光發射二極體提供一個良好的光源，它具有壽命長、體積小、低功率等的優點，且容易去應用在各種方面，像是大型顯示螢幕、車用燈泡、室內照明等，特別是應用在照明系統中，而LED的發展非常迅速，他的效能已經達到可以取代現在的照明用螢光燈了。
在投影照明系統中，我們通常要去調整他的發光角度讓可用的光源能夠不浪費的打在光閥上，最後在訊號的控制下，投射到螢幕上，在這樣的要求下，要能夠去控制照明系統的發散角使發光效率提升就變的非常重要了，光學元件─鍥形導光管通常被用來解決這樣的問題，因為它能夠搭配光閥將光導入光閥中，減少亮度的損失，而若能夠了解光在導光管的行徑數學模式，將能夠幫助我們去設計導光管的應用。空心且直的導光管之光線行徑數學模組已經在之前被研究討論出來了，在這篇論文中，我們將探討鍥形導光管的光行徑數學模組，並且將鍥形導光管應用與LED陣列光源應用在照明系統中。

The Light Emitting Diode (LED) provides a better choice than convention lighting sources. With its long lifetime, thinness, low voltage, flexibility in installation and pure color, LED is replacing conventional sources in many aspects, including: large screen display, automotive head lights, interior lighting, etc. Especially in Illumination systems design, LED technology developed rapidly and would be a suitable replacement for illumination system with fluorescent lamp.
It is often necessary to correct the angle of light and the aperture size to suit the systems requirements such as an imager panel in illumination systems for projection display. Optical element tapered light pipe (TLP) is usually used to transform the output from the lamp to match the requirement of the imaging panel and it is often used to design illumination system to conserve brightness. Hence the design of tapered light pipe is important for efficiency and minimal loss of brightness. An understanding of the mechanism of irradiance distribution in light pipe would help to design for different applications. The formations of the irradiance distribution in hollow straight light pipes have researched. In this paper, we investigate the formations of the irradiance distribution in tapered light pipe and use this optical element with LED arrays for illumination system design. The uniformity and LED color mixing will be discussed as well.

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