用路人清楚識別。標示牌本身因結構簡單不易損壞，而模組化的投 射燈在維護上也不再需要實施道路封閉，達到降低維護時間與成本之 巨大優勢。 ;This thesis focuses on the design, comparison, and analysis of solid state light sources and reflector-based automotive lamps. We propose the concept of a linear shift-invariant system and combine correlation and convolution operations for optical simulations of light distribution. We also explore the linear shift-invariant range of second-order optical systems to obtain imaging results equivalent to a planar light source by convolving with the impulse response within that range. In this study, we define the linear shift-invariant range of the reflective mechanism on the light source surface and make an ideal assumption based on this characteristic. We assume the linear shift-invariant range on the entire light source surface using the linear shift-invariant intervals in two axes, attempting to identify the range of linear shift-invariant regions within the second-order optical system. This confirms the existence of a certain range of linear shift invariant systems even in complex lighting systems. After demonstrating the feasibility of linear shift systems in lighting systems, we propose a simple method for partitioning the linear shift-invariant range using an equidistant grid on the light source surface. The light source is divided into 100 equidistant grids, and each grid is replaced with a point light source placed at the center. Simulations are performed on two types of reflectors, comparing the results with those obtained from simulations of a square Lambertian light source with an equivalent area. The normalized cross correlation (NCC) value exceeds 99.06%. By utilizing image processing techniques, we can reduce the number of grids and the number of rays required for simulation, significantly improving computational speed. By the calculation method, it will reduce 99% of the calculation time compare to Lambertian light source calculation while the NCC still higher then 99%. This thesis proposes an efficient signage design based on solid-state illumination light sources. By incorporating a high-efficiency long distance projection lamp design, along with a combination of retroreflection structures and diffusers, passersby can clearly identify the signage. The signage itself becomes structurally simple and less prone to damage, while the modular projection lamps no longer require road closures for maintenance, offering the advantages of easy replacement and maintenance.
